Daily Papers

The integration of long-context capabilities with visual understanding unlocks unprecedented potential for Vision Language Models (VLMs). However, the quadratic attention complexity during the pre-filling phase remains a significant obstacle to real-world deployment. To overcome this limitation, we introduce MMInference (Multimodality Million tokens Inference), a dynamic sparse attention method that accelerates the prefilling stage for long-context multi-modal inputs. First, our analysis reveals that the temporal and spatial locality of video input leads to a unique sparse pattern, the Grid pattern. Simultaneously, VLMs exhibit markedly different sparse distributions across different modalities. We introduce a permutation-based method to leverage the unique Grid pattern and handle modality boundary issues. By offline search the optimal sparse patterns for each head, MMInference constructs the sparse distribution dynamically based on the input. We also provide optimized GPU kernels for efficient sparse computations. Notably, MMInference integrates seamlessly into existing VLM pipelines without any model modifications or fine-tuning. Experiments on multi-modal benchmarks-including Video QA, Captioning, VisionNIAH, and Mixed-Modality NIAH-with state-of-the-art long-context VLMs (LongVila, LlavaVideo, VideoChat-Flash, Qwen2.5-VL) show that MMInference accelerates the pre-filling stage by up to 8.3x at 1M tokens while maintaining accuracy. Our code is available at https://aka.ms/MMInference.

Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an encoder-decoder architecture, where the encoder is trained to extract embeddings that are used as inputs to generate predictions from the decoder. However, the learned embeddings have sparse distribution in the feature space, which leads to worse generalization results during testing. To address these problems, this paper proposes a hyperspherical module, which transforms and normalizes embeddings from the encoder to be on a unit hypersphere. With the proposed module, the magnitude and direction of the output hyperspherical embedding are decoupled and only the directional information is optimized. We theoretically analyze the hyperspherical embedding and show that it enables more stable training with a wider range of learning rates and more compact embedding distributions. Experiment results show consistent improvement of point cloud completion in both single-task and multi-task learning, which demonstrates the effectiveness of the proposed method.

The advancement of remote sensing technology has improved the spatial resolution of satellite imagery, facilitating more detailed visual representations for diverse interpretations. However, existing methods exhibit limited generalization capabilities across varied applications. While some contemporary foundation models demonstrate potential, they are hindered by insufficient cross-task adaptability and primarily process low-resolution imagery of restricted sizes, thus failing to fully exploit high-resolution data or leverage comprehensive large-scene semantics. Crucially, remote sensing imagery differs fundamentally from natural images, as key foreground targets (eg., maritime objects, artificial structures) often occupy minimal spatial proportions (~1%) and exhibit sparse distributions. Efficiently modeling cross-task generalizable knowledge from lengthy 2D tokens (~100,000) poses a significant challenge yet remains critical for remote sensing image understanding. Motivated by the selective attention mechanisms inherent to the human visual system, we propose DynamicVis, a dynamic visual perception foundation model for remote sensing imagery. The framework integrates a novel dynamic region perception backbone based on the selective state space model, which strategically balances localized detail extraction with global contextual integration, enabling computationally efficient encoding of large-scale data while maintaining architectural scalability. To enhance cross-task knowledge transferring, we introduce a multi-instance learning paradigm utilizing meta-embedding representations, trained on million-scale region-level annotations. Evaluations across nine downstream tasks demonstrate the model's versatility. DynamicVis achieves multi-level feature modeling with exceptional efficiency, processing (2048x2048) pixels with 97 ms latency (6% of ViT's) and 833 MB GPU memory (3% of ViT's).

We propose a novel architecture and method of explainable classification with Concept Bottleneck Models (CBMs). While SOTA approaches to Image Classification task work as a black box, there is a growing demand for models that would provide interpreted results. Such a models often learn to predict the distribution over class labels using additional description of this target instances, called concepts. However, existing Bottleneck methods have a number of limitations: their accuracy is lower than that of a standard model and CBMs require an additional set of concepts to leverage. We provide a framework for creating Concept Bottleneck Model from pre-trained multi-modal encoder and new CLIP-like architectures. By introducing a new type of layers known as Concept Bottleneck Layers, we outline three methods for training them: with ell_1-loss, contrastive loss and loss function based on Gumbel-Softmax distribution (Sparse-CBM), while final FC layer is still trained with Cross-Entropy. We show a significant increase in accuracy using sparse hidden layers in CLIP-based bottleneck models. Which means that sparse representation of concepts activation vector is meaningful in Concept Bottleneck Models. Moreover, with our Concept Matrix Search algorithm we can improve CLIP predictions on complex datasets without any additional training or fine-tuning. The code is available at: https://github.com/Andron00e/SparseCBM.

Whisper is a powerful automatic speech recognition (ASR) model. Nevertheless, its zero-shot performance on low-resource speech requires further improvement. Child speech, as a representative type of low-resource speech, is leveraged for adaptation. Recently, parameter-efficient fine-tuning (PEFT) in NLP was shown to be comparable and even better than full fine-tuning, while only needing to tune a small set of trainable parameters. However, current PEFT methods have not been well examined for their effectiveness on Whisper. In this paper, only parameter composition types of PEFT approaches such as LoRA and Bitfit are investigated as they do not bring extra inference costs. Different popular PEFT methods are examined. Particularly, we compare LoRA and AdaLoRA and figure out the learnable rank coefficient is a good design. Inspired by the sparse rank distribution allocated by AdaLoRA, a novel PEFT approach Sparsely Shared LoRA (S2-LoRA) is proposed. The two low-rank decomposed matrices are globally shared. Each weight matrix only has to maintain its specific rank coefficients that are constrained to be sparse. Experiments on low-resource Chinese child speech show that with much fewer trainable parameters, S2-LoRA can achieve comparable in-domain adaptation performance to AdaLoRA and exhibit better generalization ability on out-of-domain data. In addition, the rank distribution automatically learned by S2-LoRA is found to have similar patterns to AdaLoRA's allocation.

Recent advances in large language models (LLMs) have showcased exceptional performance in long-context tasks, while facing significant inference efficiency challenges with limited GPU memory. Existing solutions first proposed the sliding-window approach to accumulate a set of historical key-value (KV) pairs for reuse, then further improvements selectively retain its subsets at each step. However, due to the sparse attention distribution across a long context, it is hard to identify and recall relevant KV pairs, as the attention is distracted by massive candidate pairs. Additionally, we found it promising to select representative tokens as probe-Query in each sliding window to effectively represent the entire context, which is an approach overlooked by existing methods. Thus, we propose ActQKV, a training-free, Activation-aware approach that dynamically determines probe-Query and leverages it to retrieve the relevant KV pairs for inference. Specifically, ActQKV monitors a token-level indicator, Activation Bias, within each context window, enabling the proper construction of probe-Query for retrieval at pre-filling stage. To accurately recall the relevant KV pairs and minimize the irrelevant ones, we design a dynamic KV cut-off mechanism guided by information density across layers at the decoding stage. Experiments on the Long-Bench and infty Benchmarks demonstrate its state-of-the-art performance with competitive inference quality and resource efficiency.

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or {\epsilon}-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.

3D detection technology is widely used in the field of autonomous driving, with its application scenarios gradually expanding from enclosed highways to open conventional roads. For rare anomaly categories that appear on the road, 3D detection models trained on closed sets often misdetect or fail to detect anomaly objects. To address this risk, it is necessary to enhance the generalization ability of 3D detection models for targets of arbitrary shapes and to possess the capability to filter out anomalies. The generalization of 3D detection is limited by two factors: the coupled training of 2D and 3D, and the insufficient diversity in the scale distribution of training samples. This paper proposes a Stereo-based 3D Anomaly object Detection (S3AD) algorithm, which decouples the training strategy of 3D and 2D to release the generalization ability for arbitrary 3D foreground detection, and proposes an anomaly scoring algorithm based on foreground confidence prediction, achieving target-level anomaly scoring. In order to further verify and enhance the generalization of anomaly detection, we use a 3D rendering method to synthesize two augmented reality binocular stereo 3D detection datasets which named KITTI-AR. KITTI-AR extends upon KITTI by adding 97 new categories, totaling 6k pairs of stereo images. The KITTI-AR-ExD subset includes 39 common categories as extra training data to address the sparse sample distribution issue. Additionally, 58 rare categories form the KITTI-AR-OoD subset, which are not used in training to simulate zero-shot scenarios in real-world settings, solely for evaluating 3D anomaly detection. Finally, the performance of the algorithm and the dataset is verified in the experiments. (Code and dataset can be obtained at https://github.com/shiyi-mu/S3AD-Code).

The development of open benchmarking platforms could greatly accelerate the adoption of AI agents in retail. This paper presents comprehensive simulations of customer shopping behaviors for the purpose of benchmarking reinforcement learning (RL) agents that optimize coupon targeting. The difficulty of this learning problem is largely driven by the sparsity of customer purchase events. We trained agents using offline batch data comprising summarized customer purchase histories to help mitigate this effect. Our experiments revealed that contextual bandit and deep RL methods that are less prone to over-fitting the sparse reward distributions significantly outperform static policies. This study offers a practical framework for simulating AI agents that optimize the entire retail customer journey. It aims to inspire the further development of simulation tools for retail AI systems.

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from computation for efficient inference. Sparse attention inference methods aim to reduce this computational burden; however, they also come with a troublesome performance degradation. We discover that one reason for this degradation is that the sparse calculation induces a distributional shift in the attention outputs. The distributional shift causes decoding-time queries to fail to align well with the appropriate keys from the prefill stage, leading to a drop in performance. We propose a simple, novel, and effective procedure for correcting this distributional shift, bringing the distribution of sparse attention outputs closer to that of quadratic attention. Our method can be applied on top of any sparse attention method, and results in an average 36%pt performance increase, recovering 88% of quadratic attention accuracy on the 131K RULER benchmark when applied on top of sliding window attention with sink tokens while only adding a small overhead. Our method can maintain approximately 98.5% sparsity over full quadratic attention, making our model 32 times faster than Flash Attention 2 when processing 1M token prefills.

We present UI-Venus, a native UI agent that takes only screenshots as input based on a multimodal large language model. UI-Venus achieves SOTA performance on both UI grounding and navigation tasks using only several hundred thousand high-quality training samples through reinforcement finetune (RFT) based on Qwen2.5-VL. Specifically, the 7B and 72B variants of UI-Venus obtain 94.1% / 50.8% and 95.3% / 61.9% on the standard grounding benchmarks, i.e., Screenspot-V2 / Pro, surpassing the previous SOTA baselines including open-source GTA1 and closed-source UI-TARS-1.5.To show UI-Venus's summary and planing ability, we also evaluate it on the AndroidWorld, an online UI navigation arena, on which our 7B and 72B variants achieve 49.1% and 65.9% success rate, also beating existing models.To achieve this, we introduce carefully designed reward functions for both UI grounding and navigation tasks and corresponding efficient data cleaning strategies.To further boost navigation performance, we propose Self-Evolving Trajectory History Alignment \& Sparse Action Enhancement that refine historical reasoning traces and balances the distribution of sparse but critical actions, leading to more coherent planning and better generalization in complex UI tasks. Our contributions include the publish of SOTA open-source UI agents, comprehensive data cleaning protocols and a novel self-evolving framework for improving navigation performance, which encourage further research and development in the community. Code is available at https://github.com/antgroup/UI-Venus.

Handling distribution shifts from training data, known as out-of-distribution (OOD) generalization, poses a significant challenge in the field of machine learning. While a pre-trained vision-language model like CLIP has demonstrated remarkable zero-shot performance, further adaptation of the model to downstream tasks leads to undesirable degradation for OOD data. In this work, we introduce Sparse Adaptation for Fine-Tuning (SAFT), a method that prevents fine-tuning from forgetting the general knowledge in the pre-trained model. SAFT only updates a small subset of important parameters whose gradient magnitude is large, while keeping the other parameters frozen. SAFT is straightforward to implement and conceptually simple. Extensive experiments show that with only 0.1% of the model parameters, SAFT can significantly improve the performance of CLIP. It consistently outperforms baseline methods across several benchmarks. On the few-shot learning benchmark of ImageNet and its variants, SAFT gives a gain of 5.15% on average over the conventional fine-tuning method in OOD settings.

Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems. That changed with the recent development of approximate algorithms that leverage the distributional properties of sparse embeddings to speed up retrieval. Nonetheless, in much of the existing literature, evaluation has been limited to datasets with only a few million documents such as MSMARCO. It remains unclear how these systems behave on much larger datasets and what challenges lurk in larger scales. To bridge that gap, we investigate the behavior of state-of-the-art retrieval algorithms on massive datasets. We compare and contrast the recently-proposed Seismic and graph-based solutions adapted from dense retrieval. We extensively evaluate Splade embeddings of 138M passages from MsMarco-v2 and report indexing time and other efficiency and effectiveness metrics.

Human visual perception can easily generalize to out-of-distributed visual data, which is far beyond the capability of modern machine learning models. Domain generalization (DG) aims to close this gap, with existing DG methods mainly focusing on the loss function design. In this paper, we propose to explore an orthogonal direction, i.e., the design of the backbone architecture. It is motivated by an empirical finding that transformer-based models trained with empirical risk minimization (ERM) outperform CNN-based models employing state-of-the-art (SOTA) DG algorithms on multiple DG datasets. We develop a formal framework to characterize a network's robustness to distribution shifts by studying its architecture's alignment with the correlations in the dataset. This analysis guides us to propose a novel DG model built upon vision transformers, namely Generalizable Mixture-of-Experts (GMoE). Extensive experiments on DomainBed demonstrate that GMoE trained with ERM outperforms SOTA DG baselines by a large margin. Moreover, GMoE is complementary to existing DG methods and its performance is substantially improved when trained with DG algorithms.

Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and expressiveness of PCs. However, PC training performance plateaus as model size increases. We discover that most capacity in existing large PC structures is wasted: fully-connected parameter layers are only sparsely used. We propose two operations: pruning and growing, that exploit the sparsity of PC structures. Specifically, the pruning operation removes unimportant sub-networks of the PC for model compression and comes with theoretical guarantees. The growing operation increases model capacity by increasing the size of the latent space. By alternatingly applying pruning and growing, we increase the capacity that is meaningfully used, allowing us to significantly scale up PC learning. Empirically, our learner achieves state-of-the-art likelihoods on MNIST-family image datasets and on Penn Tree Bank language data compared to other PC learners and less tractable deep generative models such as flow-based models and variational autoencoders (VAEs).

Neural networks can be significantly compressed by pruning, yielding sparse models with reduced storage and computational demands while preserving predictive performance. Model soups (Wortsman et al., 2022) enhance generalization and out-of-distribution (OOD) performance by averaging the parameters of multiple models into a single one, without increasing inference time. However, achieving both sparsity and parameter averaging is challenging as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. This work addresses these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varied hyperparameter configurations such as batch ordering or weight decay yields models suitable for averaging, sharing identical sparse connectivity by design. Averaging these models significantly enhances generalization and OOD performance over their individual counterparts. Building on this, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model from the previous phase. SMS preserves sparsity, exploits sparse network benefits, is modular and fully parallelizable, and substantially improves IMP's performance. We further demonstrate that SMS can be adapted to enhance state-of-the-art pruning-during-training approaches.

Offline reinforcement learning (RL) offers a promising direction for learning policies from pre-collected datasets without requiring further interactions with the environment. However, existing methods struggle to handle out-of-distribution (OOD) extrapolation errors, especially in sparse reward or scarce data settings. In this paper, we propose a novel training algorithm called Conservative Density Estimation (CDE), which addresses this challenge by explicitly imposing constraints on the state-action occupancy stationary distribution. CDE overcomes the limitations of existing approaches, such as the stationary distribution correction method, by addressing the support mismatch issue in marginal importance sampling. Our method achieves state-of-the-art performance on the D4RL benchmark. Notably, CDE consistently outperforms baselines in challenging tasks with sparse rewards or insufficient data, demonstrating the advantages of our approach in addressing the extrapolation error problem in offline RL.

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

As large language models (LLMs) grow in scale and capability, understanding their internal mechanisms becomes increasingly critical. Sparse autoencoders (SAEs) have emerged as a key tool in mechanistic interpretability, enabling the extraction of human-interpretable features from LLMs. However, existing SAE training methods are primarily designed for base models, resulting in reduced reconstruction quality and interpretability when applied to instruct models. To bridge this gap, we propose textbf{F}inetuning-textbf{a}ligned textbf{S}equential textbf{T}raining (FAST), a novel training method specifically tailored for instruct models. FAST aligns the training process with the data distribution and activation patterns characteristic of instruct models, resulting in substantial improvements in both reconstruction and feature interpretability. On Qwen2.5-7B-Instruct, FAST achieves a mean squared error of 0.6468 in token reconstruction, significantly outperforming baseline methods with errors of 5.1985 and 1.5096. In feature interpretability, FAST yields a higher proportion of high-quality features, for Llama3.2-3B-Instruct, 21.1% scored in the top range, compared to 7.0% and 10.2% for BT(P) and BT(F). Surprisingly, we discover that intervening on the activations of special tokens via the SAEs leads to improvements in output quality, suggesting new opportunities for fine-grained control of model behavior. Code, data, and 240 trained SAEs are available at https://github.com/Geaming2002/FAST.

We describe HypotheSAEs, a general method to hypothesize interpretable relationships between text data (e.g., headlines) and a target variable (e.g., clicks). HypotheSAEs has three steps: (1) train a sparse autoencoder on text embeddings to produce interpretable features describing the data distribution, (2) select features that predict the target variable, and (3) generate a natural language interpretation of each feature (e.g., "mentions being surprised or shocked") using an LLM. Each interpretation serves as a hypothesis about what predicts the target variable. Compared to baselines, our method better identifies reference hypotheses on synthetic datasets (at least +0.06 in F1) and produces more predictive hypotheses on real datasets (~twice as many significant findings), despite requiring 1-2 orders of magnitude less compute than recent LLM-based methods. HypotheSAEs also produces novel discoveries on two well-studied tasks: explaining partisan differences in Congressional speeches and identifying drivers of engagement with online headlines.

Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

Federated Learning (FL) aims to train machine learning models for multiple clients without sharing their own private data. Due to the heterogeneity of clients' local data distribution, recent studies explore the personalized FL that learns and deploys distinct local models with the help of auxiliary global models. However, the clients can be heterogeneous in terms of not only local data distribution, but also their computation and communication resources. The capacity and efficiency of personalized models are restricted by the lowest-resource clients, leading to sub-optimal performance and limited practicality of personalized FL. To overcome these challenges, we propose a novel approach named pFedGate for efficient personalized FL by adaptively and efficiently learning sparse local models. With a lightweight trainable gating layer, pFedGate enables clients to reach their full potential in model capacity by generating different sparse models accounting for both the heterogeneous data distributions and resource constraints. Meanwhile, the computation and communication efficiency are both improved thanks to the adaptability between the model sparsity and clients' resources. Further, we theoretically show that the proposed pFedGate has superior complexity with guaranteed convergence and generalization error. Extensive experiments show that pFedGate achieves superior global accuracy, individual accuracy and efficiency simultaneously over state-of-the-art methods. We also demonstrate that pFedGate performs better than competitors in the novel clients participation and partial clients participation scenarios, and can learn meaningful sparse local models adapted to different data distributions.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

Knowledge distillation can be a cost-effective technique to distill knowledge in Large Language Models, if the teacher output logits can be pre-computed and cached. However, successfully applying this to pre-training remains largely unexplored. In this work, we prove that naive approaches for sparse knowledge distillation such as caching Top-K probabilities, while intuitive, provide biased estimates of teacher probability distribution to the student, resulting in suboptimal performance and calibration. We propose an importance-sampling-based method `Random Sampling Knowledge Distillation', which provides unbiased estimates, preserves the gradient in expectation, and requires storing significantly sparser logits. Our method enables faster training of student models with marginal overhead (<10%) compared to cross-entropy based training, while maintaining competitive performance compared to full distillation, across a range of model sizes from 300M to 3B.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

Recent implicit neural representations have shown great results for novel view synthesis. However, existing methods require expensive per-scene optimization from many views hence limiting their application to real-world unbounded urban settings where the objects of interest or backgrounds are observed from very few views. To mitigate this challenge, we introduce a new approach called NeO 360, Neural fields for sparse view synthesis of outdoor scenes. NeO 360 is a generalizable method that reconstructs 360{\deg} scenes from a single or a few posed RGB images. The essence of our approach is in capturing the distribution of complex real-world outdoor 3D scenes and using a hybrid image-conditional triplanar representation that can be queried from any world point. Our representation combines the best of both voxel-based and bird's-eye-view (BEV) representations and is more effective and expressive than each. NeO 360's representation allows us to learn from a large collection of unbounded 3D scenes while offering generalizability to new views and novel scenes from as few as a single image during inference. We demonstrate our approach on the proposed challenging 360{\deg} unbounded dataset, called NeRDS 360, and show that NeO 360 outperforms state-of-the-art generalizable methods for novel view synthesis while also offering editing and composition capabilities. Project page: https://zubair-irshad.github.io/projects/neo360.html

Modeling and estimating mixed memberships for overlapping unipartite un-weighted networks has been well studied in recent years. However, to our knowledge, there is no model for a more general case, the overlapping bipartite weighted networks. To close this gap, we introduce a novel model, the Bipartite Mixed Membership Distribution-Free (BiMMDF) model. Our model allows an adjacency matrix to follow any distribution as long as its expectation has a block structure related to node membership. In particular, BiMMDF can model overlapping bipartite signed networks and it is an extension of many previous models, including the popular mixed membership stochastic blcokmodels. An efficient algorithm with a theoretical guarantee of consistent estimation is applied to fit BiMMDF. We then obtain the separation conditions of BiMMDF for different distributions. Furthermore, we also consider missing edges for sparse networks. The advantage of BiMMDF is demonstrated in extensive synthetic networks and eight real-world networks.

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at https://github.com/Ma-Lab-Berkeley/CRATE.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

Steering vectors are a promising approach to control the behaviour of large language models. However, their underlying mechanisms remain poorly understood. While sparse autoencoders (SAEs) may offer a potential method to interpret steering vectors, recent findings show that SAE-reconstructed vectors often lack the steering properties of the original vectors. This paper investigates why directly applying SAEs to steering vectors yields misleading decompositions, identifying two reasons: (1) steering vectors fall outside the input distribution for which SAEs are designed, and (2) steering vectors can have meaningful negative projections in feature directions, which SAEs are not designed to accommodate. These limitations hinder the direct use of SAEs for interpreting steering vectors.

Diffusion Transformers (DiT) have become the de-facto model for generating high-quality visual content like videos and images. A huge bottleneck is the attention mechanism where complexity scales quadratically with resolution and video length. One logical way to lessen this burden is sparse attention, where only a subset of tokens or patches are included in the calculation. However, existing techniques fail to preserve visual quality at extremely high sparsity levels and might even incur non-negligible compute overheads. % To address this concern, we propose Re-ttention, which implements very high sparse attention for visual generation models by leveraging the temporal redundancy of Diffusion Models to overcome the probabilistic normalization shift within the attention mechanism. Specifically, Re-ttention reshapes attention scores based on the prior softmax distribution history in order to preserve the visual quality of the full quadratic attention at very high sparsity levels. % Experimental results on T2V/T2I models such as CogVideoX and the PixArt DiTs demonstrate that Re-ttention requires as few as 3.1\% of the tokens during inference, outperforming contemporary methods like FastDiTAttn, Sparse VideoGen and MInference. Further, we measure latency to show that our method can attain over 45\% end-to-end % and over 92\% self-attention latency reduction on an H100 GPU at negligible overhead cost. Code available online here: https://github.com/cccrrrccc/Re-ttention{https://github.com/cccrrrccc/Re-ttention}

With the tremendous success of large transformer models in natural language understanding, down-sizing them for cost-effective deployments has become critical. Recent studies have explored the low-rank weight factorization techniques which are efficient to train, and apply out-of-the-box to any transformer architecture. Unfortunately, the low-rank assumption tends to be over-restrictive and hinders the expressiveness of the compressed model. This paper proposes, DSFormer, a simple alternative factorization scheme which expresses a target weight matrix as the product of a small dense and a semi-structured sparse matrix. The resulting approximation is more faithful to the weight distribution in transformers and therefore achieves a stronger efficiency-accuracy trade-off. Another concern with existing factorizers is their dependence on a task-unaware initialization step which degrades the accuracy of the resulting model. DSFormer addresses this issue through a novel Straight-Through Factorizer (STF) algorithm that jointly learns all the weight factorizations to directly maximize the final task accuracy. Extensive experiments on multiple natural language understanding benchmarks demonstrate that DSFormer obtains up to 40% better compression than the state-of-the-art low-rank factorizers, leading semi-structured sparsity baselines and popular knowledge distillation approaches. Our approach is also orthogonal to mainstream compressors and offers up to 50% additional compression when added to popular distilled, layer-shared and quantized transformers. We empirically evaluate the benefits of STF over conventional optimization practices.

Sparse training is emerging as a promising avenue for reducing the computational cost of training neural networks. Several recent studies have proposed pruning methods using learnable thresholds to efficiently explore the non-uniform distribution of sparsity inherent within the models. In this paper, we propose Gradient Annealing (GA), where gradients of masked weights are scaled down in a non-linear manner. GA provides an elegant trade-off between sparsity and accuracy without the need for additional sparsity-inducing regularization. We integrated GA with the latest learnable pruning methods to create an automated sparse training algorithm called AutoSparse, which achieves better accuracy and/or training/inference FLOPS reduction than existing learnable pruning methods for sparse ResNet50 and MobileNetV1 on ImageNet-1K: AutoSparse achieves (2x, 7x) reduction in (training,inference) FLOPS for ResNet50 on ImageNet at 80% sparsity. Finally, AutoSparse outperforms sparse-to-sparse SotA method MEST (uniform sparsity) for 80% sparse ResNet50 with similar accuracy, where MEST uses 12% more training FLOPS and 50% more inference FLOPS.

Sparse Autoencoders (SAEs) have emerged as a popular tool for interpreting the hidden states of large language models (LLMs). By learning to reconstruct activations from a sparse bottleneck layer, SAEs discover interpretable features from the high-dimensional internal representations of LLMs. Despite their popularity with language models, SAEs remain understudied in the visual domain. In this work, we provide an extensive evaluation the representational power of SAEs for vision models using a broad range of image-based tasks. Our experimental results demonstrate that SAE features are semantically meaningful, improve out-of-distribution generalization, and enable controllable generation across three vision model architectures: vision embedding models, multi-modal LMMs and diffusion models. In vision embedding models, we find that learned SAE features can be used for OOD detection and provide evidence that they recover the ontological structure of the underlying model. For diffusion models, we demonstrate that SAEs enable semantic steering through text encoder manipulation and develop an automated pipeline for discovering human-interpretable attributes. Finally, we conduct exploratory experiments on multi-modal LLMs, finding evidence that SAE features reveal shared representations across vision and language modalities. Our study provides a foundation for SAE evaluation in vision models, highlighting their strong potential improving interpretability, generalization, and steerability in the visual domain.

In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Efficient long-sequence generation is a critical challenge for Large Language Models. While recent sparse decoding methods improve efficiency, they suffer from KV cache misalignment, where approximation errors accumulate and degrade generation quality. In this work, we propose Rectified Sparse Attention (ReSA), a simple yet effective method that combines block-sparse attention with periodic dense rectification. By refreshing the KV cache at fixed intervals using a dense forward pass, ReSA bounds error accumulation and preserves alignment with the pretraining distribution. Experiments across math reasoning, language modeling, and retrieval tasks demonstrate that ReSA achieves near-lossless generation quality with significantly improved efficiency. Notably, ReSA delivers up to 2.42times end-to-end speedup under decoding at 256K sequence length, making it a practical solution for scalable long-context inference. Code is available at https://aka.ms/ReSA-LM.

We propose Strivec, a novel neural representation that models a 3D scene as a radiance field with sparsely distributed and compactly factorized local tensor feature grids. Our approach leverages tensor decomposition, following the recent work TensoRF, to model the tensor grids. In contrast to TensoRF which uses a global tensor and focuses on their vector-matrix decomposition, we propose to utilize a cloud of local tensors and apply the classic CANDECOMP/PARAFAC (CP) decomposition to factorize each tensor into triple vectors that express local feature distributions along spatial axes and compactly encode a local neural field. We also apply multi-scale tensor grids to discover the geometry and appearance commonalities and exploit spatial coherence with the tri-vector factorization at multiple local scales. The final radiance field properties are regressed by aggregating neural features from multiple local tensors across all scales. Our tri-vector tensors are sparsely distributed around the actual scene surface, discovered by a fast coarse reconstruction, leveraging the sparsity of a 3D scene. We demonstrate that our model can achieve better rendering quality while using significantly fewer parameters than previous methods, including TensoRF and Instant-NGP.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

Attention mechanisms have become ubiquitous in NLP. Recent architectures, notably the Transformer, learn powerful context-aware word representations through layered, multi-headed attention. The multiple heads learn diverse types of word relationships. However, with standard softmax attention, all attention heads are dense, assigning a non-zero weight to all context words. In this work, we introduce the adaptively sparse Transformer, wherein attention heads have flexible, context-dependent sparsity patterns. This sparsity is accomplished by replacing softmax with alpha-entmax: a differentiable generalization of softmax that allows low-scoring words to receive precisely zero weight. Moreover, we derive a method to automatically learn the alpha parameter -- which controls the shape and sparsity of alpha-entmax -- allowing attention heads to choose between focused or spread-out behavior. Our adaptively sparse Transformer improves interpretability and head diversity when compared to softmax Transformers on machine translation datasets. Findings of the quantitative and qualitative analysis of our approach include that heads in different layers learn different sparsity preferences and tend to be more diverse in their attention distributions than softmax Transformers. Furthermore, at no cost in accuracy, sparsity in attention heads helps to uncover different head specializations.

Sparse Autoencoders (SAEs) have emerged as a promising solution for decomposing large language model representations into interpretable features. However, Paulo and Belrose (2025) have highlighted instability across different initialization seeds, and Heap et al. (2025) have pointed out that SAEs may not capture model-internal features. These problems likely stem from training SAEs on external datasets - either collected from the Web or generated by another model - which may contain out-of-distribution (OOD) data beyond the model's generalisation capabilities. This can result in hallucinated SAE features, which we term "Fake Features", that misrepresent the model's internal activations. To address these issues, we propose FaithfulSAE, a method that trains SAEs on the model's own synthetic dataset. Using FaithfulSAEs, we demonstrate that training SAEs on less-OOD instruction datasets results in SAEs being more stable across seeds. Notably, FaithfulSAEs outperform SAEs trained on web-based datasets in the SAE probing task and exhibit a lower Fake Feature Ratio in 5 out of 7 models. Overall, our approach eliminates the dependency on external datasets, advancing interpretability by better capturing model-internal features while highlighting the often neglected importance of SAE training datasets.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Estimating 3D full-body avatars from AR/VR devices is essential for creating immersive experiences in AR/VR applications. This task is challenging due to the limited input from Head Mounted Devices, which capture only sparse observations from the head and hands. Predicting the full-body avatars, particularly the lower body, from these sparse observations presents significant difficulties. In this paper, we are inspired by the inherent property of the kinematic tree defined in the Skinned Multi-Person Linear (SMPL) model, where the upper body and lower body share only one common ancestor node, bringing the potential of decoupled reconstruction. We propose a stratified approach to decouple the conventional full-body avatar reconstruction pipeline into two stages, with the reconstruction of the upper body first and a subsequent reconstruction of the lower body conditioned on the previous stage. To implement this straightforward idea, we leverage the latent diffusion model as a powerful probabilistic generator, and train it to follow the latent distribution of decoupled motions explored by a VQ-VAE encoder-decoder model. Extensive experiments on AMASS mocap dataset demonstrate our state-of-the-art performance in the reconstruction of full-body motions.

Explaining multivariate time series is a compound challenge, as it requires identifying important locations in the time series and matching complex temporal patterns. Although previous saliency-based methods addressed the challenges, their perturbation may not alleviate the distribution shift issue, which is inevitable especially in heterogeneous samples. We present ContraLSP, a locally sparse model that introduces counterfactual samples to build uninformative perturbations but keeps distribution using contrastive learning. Furthermore, we incorporate sample-specific sparse gates to generate more binary-skewed and smooth masks, which easily integrate temporal trends and select the salient features parsimoniously. Empirical studies on both synthetic and real-world datasets show that ContraLSP outperforms state-of-the-art models, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at https://github.com/zichuan-liu/ContraLSP.

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a small subset of these parameters for a given sample. However, it has been observed that SMoE suffers from unstable training and has difficulty adapting to new distributions, leading to the model's lack of robustness to data contamination. To overcome these limitations, we first establish a connection between the dynamics of the expert representations in SMoEs and gradient descent on a multi-objective optimization problem. Leveraging our framework, we then integrate momentum into SMoE and propose a new family of SMoEs named MomentumSMoE. We theoretically prove and numerically demonstrate that MomentumSMoE is more stable and robust than SMoE. In particular, we verify the advantages of MomentumSMoE over SMoE on a variety of practical tasks including ImageNet-1K object recognition and WikiText-103 language modeling. We demonstrate the applicability of MomentumSMoE to many types of SMoE models, including those in the Sparse MoE model for vision (V-MoE) and the Generalist Language Model (GLaM). We also show that other advanced momentum-based optimization methods, such as Adam, can be easily incorporated into the MomentumSMoE framework for designing new SMoE models with even better performance, almost negligible additional computation cost, and simple implementations.

Learned sparse retrieval systems aim to combine the effectiveness of contextualized language models with the scalability of conventional data structures such as inverted indexes. Nevertheless, the indexes generated by these systems exhibit significant deviations from the ones that use traditional retrieval models, leading to a discrepancy in the performance of existing query optimizations that were specifically developed for traditional structures. These disparities arise from structural variations in query and document statistics, including sub-word tokenization, leading to longer queries, smaller vocabularies, and different score distributions within posting lists. This paper introduces Block-Max Pruning (BMP), an innovative dynamic pruning strategy tailored for indexes arising in learned sparse retrieval environments. BMP employs a block filtering mechanism to divide the document space into small, consecutive document ranges, which are then aggregated and sorted on the fly, and fully processed only as necessary, guided by a defined safe early termination criterion or based on approximate retrieval requirements. Through rigorous experimentation, we show that BMP substantially outperforms existing dynamic pruning strategies, offering unparalleled efficiency in safe retrieval contexts and improved tradeoffs between precision and efficiency in approximate retrieval tasks.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Transformers provide a class of expressive architectures that are extremely effective for sequence modeling. However, the key limitation of transformers is their quadratic memory and time complexity O(L^2) with respect to the sequence length in attention layers, which restricts application in extremely long sequences. Most existing approaches leverage sparsity or low-rank assumptions in the attention matrix to reduce cost, but sacrifice expressiveness. Instead, we propose Combiner, which provides full attention capability in each attention head while maintaining low computation and memory complexity. The key idea is to treat the self-attention mechanism as a conditional expectation over embeddings at each location, and approximate the conditional distribution with a structured factorization. Each location can attend to all other locations, either via direct attention, or through indirect attention to abstractions, which are again conditional expectations of embeddings from corresponding local regions. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention, resulting in the same sub-quadratic cost (O(Llog(L)) or O(LL)). Combiner is a drop-in replacement for attention layers in existing transformers and can be easily implemented in common frameworks. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach, yielding state-of-the-art results on several image and text modeling tasks.

Diffusion transformers currently lead the field in high-quality video generation, but their slow iterative denoising process and prohibitive quadratic attention costs for long sequences create significant inference bottlenecks. While both step distillation and sparse attention mechanisms have shown promise as independent acceleration strategies, effectively combining these approaches presents critical challenges -- training-free integration yields suboptimal results, while separately training sparse attention after step distillation requires prohibitively expensive high-quality video data. To overcome these limitations, we propose BLADE, an innovative data-free joint training framework that introduces: (1) an Adaptive Block-Sparse Attention (ASA) mechanism for dynamically generating content-aware sparsity masks to focus computation on salient spatiotemporal features, and (2) a sparsity-aware step distillation paradigm built upon Trajectory Distribution Matching (TDM) that directly incorporates sparsity into the distillation process rather than treating it as a separate compression step, with fast convergence. We validate BLADE on text-to-video models like CogVideoX-5B and Wan2.1-1.3B. Our framework demonstrates remarkable efficiency gains across different scales. On Wan2.1-1.3B, BLADE achieves a 14.10x end-to-end inference acceleration over a 50-step baseline. Moreover, on models such as CogVideoX-5B with short video sequence lengths, our framework delivers a robust 8.89x speedup. Crucially, the acceleration is accompanied by a consistent quality improvement. On the VBench-2.0 benchmark, BLADE boosts the score of CogVideoX-5B to 0.569 (from 0.534) and Wan2.1-1.3B to 0.570 (from 0.563), results that are further corroborated by superior ratings in human evaluations. Our code and model weights are publicly available at: http://ziplab.co/BLADE-Homepage/.

Recovering camera poses from a set of images is a foundational task in 3D computer vision, which powers key applications such as 3D scene/object reconstructions. Classic methods often depend on feature correspondence, such as keypoints, which require the input images to have large overlap and small viewpoint changes. Such requirements present considerable challenges in scenarios with sparse views. Recent data-driven approaches aim to directly output camera poses, either through regressing the 6DoF camera poses or formulating rotation as a probability distribution. However, each approach has its limitations. On one hand, directly regressing the camera poses can be ill-posed, since it assumes a single mode, which is not true under symmetry and leads to sub-optimal solutions. On the other hand, probabilistic approaches are capable of modeling the symmetry ambiguity, yet they sample the entire space of rotation uniformly by brute-force. This leads to an inevitable trade-off between high sample density, which improves model precision, and sample efficiency that determines the runtime. In this paper, we propose ADen to unify the two frameworks by employing a generator and a discriminator: the generator is trained to output multiple hypotheses of 6DoF camera pose to represent a distribution and handle multi-mode ambiguity, and the discriminator is trained to identify the hypothesis that best explains the data. This allows ADen to combine the best of both worlds, achieving substantially higher precision as well as lower runtime than previous methods in empirical evaluations.

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently highly sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20x compression in model size with under 3\% performance drop, and up to 20x FLOPs reduction during training compared with dense VI training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs on both accuracy and uncertainty metrics.

Identifying the features learned by neural networks is a core challenge in mechanistic interpretability. Sparse autoencoders (SAEs), which learn a sparse, overcomplete dictionary that reconstructs a network's internal activations, have been used to identify these features. However, SAEs may learn more about the structure of the datatset than the computational structure of the network. There is therefore only indirect reason to believe that the directions found in these dictionaries are functionally important to the network. We propose end-to-end (e2e) sparse dictionary learning, a method for training SAEs that ensures the features learned are functionally important by minimizing the KL divergence between the output distributions of the original model and the model with SAE activations inserted. Compared to standard SAEs, e2e SAEs offer a Pareto improvement: They explain more network performance, require fewer total features, and require fewer simultaneously active features per datapoint, all with no cost to interpretability. We explore geometric and qualitative differences between e2e SAE features and standard SAE features. E2e dictionary learning brings us closer to methods that can explain network behavior concisely and accurately. We release our library for training e2e SAEs and reproducing our analysis at https://github.com/ApolloResearch/e2e_sae

Large language models (LLMs) encode a diverse range of linguistic features within their latent representations, which can be harnessed to steer their output toward specific target characteristics. In this paper, we modify the internal structure of LLMs by training sparse autoencoders to learn a sparse representation of the query embedding, allowing precise control over the model's attention distribution. We demonstrate that manipulating this sparse representation effectively transforms the output toward different stylistic and cognitive targets. Specifically, in an educational setting, we show that the cognitive complexity of LLM-generated feedback can be systematically adjusted by modifying the encoded query representation at a specific layer. To achieve this, we guide the learned sparse embedding toward the representation of samples from the desired cognitive complexity level, using gradient-based optimization in the latent space.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

ProSper is a python library containing probabilistic algorithms to learn dictionaries. Given a set of data points, the implemented algorithms seek to learn the elementary components that have generated the data. The library widens the scope of dictionary learning approaches beyond implementations of standard approaches such as ICA, NMF or standard L1 sparse coding. The implemented algorithms are especially well-suited in cases when data consist of components that combine non-linearly and/or for data requiring flexible prior distributions. Furthermore, the implemented algorithms go beyond standard approaches by inferring prior and noise parameters of the data, and they provide rich a-posteriori approximations for inference. The library is designed to be extendable and it currently includes: Binary Sparse Coding (BSC), Ternary Sparse Coding (TSC), Discrete Sparse Coding (DSC), Maximal Causes Analysis (MCA), Maximum Magnitude Causes Analysis (MMCA), and Gaussian Sparse Coding (GSC, a recent spike-and-slab sparse coding approach). The algorithms are scalable due to a combination of variational approximations and parallelization. Implementations of all algorithms allow for parallel execution on multiple CPUs and multiple machines for medium to large-scale applications. Typical large-scale runs of the algorithms can use hundreds of CPUs to learn hundreds of dictionary elements from data with tens of millions of floating-point numbers such that models with several hundred thousand parameters can be optimized. The library is designed to have minimal dependencies and to be easy to use. It targets users of dictionary learning algorithms and Machine Learning researchers.

Parameter-efficient fine-tuning (PEFT) is crucial for customizing Large Language Models (LLMs) with constrained resources. Although there have been various PEFT methods for dense-architecture LLMs, PEFT for sparse-architecture LLMs is still underexplored. In this work, we study the PEFT method for LLMs with the Mixture-of-Experts (MoE) architecture and the contents of this work are mainly threefold: (1) We investigate the dispersion degree of the activated experts in customized tasks, and found that the routing distribution for a specific task tends to be highly concentrated, while the distribution of activated experts varies significantly across different tasks. (2) We propose Expert-Specialized Fine-Tuning, or ESFT, which tunes the experts most relevant to downstream tasks while freezing the other experts and modules; experimental results demonstrate that our method not only improves the tuning efficiency, but also matches or even surpasses the performance of full-parameter fine-tuning. (3) We further analyze the impact of the MoE architecture on expert-specialized fine-tuning. We find that MoE models with finer-grained experts are more advantageous in selecting the combination of experts that are most relevant to downstream tasks, thereby enhancing both the training efficiency and effectiveness.

Random pruning is arguably the most naive way to attain sparsity in neural networks, but has been deemed uncompetitive by either post-training pruning or sparse training. In this paper, we focus on sparse training and highlight a perhaps counter-intuitive finding, that random pruning at initialization can be quite powerful for the sparse training of modern neural networks. Without any delicate pruning criteria or carefully pursued sparsity structures, we empirically demonstrate that sparsely training a randomly pruned network from scratch can match the performance of its dense equivalent. There are two key factors that contribute to this revival: (i) the network sizes matter: as the original dense networks grow wider and deeper, the performance of training a randomly pruned sparse network will quickly grow to matching that of its dense equivalent, even at high sparsity ratios; (ii) appropriate layer-wise sparsity ratios can be pre-chosen for sparse training, which shows to be another important performance booster. Simple as it looks, a randomly pruned subnetwork of Wide ResNet-50 can be sparsely trained to outperforming a dense Wide ResNet-50, on ImageNet. We also observed such randomly pruned networks outperform dense counterparts in other favorable aspects, such as out-of-distribution detection, uncertainty estimation, and adversarial robustness. Overall, our results strongly suggest there is larger-than-expected room for sparse training at scale, and the benefits of sparsity might be more universal beyond carefully designed pruning. Our source code can be found at https://github.com/VITA-Group/Random_Pruning.

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

Ad-hoc search calls for the selection of appropriate answers from a massive-scale corpus. Nowadays, the embedding-based retrieval (EBR) becomes a promising solution, where deep learning based document representation and ANN search techniques are allied to handle this task. However, a major challenge is that the ANN index can be too large to fit into memory, given the considerable size of answer corpus. In this work, we tackle this problem with Bi-Granular Document Representation, where the lightweight sparse embeddings are indexed and standby in memory for coarse-grained candidate search, and the heavyweight dense embeddings are hosted in disk for fine-grained post verification. For the best of retrieval accuracy, a Progressive Optimization framework is designed. The sparse embeddings are learned ahead for high-quality search of candidates. Conditioned on the candidate distribution induced by the sparse embeddings, the dense embeddings are continuously learned to optimize the discrimination of ground-truth from the shortlisted candidates. Besides, two techniques: the contrastive quantization and the locality-centric sampling are introduced for the learning of sparse and dense embeddings, which substantially contribute to their performances. Thanks to the above features, our method effectively handles massive-scale EBR with strong advantages in accuracy: with up to +4.3% recall gain on million-scale corpus, and up to +17.5% recall gain on billion-scale corpus. Besides, Our method is applied to a major sponsored search platform with substantial gains on revenue (+1.95%), Recall (+1.01%) and CTR (+0.49%). Our code is available at https://github.com/microsoft/BiDR.

Concept shift is a prevailing problem in natural tasks like medical image segmentation where samples usually come from different subpopulations with variant correlations between features and labels. One common type of concept shift in medical image segmentation is the "information imbalance" between label-sparse samples with few (if any) segmentation labels and label-dense samples with plentiful labeled pixels. Existing distributionally robust algorithms have focused on adaptively truncating/down-weighting the "less informative" (i.e., label-sparse in our context) samples. To exploit data features of label-sparse samples more efficiently, we propose an adaptively weighted online optimization algorithm -- AdaWAC -- to incorporate data augmentation consistency regularization in sample reweighting. Our method introduces a set of trainable weights to balance the supervised loss and unsupervised consistency regularization of each sample separately. At the saddle point of the underlying objective, the weights assign label-dense samples to the supervised loss and label-sparse samples to the unsupervised consistency regularization. We provide a convergence guarantee by recasting the optimization as online mirror descent on a saddle point problem. Our empirical results demonstrate that AdaWAC not only enhances the segmentation performance and sample efficiency but also improves the robustness to concept shift on various medical image segmentation tasks with different UNet-style backbones.

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of K-sparse degree-d PTFs on R^n, where any such concept depends only on K out of n attributes of the input. Our main contribution is a new algorithm that runs in time ({nd}/{epsilon})^{O(d)} and under the Gaussian marginal distribution, PAC learns the class up to error rate epsilon with O(K^{4d}{epsilon^{2d}} cdot log^{5d} n) samples even when an eta leq O(epsilon^d) fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-2d polynomial as a filter to detect corrupted samples.

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

Graphical User Interface (GUI) grounding maps natural language instructions to precise interface locations for autonomous interaction. Current reinforcement learning approaches use binary rewards that treat elements as hit-or-miss targets, creating sparse signals that ignore the continuous nature of spatial interactions. Motivated by human clicking behavior that naturally forms Gaussian distributions centered on target elements, we introduce GUI Gaussian Grounding Rewards (GUI-G^2), a principled reward framework that models GUI elements as continuous Gaussian distributions across the interface plane. GUI-G^2 incorporates two synergistic mechanisms: Gaussian point rewards model precise localization through exponentially decaying distributions centered on element centroids, while coverage rewards assess spatial alignment by measuring the overlap between predicted Gaussian distributions and target regions. To handle diverse element scales, we develop an adaptive variance mechanism that calibrates reward distributions based on element dimensions. This framework transforms GUI grounding from sparse binary classification to dense continuous optimization, where Gaussian distributions generate rich gradient signals that guide models toward optimal interaction positions. Extensive experiments across ScreenSpot, ScreenSpot-v2, and ScreenSpot-Pro benchmarks demonstrate that GUI-G^2, substantially outperforms state-of-the-art method UI-TARS-72B, with the most significant improvement of 24.7% on ScreenSpot-Pro. Our analysis reveals that continuous modeling provides superior robustness to interface variations and enhanced generalization to unseen layouts, establishing a new paradigm for spatial reasoning in GUI interaction tasks.

LiDAR-based 3D point cloud recognition has benefited various applications. Without specially considering the LiDAR point distribution, most current methods suffer from information disconnection and limited receptive field, especially for the sparse distant points. In this work, we study the varying-sparsity distribution of LiDAR points and present SphereFormer to directly aggregate information from dense close points to the sparse distant ones. We design radial window self-attention that partitions the space into multiple non-overlapping narrow and long windows. It overcomes the disconnection issue and enlarges the receptive field smoothly and dramatically, which significantly boosts the performance of sparse distant points. Moreover, to fit the narrow and long windows, we propose exponential splitting to yield fine-grained position encoding and dynamic feature selection to increase model representation ability. Notably, our method ranks 1st on both nuScenes and SemanticKITTI semantic segmentation benchmarks with 81.9% and 74.8% mIoU, respectively. Also, we achieve the 3rd place on nuScenes object detection benchmark with 72.8% NDS and 68.5% mAP. Code is available at https://github.com/dvlab-research/SphereFormer.git.

We propose a probabilistic shape completion method extended to the continuous geometry of large-scale 3D scenes. Real-world scans of 3D scenes suffer from a considerable amount of missing data cluttered with unsegmented objects. The problem of shape completion is inherently ill-posed, and high-quality result requires scalable solutions that consider multiple possible outcomes. We employ the Generative Cellular Automata that learns the multi-modal distribution and transform the formulation to process large-scale continuous geometry. The local continuous shape is incrementally generated as a sparse voxel embedding, which contains the latent code for each occupied cell. We formally derive that our training objective for the sparse voxel embedding maximizes the variational lower bound of the complete shape distribution and therefore our progressive generation constitutes a valid generative model. Experiments show that our model successfully generates diverse plausible scenes faithful to the input, especially when the input suffers from a significant amount of missing data. We also demonstrate that our approach outperforms deterministic models even in less ambiguous cases with a small amount of missing data, which infers that probabilistic formulation is crucial for high-quality geometry completion on input scans exhibiting any levels of completeness.

Word embeddings and language models have transformed natural language processing (NLP) by facilitating the representation of linguistic elements in continuous vector spaces. This review visits foundational concepts such as the distributional hypothesis and contextual similarity, tracing the evolution from sparse representations like one-hot encoding to dense embeddings including Word2Vec, GloVe, and fastText. We examine both static and contextualized embeddings, underscoring advancements in models such as ELMo, BERT, and GPT and their adaptations for cross-lingual and personalized applications. The discussion extends to sentence and document embeddings, covering aggregation methods and generative topic models, along with the application of embeddings in multimodal domains, including vision, robotics, and cognitive science. Advanced topics such as model compression, interpretability, numerical encoding, and bias mitigation are analyzed, addressing both technical challenges and ethical implications. Additionally, we identify future research directions, emphasizing the need for scalable training techniques, enhanced interpretability, and robust grounding in non-textual modalities. By synthesizing current methodologies and emerging trends, this survey offers researchers and practitioners an in-depth resource to push the boundaries of embedding-based language models.

In this paper, we aim to build a robust question answering system that can adapt to out-of-domain datasets. A single network may overfit to the superficial correlation in the training distribution, but with a meaningful number of expert sub-networks, a gating network that selects a sparse combination of experts for each input, and careful balance on the importance of expert sub-networks, the Mixture-of-Experts (MoE) model allows us to train a multi-task learner that can be generalized to out-of-domain datasets. We also explore the possibility of bringing the MoE layers up to the middle of the DistilBERT and replacing the dense feed-forward network with a sparsely-activated switch FFN layers, similar to the Switch Transformer architecture, which simplifies the MoE routing algorithm with reduced communication and computational costs. In addition to model architectures, we explore techniques of data augmentation including Easy Data Augmentation (EDA) and back translation, to create more meaningful variance among the small out-of-domain training data, therefore boosting the performance and robustness of our models. In this paper, we show that our combination of best architecture and data augmentation techniques achieves a 53.477 F1 score in the out-of-domain evaluation, which is a 9.52% performance gain over the baseline. On the final test set, we reported a higher 59.506 F1 and 41.651 EM. We successfully demonstrate the effectiveness of Mixture-of-Expert architecture in a Robust QA task.

Mixture-of-Experts (MoE) large language models (LLMs), which leverage dynamic routing and sparse activation to enhance efficiency and scalability, have achieved higher performance while reducing computational costs. However, these models face significant memory overheads, limiting their practical deployment and broader adoption. Post-training quantization (PTQ), a widely used method for compressing LLMs, encounters severe accuracy degradation and diminished generalization performance when applied to MoE models. This paper investigates the impact of MoE's sparse and dynamic characteristics on quantization and identifies two primary challenges: (1) Inter-expert imbalance, referring to the uneven distribution of samples across experts, which leads to insufficient and biased calibration for less frequently utilized experts; (2) Intra-expert imbalance, arising from MoE's unique aggregation mechanism, which leads to varying degrees of correlation between different samples and their assigned experts. To address these challenges, we propose MoEQuant, a novel quantization framework tailored for MoE LLMs. MoE-Quant includes two novel techniques: 1) Expert-Balanced Self-Sampling (EBSS) is an efficient sampling method that efficiently constructs a calibration set with balanced expert distributions by leveraging the cumulative probabilities of tokens and expert balance metrics as guiding factors. 2) Affinity-Guided Quantization (AGQ), which incorporates affinities between experts and samples into the quantization process, thereby accurately assessing the impact of individual samples on different experts within the MoE layer. Experiments demonstrate that MoEQuant achieves substantial performance gains (more than 10 points accuracy gain in the HumanEval for DeepSeekMoE-16B under 4-bit quantization) and boosts efficiency.

Large Vision-Language Models (LVLMs) may produce outputs that are unfaithful to reality, also known as visual hallucinations (VH), which significantly impedes their real-world usage. To alleviate VH, various decoding strategies have been proposed to enhance visual information. However, many of these methods may require secondary decoding and rollback, which significantly reduces inference speed. In this work, we propose an efficient plug-and-play decoding algorithm via Visual-Aware Sparsification (VASparse) from the perspective of token sparsity for mitigating VH. VASparse is inspired by empirical observations: (1) the sparse activation of attention in LVLMs, and (2) visual-agnostic tokens sparsification exacerbates VH. Based on these insights, we propose a novel token sparsification strategy that balances efficiency and trustworthiness. Specifically, VASparse implements a visual-aware token selection strategy during decoding to reduce redundant tokens while preserving visual context effectively. Additionally, we innovatively introduce a sparse-based visual contrastive decoding method to recalibrate the distribution of hallucinated outputs without the time overhead associated with secondary decoding. Subsequently, VASparse recalibrates attention scores to penalize attention sinking of LVLMs towards text tokens. Extensive experiments across four popular benchmarks confirm the effectiveness of VASparse in mitigating VH across different LVLM families without requiring additional training or post-processing. Impressively, VASparse achieves state-of-the-art performance for mitigating VH while maintaining competitive decoding speed. Code is available at https://github.com/mengchuang123/VASparse-github.

We present a self-supervised framework that learns population-level codes for arbitrary ensembles of neural recordings at scale. We address two key challenges in scaling models with neural time-series data: sparse and variable electrode distribution across subjects and datasets. The Population Transformer (PopT) stacks on top of pretrained representations and enhances downstream decoding by enabling learned aggregation of multiple spatially-sparse data channels. The pretrained PopT lowers the amount of data required for downstream decoding experiments, while increasing accuracy, even on held-out subjects and tasks. Compared to end-to-end methods, this approach is computationally lightweight and more interpretable, while still retaining competitive performance. We further show how our framework is generalizable to multiple time-series embeddings and neural data modalities. Beyond decoding, we interpret the pretrained PopT and fine-tuned models to show how they can be used to extract neuroscience insights from massive amounts of data. We release our code as well as a pretrained PopT to enable off-the-shelf improvements in multi-channel intracranial data decoding and interpretability.

A commonly observed failure mode of Neural Radiance Field (NeRF) is fitting incorrect geometries when given an insufficient number of input views. One potential reason is that standard volumetric rendering does not enforce the constraint that most of a scene's geometry consist of empty space and opaque surfaces. We formalize the above assumption through DS-NeRF (Depth-supervised Neural Radiance Fields), a loss for learning radiance fields that takes advantage of readily-available depth supervision. We leverage the fact that current NeRF pipelines require images with known camera poses that are typically estimated by running structure-from-motion (SFM). Crucially, SFM also produces sparse 3D points that can be used as "free" depth supervision during training: we add a loss to encourage the distribution of a ray's terminating depth matches a given 3D keypoint, incorporating depth uncertainty. DS-NeRF can render better images given fewer training views while training 2-3x faster. Further, we show that our loss is compatible with other recently proposed NeRF methods, demonstrating that depth is a cheap and easily digestible supervisory signal. And finally, we find that DS-NeRF can support other types of depth supervision such as scanned depth sensors and RGB-D reconstruction outputs.

Mining data streams with multi-label outputs poses significant challenges due to evolving distributions, high-dimensional label spaces, sparse label occurrences, and complex label dependencies. Moreover, concept drift affects not only input distributions but also label correlations and imbalance ratios over time, complicating model adaptation. To address these challenges, structured learners are categorized into local and global methods. Local methods break down the task into simpler components, while global methods adapt the algorithm to the full output space, potentially yielding better predictions by exploiting label correlations. This work introduces iHOMER (Incremental Hierarchy Of Multi-label Classifiers), an online multi-label learning framework that incrementally partitions the label space into disjoint, correlated clusters without relying on predefined hierarchies. iHOMER leverages online divisive-agglomerative clustering based on Jaccard similarity and a global tree-based learner driven by a multivariate Bernoulli process to guide instance partitioning. To address non-stationarity, it integrates drift detection mechanisms at both global and local levels, enabling dynamic restructuring of label partitions and subtrees. Experiments across 23 real-world datasets show iHOMER outperforms 5 state-of-the-art global baselines, such as MLHAT, MLHT of Pruned Sets and iSOUPT, by 23\%, and 12 local baselines, such as binary relevance transformations of kNN, EFDT, ARF, and ADWIN bagging/boosting ensembles, by 32\%, establishing its robustness for online multi-label classification.

DIFF Transformer improves attention allocation by enhancing focus on relevant context while suppressing noise. It introduces a differential attention mechanism that calculates the difference between two independently generated attention distributions, effectively reducing noise and promoting sparse attention patterns. However, the independent signal generation in DIFF Transformer results in parameter redundancy and suboptimal utilization of information. In this work, we propose Shared DIFF Transformer, which draws on the idea of a differential amplifier by introducing a shared base matrix to model global patterns and incorporating low-rank updates to enhance task-specific flexibility. This design significantly reduces parameter redundancy, improves efficiency, and retains strong noise suppression capabilities. Experimental results show that, compared to DIFF Transformer, our method achieves better performance in tasks such as long-sequence modeling, key information retrieval, and in-context learning. Our work provides a novel and efficient approach to optimizing differential attention mechanisms and advancing robust Transformer architectures.

The rapid advancement of face forgery techniques has introduced a growing variety of forgeries. Incremental Face Forgery Detection (IFFD), involving gradually adding new forgery data to fine-tune the previously trained model, has been introduced as a promising strategy to deal with evolving forgery methods. However, a naively trained IFFD model is prone to catastrophic forgetting when new forgeries are integrated, as treating all forgeries as a single ''Fake" class in the Real/Fake classification can cause different forgery types overriding one another, thereby resulting in the forgetting of unique characteristics from earlier tasks and limiting the model's effectiveness in learning forgery specificity and generality. In this paper, we propose to stack the latent feature distributions of previous and new tasks brick by brick, i.e., achieving aligned feature isolation. In this manner, we aim to preserve learned forgery information and accumulate new knowledge by minimizing distribution overriding, thereby mitigating catastrophic forgetting. To achieve this, we first introduce Sparse Uniform Replay (SUR) to obtain the representative subsets that could be treated as the uniformly sparse versions of the previous global distributions. We then propose a Latent-space Incremental Detector (LID) that leverages SUR data to isolate and align distributions. For evaluation, we construct a more advanced and comprehensive benchmark tailored for IFFD. The leading experimental results validate the superiority of our method.

Due to the cost-prohibitive nature of training Large Language Models (LLMs), fine-tuning has emerged as an attractive alternative for specializing LLMs for specific tasks using limited compute resources in a cost-effective manner. In this paper, we characterize sparse Mixture of Experts (MoE) based LLM fine-tuning to understand their accuracy and runtime performance on a single GPU. Our evaluation provides unique insights into the training efficacy of sparse and dense versions of MoE models, as well as their runtime characteristics, including maximum batch size, execution time breakdown, end-to-end throughput, GPU hardware utilization, and load distribution. Our study identifies the optimization of the MoE layer as crucial for further improving the performance of LLM fine-tuning. Using our profiling results, we also develop and validate an analytical model to estimate the cost of LLM fine-tuning on the cloud. This model, based on parameters of the model and GPU architecture, estimates LLM throughput and the cost of training, aiding practitioners in industry and academia to budget the cost of fine-tuning a specific model.

Near-field radar imaging systems are recently used in a wide range of applications, such as medical diagnosis, through-wall imaging, concealed weapon detection, and nondestructive evaluation. In this paper, we consider the problem of reconstructing the three-dimensional (3D) complex-valued reflectivity distribution of the near-field scene from sparse multiple-input multiple-output (MIMO) array measurements. Using the alternating direction method of multipliers (ADMM) framework, we solve this inverse problem by enforcing regularization on the magnitude of the complex-valued reflectivity distribution. For this, we provide a general expression for the proximal mapping associated with such regularization functionals. This equivalently corresponds to the solution of a complex-valued denoising problem which involves regularization on the magnitude. By utilizing this expression, we develop a novel and efficient plug-and-play (PnP) reconstruction method that consists of simple update steps. Due to the success of data-adaptive deep priors in various imaging problems, we also train a 3D deep denoiser to exploit within the developed PnP framework for MIMO imaging. The effectiveness of the developed learning-based PnP approach is illustrated under various compressive and noisy observation scenarios using both simulated data and experimental measurements. The performance is also compared with sparsity priors and the commonly used analytical approaches such as back-projection and Kirchhoff migration. The results demonstrate that the developed technique not only provides state-of-the-art reconstruction performance for 3D real-world targets, but also enables fast computation. Our approach provides a unified general framework to effectively handle arbitrary regularization on the magnitude of a complex-valued unknown and is equally applicable to other radar image formation problems (including SAR).

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of k patches, each of dimension d, and the label is determined by a d-sparse signal vector that can freely appear in any one of the k patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require O(k+d) samples, whereas LCNs require Omega(kd) samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need O(k(k+d)) samples, compared to Omega(k^2d) samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

Large language models (LLMs) have shown remarkable potential as autonomous agents, particularly in web-based tasks. However, existing LLM web agents heavily rely on expensive proprietary LLM APIs, while open LLMs lack the necessary decision-making capabilities. This paper introduces WebRL, a self-evolving online curriculum reinforcement learning framework designed to train high-performance web agents using open LLMs. WebRL addresses three key challenges in building LLM web agents, including the scarcity of training tasks, sparse feedback signals, and policy distribution drift in online learning. Specifically, WebRL incorporates 1) a self-evolving curriculum that generates new tasks from unsuccessful attempts, 2) a robust outcome-supervised reward model (ORM), and 3) adaptive reinforcement learning strategies to ensure consistent improvements. We apply WebRL to transform open Llama-3.1 and GLM-4 models into proficient web agents. On WebArena-Lite, WebRL improves the success rate of Llama-3.1-8B from 4.8% to 42.4%, and from 6.1% to 43% for GLM-4-9B. These open models significantly surpass the performance of GPT-4-Turbo (17.6%) and GPT-4o (13.9%) and outperform previous state-of-the-art web agents trained on open LLMs (AutoWebGLM, 18.2%). Our findings demonstrate WebRL's effectiveness in bridging the gap between open and proprietary LLM-based web agents, paving the way for more accessible and powerful autonomous web interaction systems.

To mitigate the privacy leakages and communication burdens of Federated Learning (FL), decentralized FL (DFL) discards the central server and each client only communicates with its neighbors in a decentralized communication network. However, existing DFL suffers from high inconsistency among local clients, which results in severe distribution shift and inferior performance compared with centralized FL (CFL), especially on heterogeneous data or sparse communication topology. To alleviate this issue, we propose two DFL algorithms named DFedSAM and DFedSAM-MGS to improve the performance of DFL. Specifically, DFedSAM leverages gradient perturbation to generate local flat models via Sharpness Aware Minimization (SAM), which searches for models with uniformly low loss values. DFedSAM-MGS further boosts DFedSAM by adopting Multiple Gossip Steps (MGS) for better model consistency, which accelerates the aggregation of local flat models and better balances communication complexity and generalization. Theoretically, we present improved convergence rates small Obig(1{KT}+1{T}+1{K^{1/2}T^{3/2}(1-lambda)^2}big) and small Obig(1{KT}+1{T}+lambda^Q+1{K^{1/2}T^{3/2}(1-lambda^Q)^2}big) in non-convex setting for DFedSAM and DFedSAM-MGS, respectively, where 1-lambda is the spectral gap of gossip matrix and Q is the number of MGS. Empirically, our methods can achieve competitive performance compared with CFL methods and outperform existing DFL methods.

LLMs are seeing growing use for applications such as document analysis and summarization which require large context windows, and with these large context windows KV cache activations surface as the dominant contributor to memory consumption during inference. Quantization is a promising approach for compressing KV cache activations; however, existing solutions fail to represent activations accurately in ultra-low precisions, such as sub-4-bit. In this work, we present KVQuant, which addresses this problem by incorporating novel methods for quantizing cached KV activations, including: (i) Per-Channel Key Quantization, where we adjust the dimension along which we quantize the Key activations to better match the distribution; (ii) Pre-RoPE Key Quantization, where we quantize Key activations before the rotary positional embedding to mitigate its impact on quantization; (iii) Non-Uniform KV Cache Quantization, where we derive per-layer sensitivity-weighted non-uniform datatypes that better represent the distributions; (iv) Per-Vector Dense-and-Sparse Quantization, where we isolate outliers separately for each vector to minimize skews in quantization ranges; and (v) Q-Norm, where we normalize quantization centroids in order to mitigate distribution shift, providing additional benefits for 2-bit quantization. By applying our method to the LLaMA, LLaMA-2, and Mistral models, we achieve <0.1 perplexity degradation with 3-bit quantization on both Wikitext-2 and C4, outperforming existing approaches. Our method enables serving the LLaMA-7B model with a context length of up to 1 million on a single A100-80GB GPU and up to 10 million on an 8-GPU system.

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity 1 / log(1/sparsity). This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

Sparse neural networks have shown similar or better generalization performance than their dense counterparts while having higher parameter efficiency. This has motivated a number of works to learn or search for high performing sparse networks. While reports of task performance or efficiency gains are impressive, standard baselines are lacking leading to poor comparability and unreliable reproducibility across methods. In this work, we propose Random Search as a baseline algorithm for finding good sparse configurations and study its performance. We apply Random Search on the node space of an overparameterized network with the goal of finding better initialized sparse sub-networks that are positioned more advantageously in the loss landscape. We record the post-training performances of the found sparse networks and at various levels of sparsity, and compare against both their fully connected parent networks and random sparse configurations at the same sparsity levels. First, we demonstrate performance at different levels of sparsity and highlight that a significant level of performance can still be preserved even when the network is highly sparse. Second, we observe that for this sparse architecture search task, initialized sparse networks found by Random Search neither perform better nor converge more efficiently than their random counterparts. Thus we conclude that Random Search may be viewed as a reasonable neutral baseline for sparsity search methods.

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Sparse neural networks are a key factor in developing resource-efficient machine learning applications. We propose the novel and powerful sparse learning method Adaptive Regularized Training (ART) to compress dense into sparse networks. Instead of the commonly used binary mask during training to reduce the number of model weights, we inherently shrink weights close to zero in an iterative manner with increasing weight regularization. Our method compresses the pre-trained model knowledge into the weights of highest magnitude. Therefore, we introduce a novel regularization loss named HyperSparse that exploits the highest weights while conserving the ability of weight exploration. Extensive experiments on CIFAR and TinyImageNet show that our method leads to notable performance gains compared to other sparsification methods, especially in extremely high sparsity regimes up to 99.8 percent model sparsity. Additional investigations provide new insights into the patterns that are encoded in weights with high magnitudes.

Sparse expert models are a thirty-year old concept re-emerging as a popular architecture in deep learning. This class of architecture encompasses Mixture-of-Experts, Switch Transformers, Routing Networks, BASE layers, and others, all with the unifying idea that each example is acted on by a subset of the parameters. By doing so, the degree of sparsity decouples the parameter count from the compute per example allowing for extremely large, but efficient models. The resulting models have demonstrated significant improvements across diverse domains such as natural language processing, computer vision, and speech recognition. We review the concept of sparse expert models, provide a basic description of the common algorithms, contextualize the advances in the deep learning era, and conclude by highlighting areas for future work.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

As deep learning models grow, sparsity is becoming an increasingly critical component of deep neural networks, enabling improved performance and reduced storage. However, existing frameworks offer poor support for sparsity. Specialized sparsity engines focus exclusively on sparse inference, while general frameworks primarily focus on sparse tensors in classical formats and neglect the broader sparsification pipeline necessary for using sparse models, especially during training. Further, existing frameworks are not easily extensible: adding a new sparse tensor format or operator is challenging and time-consuming. To address this, we propose STen, a sparsity programming model and interface for PyTorch, which incorporates sparsity layouts, operators, and sparsifiers, in an efficient, customizable, and extensible framework that supports virtually all sparsification methods. We demonstrate this by developing a high-performance grouped n:m sparsity layout for CPU inference at moderate sparsity. STen brings high performance and ease of use to the ML community, making sparsity easily accessible.

Recent works have explored the use of weight sparsity to improve the training efficiency (test accuracy w.r.t training FLOPs) of deep neural networks (DNNs). These works aim to reduce training FLOPs but training with sparse weights often leads to accuracy loss or requires longer training schedules, making the resulting training efficiency less clear. In contrast, we focus on using sparsity to increase accuracy while using the same FLOPs as the dense model and show training efficiency gains through higher accuracy. In this work, we introduce Sparse-IFT, a family of Sparse Iso-FLOP Transformations which are used as drop-in replacements for dense layers to improve their representational capacity and FLOP efficiency. Each transformation is parameterized by a single hyperparameter (sparsity level) and provides a larger search space to find optimal sparse masks. Without changing any training hyperparameters, replacing dense layers with Sparse-IFT leads to significant improvements across computer vision (CV) and natural language processing (NLP) tasks, including ResNet-18 on ImageNet (+3.5%) and GPT-3 Small on WikiText-103 (-0.4 PPL), both matching larger dense model variants that use 2x or more FLOPs. To our knowledge, this is the first work to demonstrate the use of sparsity for improving the accuracy of dense models via a simple-to-use set of sparse transformations. Code is available at: https://github.com/CerebrasResearch/Sparse-IFT.

Dynamic Sparse Training (DST) methods achieve state-of-the-art results in sparse neural network training, matching the generalization of dense models while enabling sparse training and inference. Although the resulting models are highly sparse and theoretically less computationally expensive, achieving speedups with unstructured sparsity on real-world hardware is challenging. In this work, we propose a sparse-to-sparse DST method, Structured RigL (SRigL), to learn a variant of fine-grained structured N:M sparsity by imposing a constant fan-in constraint. Using our empirical analysis of existing DST methods at high sparsity, we additionally employ a neuron ablation method which enables SRigL to achieve state-of-the-art sparse-to-sparse structured DST performance on a variety of Neural Network (NN) architectures. We demonstrate reduced real-world timings on CPU for online inference -- 3.6x/2x faster at 90% sparsity than equivalent dense/unstructured sparse layers, respectively. Our source code is available at https://github.com/calgaryml/condensed-sparsity

Hyperspectral unmixing is one of the crucial steps for many hyperspectral applications. The problem of hyperspectral unmixing has proven to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown. What is more, this task becomes more challenging in the case that the spectral bands are degraded with noise. This paper presents a robust model for unsupervised hyperspectral unmixing. Specifically, our model is developed with the correntropy based metric where the non-negative constraints on both endmembers and abundances are imposed to keep physical significance. In addition, a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember. To solve our model, a half-quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively re-weighted NMF with sparsity constraints. As a result, the optimization of our model can adaptively assign small weights to noisy bands and give more emphasis on noise-free bands. In addition, with sparsity constraints, our model can naturally generate sparse abundances. Experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state-of-the-art unmixing models.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

The deployment of Deep Neural Networks (DNNs) on edge devices is hindered by the substantial gap between performance requirements and available processing power. While recent research has made significant strides in developing pruning methods to build a sparse network for reducing the computing overhead of DNNs, there remains considerable accuracy loss, especially at high pruning ratios. We find that the architectures designed for dense networks by differentiable architecture search methods are ineffective when pruning mechanisms are applied to them. The main reason is that the current method does not support sparse architectures in their search space and uses a search objective that is made for dense networks and does not pay any attention to sparsity. In this paper, we propose a new method to search for sparsity-friendly neural architectures. We do this by adding two new sparse operations to the search space and modifying the search objective. We propose two novel parametric SparseConv and SparseLinear operations in order to expand the search space to include sparse operations. In particular, these operations make a flexible search space due to using sparse parametric versions of linear and convolution operations. The proposed search objective lets us train the architecture based on the sparsity of the search space operations. Quantitative analyses demonstrate that our search architectures outperform those used in the stateof-the-art sparse networks on the CIFAR-10 and ImageNet datasets. In terms of performance and hardware effectiveness, DASS increases the accuracy of the sparse version of MobileNet-v2 from 73.44% to 81.35% (+7.91% improvement) with 3.87x faster inference time.

This article does not propose any novel algorithm or new hardware for sparsity. Instead, it aims to serve the "common good" for the increasingly prosperous Sparse Neural Network (SNN) research community. We attempt to summarize some most common confusions in SNNs, that one may come across in various scenarios such as paper review/rebuttal and talks - many drawn from the authors' own bittersweet experiences! We feel that doing so is meaningful and timely, since the focus of SNN research is notably shifting from traditional pruning to more diverse and profound forms of sparsity before, during, and after training. The intricate relationships between their scopes, assumptions, and approaches lead to misunderstandings, for non-experts or even experts in SNNs. In response, we summarize ten Q\&As of SNNs from many key aspects, including dense vs. sparse, unstructured sparse vs. structured sparse, pruning vs. sparse training, dense-to-sparse training vs. sparse-to-sparse training, static sparsity vs. dynamic sparsity, before-training/during-training vs. post-training sparsity, and many more. We strive to provide proper and generically applicable answers to clarify those confusions to the best extent possible. We hope our summary provides useful general knowledge for people who want to enter and engage with this exciting community; and also provides some "mind of ease" convenience for SNN researchers to explain their work in the right contexts. At the very least (and perhaps as this article's most insignificant target functionality), if you are writing/planning to write a paper or rebuttal in the field of SNNs, we hope some of our answers could help you!

Exploiting sparsity underlying neural networks has become one of the most potential methodologies to reduce the memory footprint, I/O cost, and computation workloads during inference. And the degree of sparsity one can exploit has become higher as larger model sizes have been considered along with the trend of pre-training giant models. On the other hand, compared with quantization that has been a widely supported option, acceleration through high-degree sparsity is not supported in most computing platforms. In this work, we introduce the first commercial hardware platform supporting high-degree sparsity acceleration up to 32 times -- S4. Combined with state-of-the-art sparse pruning techniques, we demonstrate several-times practical inference speedup on S4 over mainstream inference platforms such as Nvidia T4. We also show that in practice a sparse model of larger size can achieve both higher accuracy and higher throughput on S4 than a dense model of smaller size.

Over-parameterization of deep neural networks (DNNs) has shown high prediction accuracy for many applications. Although effective, the large number of parameters hinders its popularity on resource-limited devices and has an outsize environmental impact. Sparse training (using a fixed number of nonzero weights in each iteration) could significantly mitigate the training costs by reducing the model size. However, existing sparse training methods mainly use either random-based or greedy-based drop-and-grow strategies, resulting in local minimal and low accuracy. In this work, we consider the dynamic sparse training as a sparse connectivity search problem and design an exploitation and exploration acquisition function to escape from local optima and saddle points. We further design an acquisition function and provide the theoretical guarantees for the proposed method and clarify its convergence property. Experimental results show that sparse models (up to 98\% sparsity) obtained by our proposed method outperform the SOTA sparse training methods on a wide variety of deep learning tasks. On VGG-19 / CIFAR-100, ResNet-50 / CIFAR-10, ResNet-50 / CIFAR-100, our method has even higher accuracy than dense models. On ResNet-50 / ImageNet, the proposed method has up to 8.2\% accuracy improvement compared to SOTA sparse training methods.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

With increasing demands for efficiency, information retrieval has developed a branch of sparse retrieval, further advancing towards inference-free retrieval where the documents are encoded during indexing time and there is no model-inference for queries. Existing sparse retrieval models rely on FLOPS regularization for sparsification, while this mechanism was originally designed for Siamese encoders, it is considered to be suboptimal in inference-free scenarios which is asymmetric. Previous attempts to adapt FLOPS for inference-free scenarios have been limited to rule-based methods, leaving the potential of sparsification approaches for inference-free retrieval models largely unexplored. In this paper, we explore ell_0 inspired sparsification manner for inference-free retrievers. Through comprehensive out-of-domain evaluation on the BEIR benchmark, our method achieves state-of-the-art performance among inference-free sparse retrieval models and is comparable to leading Siamese sparse retrieval models. Furthermore, we provide insights into the trade-off between retrieval effectiveness and computational efficiency, demonstrating practical value for real-world applications.

Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.

To address the challenge of increasing network size, researchers have developed sparse models through network pruning. However, maintaining model accuracy while achieving significant speedups on general computing devices remains an open problem. In this paper, we present a novel mobile inference acceleration framework SparseByteNN, which leverages fine-grained kernel sparsity to achieve real-time execution as well as high accuracy. Our framework consists of two parts: (a) A fine-grained kernel sparsity schema with a sparsity granularity between structured pruning and unstructured pruning. It designs multiple sparse patterns for different operators. Combined with our proposed whole network rearrangement strategy, the schema achieves a high compression rate and high precision at the same time. (b) Inference engine co-optimized with the sparse pattern. The conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet-v1 outperform strong dense baselines on the efficiency-accuracy curve. Experimental results on Qualcomm 855 show that for 30% sparse MobileNet-v1, SparseByteNN achieves 1.27x speedup over the dense version and 1.29x speedup over the state-of-the-art sparse inference engine MNN with a slight accuracy drop of 0.224%. The source code of SparseByteNN will be available at https://github.com/lswzjuer/SparseByteNN

Learned sparse retrieval, which can efficiently perform retrieval through mature inverted-index engines, has garnered growing attention in recent years. Particularly, the inference-free sparse retrievers are attractive as they eliminate online model inference in the retrieval phase thereby avoids huge computational cost, offering reasonable throughput and latency. However, even the state-of-the-art (SOTA) inference-free sparse models lag far behind in terms of search relevance when compared to both sparse and dense siamese models. Towards competitive search relevance for inference-free sparse retrievers, we argue that they deserve dedicated training methods other than using same ones with siamese encoders. In this paper, we propose two different approaches for performance improvement. First, we introduce the IDF-aware FLOPS loss, which introduces Inverted Document Frequency (IDF) to the sparsification of representations. We find that it mitigates the negative impact of the FLOPS regularization on search relevance, allowing the model to achieve a better balance between accuracy and efficiency. Moreover, we propose a heterogeneous ensemble knowledge distillation framework that combines siamese dense and sparse retrievers to generate supervisory signals during the pre-training phase. The ensemble framework of dense and sparse retriever capitalizes on their strengths respectively, providing a strong upper bound for knowledge distillation. To concur the diverse feedback from heterogeneous supervisors, we normalize and then aggregate the outputs of the teacher models to eliminate score scale differences. On the BEIR benchmark, our model outperforms existing SOTA inference-free sparse model by 3.3 NDCG@10 score. It exhibits search relevance comparable to siamese sparse retrievers and client-side latency only 1.1x that of BM25.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the community. Yet, much less is known about the interaction between sparsity and the standard stochastic optimization techniques used for training sparse networks, and most existing work uses standard dense schedules and hyperparameters for training sparse networks. In this work, we examine the impact of high sparsity on model training using the standard computer vision and natural language processing sparsity benchmarks. We begin by showing that using standard dense training recipes for sparse training is suboptimal, and results in under-training. We provide new approaches for mitigating this issue for both sparse pre-training of vision models (e.g. ResNet50/ImageNet) and sparse fine-tuning of language models (e.g. BERT/GLUE), achieving state-of-the-art results in both settings in the high-sparsity regime, and providing detailed analyses for the difficulty of sparse training in both scenarios. Our work sets a new threshold in terms of the accuracies that can be achieved under high sparsity, and should inspire further research into improving sparse model training, to reach higher accuracies under high sparsity, but also to do so efficiently.

Large pre-trained transformers are show-stealer in modern-day deep learning, and it becomes crucial to comprehend the parsimonious patterns that exist within them as they grow in scale. With exploding parameter counts, Lottery Ticket Hypothesis (LTH) and its variants, have lost their pragmatism in sparsifying them due to high computation and memory bottleneck of repetitive train-prune-retrain routine of iterative magnitude pruning (IMP) which worsens with increasing model size. This paper comprehensively studies induced sparse patterns across multiple large pre-trained vision and language transformers. We propose the existence of -- essential sparsity defined with a sharp dropping point beyond which the performance declines much faster w.r.t the rise of sparsity level, when we directly remove weights with the smallest magnitudes in one-shot without re-training. We also find essential sparsity to hold valid for N:M sparsity patterns as well as on modern-scale large language models (Vicuna-7B). We also present an intriguing emerging phenomenon of abrupt sparsification during the pre-training of BERT, i.e., BERT suddenly becomes heavily sparse in pre-training after certain iterations. Moreover, our observations also indicate a counter-intuitive finding that BERT trained with a larger amount of pre-training data tends to have a better ability to condense knowledge in comparatively relatively fewer parameters. Lastly, we investigate the effect of the pre-training loss on essential sparsity and discover that self-supervised learning (SSL) objectives trigger stronger emergent sparsification properties than supervised learning (SL). Our codes are available at https://github.com/VITA-Group/essential_sparsity.

We show for the first time that large-scale generative pretrained transformer (GPT) family models can be pruned to at least 50% sparsity in one-shot, without any retraining, at minimal loss of accuracy. This is achieved via a new pruning method called SparseGPT, specifically designed to work efficiently and accurately on massive GPT-family models. We can execute SparseGPT on the largest available open-source models, OPT-175B and BLOOM-176B, in under 4.5 hours, and can reach 60% unstructured sparsity with negligible increase in perplexity: remarkably, more than 100 billion weights from these models can be ignored at inference time. SparseGPT generalizes to semi-structured (2:4 and 4:8) patterns, and is compatible with weight quantization approaches. The code is available at: https://github.com/IST-DASLab/sparsegpt.

As industrial applications are increasingly automated by machine learning models, enforcing personal data ownership and intellectual property rights requires tracing training data back to their rightful owners. Membership inference algorithms approach this problem by using statistical techniques to discern whether a target sample was included in a model's training set. However, existing methods only utilize the unaltered target sample or simple augmentations of the target to compute statistics. Such a sparse sampling of the model's behavior carries little information, leading to poor inference capabilities. In this work, we use adversarial tools to directly optimize for queries that are discriminative and diverse. Our improvements achieve significantly more accurate membership inference than existing methods, especially in offline scenarios and in the low false-positive regime which is critical in legal settings. Code is available at https://github.com/YuxinWenRick/canary-in-a-coalmine.

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each sub-group. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups.

Small, highly trained, open-source large language models are widely used due to their inference efficiency, but further improving their quality remains a challenge. Sparse upcycling is a promising approach that transforms a pretrained dense model into a Mixture-of-Experts (MoE) architecture, increasing the model's parameter count and quality. In this work, we compare the effectiveness of sparse upcycling against continued pretraining (CPT) across different model sizes, compute budgets, and pretraining durations. Our experiments show that sparse upcycling can achieve better quality, with improvements of over 20% relative to CPT in certain scenarios. However, this comes with a significant inference cost, leading to 40% slowdowns in high-demand inference settings for larger models. Our findings highlight the trade-off between model quality and inference efficiency, offering insights for practitioners seeking to balance model quality and deployment constraints.

Sparse Neural Networks (SNNs) can potentially demonstrate similar performance to their dense counterparts while saving significant energy and memory at inference. However, the accuracy drop incurred by SNNs, especially at high pruning ratios, can be an issue in critical deployment conditions. While recent works mitigate this issue through sophisticated pruning techniques, we shift our focus to an overlooked factor: hyperparameters and activation functions. Our analyses have shown that the accuracy drop can additionally be attributed to (i) Using ReLU as the default choice for activation functions unanimously, and (ii) Fine-tuning SNNs with the same hyperparameters as dense counterparts. Thus, we focus on learning a novel way to tune activation functions for sparse networks and combining these with a separate hyperparameter optimization (HPO) regime for sparse networks. By conducting experiments on popular DNN models (LeNet-5, VGG-16, ResNet-18, and EfficientNet-B0) trained on MNIST, CIFAR-10, and ImageNet-16 datasets, we show that the novel combination of these two approaches, dubbed Sparse Activation Function Search, short: SAFS, results in up to 15.53%, 8.88%, and 6.33% absolute improvement in the accuracy for LeNet-5, VGG-16, and ResNet-18 over the default training protocols, especially at high pruning ratios. Our code can be found at https://github.com/automl/SAFS

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better uncertainty quantification. For the success of BNN, search an appropriate architecture of the neural networks is an important task, and various algorithms to find good sparse neural networks have been proposed. In this paper, we propose a new node-sparse BNN model which has good theoretical properties and is computationally feasible. We prove that the posterior concentration rate to the true model is near minimax optimal and adaptive to the smoothness of the true model. In particular the adaptiveness is the first of its kind for node-sparse BNNs. In addition, we develop a novel MCMC algorithm which makes the Bayesian inference of the node-sparse BNN model feasible in practice.

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements.

Overparameterized neural networks generalize well but are expensive to train. Ideally, one would like to reduce their computational cost while retaining their generalization benefits. Sparse model training is a simple and promising approach to achieve this, but there remain challenges as existing methods struggle with accuracy loss, slow training runtime, or difficulty in sparsifying all model components. The core problem is that searching for a sparsity mask over a discrete set of sparse matrices is difficult and expensive. To address this, our main insight is to optimize over a continuous superset of sparse matrices with a fixed structure known as products of butterfly matrices. As butterfly matrices are not hardware efficient, we propose simple variants of butterfly (block and flat) to take advantage of modern hardware. Our method (Pixelated Butterfly) uses a simple fixed sparsity pattern based on flat block butterfly and low-rank matrices to sparsify most network layers (e.g., attention, MLP). We empirically validate that Pixelated Butterfly is 3x faster than butterfly and speeds up training to achieve favorable accuracy--efficiency tradeoffs. On the ImageNet classification and WikiText-103 language modeling tasks, our sparse models train up to 2.5x faster than the dense MLP-Mixer, Vision Transformer, and GPT-2 medium with no drop in accuracy.

Historically, the pursuit of efficient inference has been one of the driving forces behind research into new deep learning architectures and building blocks. Some recent examples include: the squeeze-and-excitation module, depthwise separable convolutions in Xception, and the inverted bottleneck in MobileNet v2. Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new, the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly, which we open-source for the benefit of the community as part of the XNNPACK library. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1, MobileNet v2 and EfficientNet architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by 1.3-2.4times -- equivalent to approximately one entire generation of MobileNet-family improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures.

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of generalization performance of overparametrized networks. We propose in this paper a method for learning sparse neural topologies via a regularization technique which identifies non relevant weights and selectively shrinks their norm, while performing a classic update for relevant ones. This technique, which is an improvement of classical weight decay, is based on the definition of a regularization term which can be added to any loss functional regardless of its form, resulting in a unified general framework exploitable in many different contexts. The actual elimination of parameters identified as irrelevant is handled by an iterative pruning algorithm. We tested the proposed technique on different image classification and Natural language generation tasks, obtaining results on par or better then competitors in terms of sparsity and metrics, while achieving strong models compression.

Sparse autoencoders (SAEs) are a promising approach to extracting features from neural networks, enabling model interpretability as well as causal interventions on model internals. SAEs generate sparse feature representations using a sparsifying activation function that implicitly defines a set of token-feature matches. We frame the token-feature matching as a resource allocation problem constrained by a total sparsity upper bound. For example, TopK SAEs solve this allocation problem with the additional constraint that each token matches with at most k features. In TopK SAEs, the k active features per token constraint is the same across tokens, despite some tokens being more difficult to reconstruct than others. To address this limitation, we propose two novel SAE variants, Feature Choice SAEs and Mutual Choice SAEs, which each allow for a variable number of active features per token. Feature Choice SAEs solve the sparsity allocation problem under the additional constraint that each feature matches with at most m tokens. Mutual Choice SAEs solve the unrestricted allocation problem where the total sparsity budget can be allocated freely between tokens and features. Additionally, we introduce a new auxiliary loss function, aux_zipf_loss, which generalises the aux_k_loss to mitigate dead and underutilised features. Our methods result in SAEs with fewer dead features and improved reconstruction loss at equivalent sparsity levels as a result of the inherent adaptive computation. More accurate and scalable feature extraction methods provide a path towards better understanding and more precise control of foundation models.

Learned sparse and dense representations capture different successful approaches to text retrieval and the fusion of their results has proven to be more effective and robust. Prior work combines dense and sparse retrievers by fusing their model scores. As an alternative, this paper presents a simple approach to densifying sparse representations for text retrieval that does not involve any training. Our densified sparse representations (DSRs) are interpretable and can be easily combined with dense representations for end-to-end retrieval. We demonstrate that our approach can jointly learn sparse and dense representations within a single model and then combine them for dense retrieval. Experimental results suggest that combining our DSRs and dense representations yields a balanced tradeoff between effectiveness and efficiency.

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering only activation values and not the effect those activations have on downstream computations. This limits the information available to learn features, and biases the autoencoder towards neglecting features which are represented with small activation values but strongly influence model outputs. To address this, we introduce Gradient SAEs (g-SAEs), which modify the k-sparse autoencoder architecture by augmenting the TopK activation function to rely on the gradients of the input activation when selecting the k elements. For a given sparsity level, g-SAEs produce reconstructions that are more faithful to original network performance when propagated through the network. Additionally, we find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts. By considering the downstream effects of activations, our approach leverages the dual nature of neural network features as both representations, retrospectively, and actions, prospectively. While previous methods have approached the problem of feature discovery primarily focused on the former aspect, g-SAEs represent a step towards accounting for the latter as well.

Sparsity in the structure of Neural Networks can lead to less energy consumption, less memory usage, faster computation times on convenient hardware, and automated machine learning. If sparsity gives rise to certain kinds of structure, it can explain automatically obtained features during learning. We provide insights into experiments in which we show how sparsity can be achieved through prior initialization, pruning, and during learning, and answer questions on the relationship between the structure of Neural Networks and their performance. This includes the first work of inducing priors from network theory into Recurrent Neural Networks and an architectural performance prediction during a Neural Architecture Search. Within our experiments, we show how magnitude class blinded pruning achieves 97.5% on MNIST with 80% compression and re-training, which is 0.5 points more than without compression, that magnitude class uniform pruning is significantly inferior to it and how a genetic search enhanced with performance prediction achieves 82.4% on CIFAR10. Further, performance prediction for Recurrent Networks learning the Reber grammar shows an R^2 of up to 0.81 given only structural information.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is 1-sparse, and extending such bounds to the more general k-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the epsilon non-interactive LDP model and provide a lower bound of Omega(sqrt{dklog d}{nepsilon}) on the ell_2-norm estimation error for sub-Gaussian data, where n is the sample size and d is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of O({dsqrt{k}{nepsilon}}) for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of O(d) if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of Omega({sqrt{dk}{nepsilon}}). As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of O(ksqrt{d}{nepsilon}). Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

Optimal transport (OT) theory focuses, among all maps T:R^drightarrow R^d that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost c(x, T(x)) between x and its image T(x) be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when c is the ell_2^2 distance, e.g., using entropic maps [Pooladian'22], or neural networks [Makkuva'20, Korotin'20]. We propose a new model for transport maps, built on a family of translation invariant costs c(x, y):=h(x-y), where h:=1{2}|cdot|_2^2+tau and tau is a regularizer. We propose a generalization of the entropic map suitable for h, and highlight a surprising link tying it with the Bregman centroids of the divergence D_h generated by h, and the proximal operator of tau. We show that choosing a sparsity-inducing norm for tau results in maps that apply Occam's razor to transport, in the sense that the displacement vectors Delta(x):= T(x)-x they induce are sparse, with a sparsity pattern that varies depending on x. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data, in the 34000-d space of gene counts for cells, without using dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

Given the ever-increasing size of modern neural networks, the significance of sparse architectures has surged due to their accelerated inference speeds and minimal memory demands. When it comes to global pruning techniques, Iterative Magnitude Pruning (IMP) still stands as a state-of-the-art algorithm despite its simple nature, particularly in extremely sparse regimes. In light of the recent finding that the two successive matching IMP solutions are linearly connected without a loss barrier, we propose Sparse Weight Averaging with Multiple Particles (SWAMP), a straightforward modification of IMP that achieves performance comparable to an ensemble of two IMP solutions. For every iteration, we concurrently train multiple sparse models, referred to as particles, using different batch orders yet the same matching ticket, and then weight average such models to produce a single mask. We demonstrate that our method consistently outperforms existing baselines across different sparsities through extensive experiments on various data and neural network structures.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this work we propose a simple and efficient algorithm to learn basis functions. After training, this model also provides a fast and smooth approximator to the optimal representation, achieving even better accuracy than exact sparse coding algorithms on visual object recognition tasks.

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

Sparse dictionary learning has been a rapidly growing technique in mechanistic interpretability to attack superposition and extract more human-understandable features from model activations. We ask a further question based on the extracted more monosemantic features: How do we recognize circuits connecting the enormous amount of dictionary features? We propose a circuit discovery framework alternative to activation patching. Our framework suffers less from out-of-distribution and proves to be more efficient in terms of asymptotic complexity. The basic unit in our framework is dictionary features decomposed from all modules writing to the residual stream, including embedding, attention output and MLP output. Starting from any logit, dictionary feature or attention score, we manage to trace down to lower-level dictionary features of all tokens and compute their contribution to these more interpretable and local model behaviors. We dig in a small transformer trained on a synthetic task named Othello and find a number of human-understandable fine-grained circuits inside of it.

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

With growing size of Neural Networks (NNs), model sparsification to reduce the computational cost and memory demand for model inference has become of vital interest for both research and production. While many sparsification methods have been proposed and successfully applied on individual models, to the best of our knowledge their behavior and robustness has not yet been studied on large populations of models. With this paper, we address that gap by applying two popular sparsification methods on populations of models (so called model zoos) to create sparsified versions of the original zoos. We investigate the performance of these two methods for each zoo, compare sparsification layer-wise, and analyse agreement between original and sparsified populations. We find both methods to be very robust with magnitude pruning able outperform variational dropout with the exception of high sparsification ratios above 80%. Further, we find sparsified models agree to a high degree with their original non-sparsified counterpart, and that the performance of original and sparsified model is highly correlated. Finally, all models of the model zoos and their sparsified model twins are publicly available: modelzoos.cc.

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while still exploiting sparsity to generate a weighted graph with n nodes and m edges in O((n + m)log n) time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

We look at the eigenvalues of the Hessian of a loss function before and after training. The eigenvalue distribution is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. We present empirical evidence for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data.

The lottery ticket hypothesis has sparked the rapid development of pruning algorithms that aim to reduce the computational costs associated with deep learning during training and model deployment. Currently, such algorithms are primarily evaluated on imaging data, for which we lack ground truth information and thus the understanding of how sparse lottery tickets could be. To fill this gap, we develop a framework that allows us to plant and hide winning tickets with desirable properties in randomly initialized neural networks. To analyze the ability of state-of-the-art pruning to identify tickets of extreme sparsity, we design and hide such tickets solving four challenging tasks. In extensive experiments, we observe similar trends as in imaging studies, indicating that our framework can provide transferable insights into realistic problems. Additionally, we can now see beyond such relative trends and highlight limitations of current pruning methods. Based on our results, we conclude that the current limitations in ticket sparsity are likely of algorithmic rather than fundamental nature. We anticipate that comparisons to planted tickets will facilitate future developments of efficient pruning algorithms.

Sparse autoencoders (SAEs) have lately been used to uncover interpretable latent features in large language models. Here, we explore their potential for decomposing latent representations in complex and high-dimensional biological data, where the underlying variables are often unknown. On simulated data we show that generative hidden variables can be captured in learned representations in the form of superpositions. The degree to which they are learned depends on the completeness of the representations. Superpositions, however, are not identifiable if these generative variables are unknown. SAEs can to some extent recover these variables, yielding interpretable features. Applied to single-cell multi-omics data, we show that an SAE can uncover key biological processes such as carbon dioxide transport and ion homeostasis, which are crucial for red blood cell differentiation and immune function. Our findings highlight how SAEs can be used in advancing interpretability in biological and other scientific domains.

Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the compute per example. While scaling typically involves increasing both, the precise interplay between these factors and their combined contribution to overall capacity remains not fully understood. We explore this relationship in the context of sparse Mixture-of-Experts (MoEs), which allow scaling the number of parameters without proportionally increasing the FLOPs per example. We investigate how varying the sparsity level, i.e., the fraction of inactive parameters, impacts model's performance during pretraining and downstream few-shot evaluation. We find that under different constraints (e.g., parameter size and total training compute), there is an optimal level of sparsity that improves both training efficiency and model performance. These results provide a better understanding of the impact of sparsity in scaling laws for MoEs and complement existing works in this area, offering insights for designing more efficient architectures.

We show via a combination of mathematical arguments and empirical evidence that data distributions sampled from diffusion models satisfy a Concentration of Measure Property saying that any Lipschitz 1-dimensional projection of a random vector is not too far from its mean with high probability. This implies that such models are quite restrictive and gives an explanation for a fact previously observed in the literature that conventional diffusion models cannot capture "heavy-tailed" data (i.e. data x for which the norm |x|_2 does not possess a sub-Gaussian tail) well. We then proceed to train a generalized linear model using stochastic gradient descent (SGD) on the diffusion-generated data for a multiclass classification task and observe empirically that a Gaussian universality result holds for the test error. In other words, the test error depends only on the first and second order statistics of the diffusion-generated data in the linear setting. Results of such forms are desirable because they allow one to assume the data itself is Gaussian for analyzing performance of the trained classifier. Finally, we note that current approaches to proving universality do not apply to this case as the covariance matrices of the data tend to have vanishing minimum singular values for the diffusion-generated data, while the current proofs assume that this is not the case (see Subsection 3.4 for more details). This leaves extending previous mathematical universality results as an intriguing open question.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Sparse Autoencoders (SAEs) have emerged as a useful tool for interpreting the internal representations of neural networks. However, naively optimising SAEs for reconstruction loss and sparsity results in a preference for SAEs that are extremely wide and sparse. We present an information-theoretic framework for interpreting SAEs as lossy compression algorithms for communicating explanations of neural activations. We appeal to the Minimal Description Length (MDL) principle to motivate explanations of activations which are both accurate and concise. We further argue that interpretable SAEs require an additional property, "independent additivity": features should be able to be understood separately. We demonstrate an example of applying our MDL-inspired framework by training SAEs on MNIST handwritten digits and find that SAE features representing significant line segments are optimal, as opposed to SAEs with features for memorised digits from the dataset or small digit fragments. We argue that using MDL rather than sparsity may avoid potential pitfalls with naively maximising sparsity such as undesirable feature splitting and that this framework naturally suggests new hierarchical SAE architectures which provide more concise explanations.

Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and different kinds of penalties. To investigate the effectiveness of sparsity by itself, we propose the k-sparse autoencoder, which is an autoencoder with linear activation function, where in hidden layers only the k highest activities are kept. When applied to the MNIST and NORB datasets, we find that this method achieves better classification results than denoising autoencoders, networks trained with dropout, and RBMs. k-sparse autoencoders are simple to train and the encoding stage is very fast, making them well-suited to large problem sizes, where conventional sparse coding algorithms cannot be applied.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily focus on how to search feature interaction in a coarse-grained space, less attention has been given to a finer granularity. In this work, we introduce a hybrid-grained feature interaction selection approach that targets both feature field and feature value for deep sparse networks. To explore such expansive space, we propose a decomposed space which is calculated on the fly. We then develop a selection algorithm called OptFeature, which efficiently selects the feature interaction from both the feature field and the feature value simultaneously. Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

Structural neural network pruning aims to remove the redundant channels in the deep convolutional neural networks (CNNs) by pruning the filters of less importance to the final output accuracy. To reduce the degradation of performance after pruning, many methods utilize the loss with sparse regularization to produce structured sparsity. In this paper, we analyze these sparsity-training-based methods and find that the regularization of unpruned channels is unnecessary. Moreover, it restricts the network's capacity, which leads to under-fitting. To solve this problem, we propose a novel pruning method, named MaskSparsity, with pruning-aware sparse regularization. MaskSparsity imposes the fine-grained sparse regularization on the specific filters selected by a pruning mask, rather than all the filters of the model. Before the fine-grained sparse regularization of MaskSparity, we can use many methods to get the pruning mask, such as running the global sparse regularization. MaskSparsity achieves 63.03%-FLOPs reduction on ResNet-110 by removing 60.34% of the parameters, with no top-1 accuracy loss on CIFAR-10. On ILSVRC-2012, MaskSparsity reduces more than 51.07% FLOPs on ResNet-50, with only a loss of 0.76% in the top-1 accuracy. The code is released at https://github.com/CASIA-IVA-Lab/MaskSparsity. Moreover, we have integrated the code of MaskSparity into a PyTorch pruning toolkit, EasyPruner, at https://gitee.com/casia_iva_engineer/easypruner.

Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs). Due to the black-box property and various types of CAVs, how to test and evaluate CAVs adaptively remains a major challenge. Many approaches have been proposed to adaptively generate testing scenarios during the testing process. However, most existing approaches cannot be applied to complex scenarios, where the variables needed to define such scenarios are high dimensional. Towards filling this gap, the adaptive testing with sparse control variates method is proposed in this paper. Instead of adaptively generating testing scenarios, our approach evaluates CAVs' performances by adaptively utilizing the testing results. Specifically, each testing result is adjusted using multiple linear regression techniques based on control variates. As the regression coefficients can be adaptively optimized for the CAV under test, using the adjusted results can reduce the estimation variance, compared with using the testing results directly. To overcome the high dimensionality challenge, sparse control variates are utilized only for the critical variables of testing scenarios. To validate the proposed method, the high-dimensional overtaking scenarios are investigated, and the results demonstrate that our approach can further accelerate the evaluation process by about 30 times.

Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples will have arbitrarily small errors in sampling from any continuous target distribution. We set up a unifying framework that debunks this belief. We demonstrate that broad classes of deep generative models, including variational autoencoders and generative adversarial networks, are not universal generators. Under the predominant case of Gaussian latent variables, these models can only generate concentrated samples that exhibit light tails. Using tools from concentration of measure and convex geometry, we give analogous results for more general log-concave and strongly log-concave latent variable distributions. We extend our results to diffusion models via a reduction argument. We use the Gromov--Levy inequality to give similar guarantees when the latent variables lie on manifolds with positive Ricci curvature. These results shed light on the limited capacity of common deep generative models to handle heavy tails. We illustrate the empirical relevance of our work with simulations and financial data.

Sparse Autoencoders (SAEs) have been proposed as an unsupervised approach to learn a decomposition of a model's latent space. This enables useful applications such as steering - influencing the output of a model towards a desired concept - without requiring labeled data. Current methods identify SAE features to steer by analyzing the input tokens that activate them. However, recent work has highlighted that activations alone do not fully describe the effect of a feature on the model's output. In this work, we draw a distinction between two types of features: input features, which mainly capture patterns in the model's input, and output features, which have a human-understandable effect on the model's output. We propose input and output scores to characterize and locate these types of features, and show that high values for both scores rarely co-occur in the same features. These findings have practical implications: after filtering out features with low output scores, we obtain 2-3x improvements when steering with SAEs, making them competitive with supervised methods.

Diffusion models have shown impressive results in generating high-quality conditional samples using guidance techniques such as Classifier-Free Guidance (CFG). However, existing methods often require additional training or neural function evaluations (NFEs), making them incompatible with guidance-distilled models. Also, they rely on heuristic approaches that need identifying target layers. In this work, we propose a novel and efficient method, termed PLADIS, which boosts pre-trained models (U-Net/Transformer) by leveraging sparse attention. Specifically, we extrapolate query-key correlations using softmax and its sparse counterpart in the cross-attention layer during inference, without requiring extra training or NFEs. By leveraging the noise robustness of sparse attention, our PLADIS unleashes the latent potential of text-to-image diffusion models, enabling them to excel in areas where they once struggled with newfound effectiveness. It integrates seamlessly with guidance techniques, including guidance-distilled models. Extensive experiments show notable improvements in text alignment and human preference, offering a highly efficient and universally applicable solution.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to use maximum likelihood principle to optimize the model. However, softmax leaves a large margin for loss function to conduct optimizing operation when it comes to high-dimensional classification, which results in low-performance to some extent. In this paper, we provide an empirical study on a simple and concise softmax variant, namely sparse-softmax, to alleviate the problem that occurred in traditional softmax in terms of high-dimensional classification problems. We evaluate our approach in several interdisciplinary tasks, the experimental results show that sparse-softmax is simpler, faster, and produces better results than the baseline models.

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting neural networks by extracting the concepts represented in their activations. However, choosing the size of the SAE dictionary (i.e. number of learned concepts) creates a tension: as dictionary size increases to capture more relevant concepts, sparsity incentivizes features to be split or absorbed into more specific features, leaving high-level features missing or warped. We introduce Matryoshka SAEs, a novel variant that addresses these issues by simultaneously training multiple nested dictionaries of increasing size, forcing the smaller dictionaries to independently reconstruct the inputs without using the larger dictionaries. This organizes features hierarchically - the smaller dictionaries learn general concepts, while the larger dictionaries learn more specific concepts, without incentive to absorb the high-level features. We train Matryoshka SAEs on Gemma-2-2B and TinyStories and find superior performance on sparse probing and targeted concept erasure tasks, more disentangled concept representations, and reduced feature absorption. While there is a minor tradeoff with reconstruction performance, we believe Matryoshka SAEs are a superior alternative for practical tasks, as they enable training arbitrarily large SAEs while retaining interpretable features at different levels of abstraction.

Recent works have successfully demonstrated that sparse deep reinforcement learning agents can be competitive against their dense counterparts. This opens up opportunities for reinforcement learning applications in fields where inference time and memory requirements are cost-sensitive or limited by hardware. Until now, dense-to-sparse methods have relied on hand-designed sparsity schedules that are not synchronized with the agent's learning pace. Crucially, the final sparsity level is chosen as a hyperparameter, which requires careful tuning as setting it too high might lead to poor performances. In this work, we address these shortcomings by crafting a dense-to-sparse algorithm that we name Eau De Q-Network (EauDeQN). To increase sparsity at the agent's learning pace, we consider multiple online networks with different sparsity levels, where each online network is trained from a shared target network. At each target update, the online network with the smallest loss is chosen as the next target network, while the other networks are replaced by a pruned version of the chosen network. We evaluate the proposed approach on the Atari 2600 benchmark and the MuJoCo physics simulator, showing that EauDeQN reaches high sparsity levels while keeping performances high.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

We present Sparse R-CNN, a purely sparse method for object detection in images. Existing works on object detection heavily rely on dense object candidates, such as k anchor boxes pre-defined on all grids of image feature map of size Htimes W. In our method, however, a fixed sparse set of learned object proposals, total length of N, are provided to object recognition head to perform classification and location. By eliminating HWk (up to hundreds of thousands) hand-designed object candidates to N (e.g. 100) learnable proposals, Sparse R-CNN completely avoids all efforts related to object candidates design and many-to-one label assignment. More importantly, final predictions are directly output without non-maximum suppression post-procedure. Sparse R-CNN demonstrates accuracy, run-time and training convergence performance on par with the well-established detector baselines on the challenging COCO dataset, e.g., achieving 45.0 AP in standard 3times training schedule and running at 22 fps using ResNet-50 FPN model. We hope our work could inspire re-thinking the convention of dense prior in object detectors. The code is available at: https://github.com/PeizeSun/SparseR-CNN.

In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which lightens large pre-trained models by removing unimportant parameters, we propose a novel model fine-tuning method to make full use of these ineffective parameters and enable the pre-trained model with new task-specified capabilities. In this work, we first investigate the importance of parameters in pre-trained diffusion models, and discover that the smallest 10% to 20% of parameters by absolute values do not contribute to the generation process. Based on this observation, we propose a method termed SaRA that re-utilizes these temporarily ineffective parameters, equating to optimizing a sparse weight matrix to learn the task-specific knowledge. To mitigate overfitting, we propose a nuclear-norm-based low-rank sparse training scheme for efficient fine-tuning. Furthermore, we design a new progressive parameter adjustment strategy to make full use of the re-trained/finetuned parameters. Finally, we propose a novel unstructural backpropagation strategy, which significantly reduces memory costs during fine-tuning. Our method enhances the generative capabilities of pre-trained models in downstream applications and outperforms traditional fine-tuning methods like LoRA in maintaining model's generalization ability. We validate our approach through fine-tuning experiments on SD models, demonstrating significant improvements. SaRA also offers a practical advantage that requires only a single line of code modification for efficient implementation and is seamlessly compatible with existing methods.

Model compression has emerged as a mainstream solution to reduce memory usage and computational overhead. This paper presents Group Quantization and Sparse Acceleration (GQSA), a novel compression technique tailored for LLMs. Traditional methods typically focus exclusively on either quantization or sparsification, but relying on a single strategy often results in significant performance loss at high compression rates. In contrast, GQSA integrates quantization and sparsification in a tightly coupled manner, leveraging GPU-friendly structured group sparsity and quantization for efficient acceleration. Building upon system-algorithm co-design principles, we propose a two-stage sparse optimization strategy that ensures the performance superiority of the compressed model. On the engine side, we introduce a "task-centric" parallel strategy, which, to the best of our knowledge, is the first application in the domain of sparse computing. Compared to the traditional 2:4 sparse method, the GQSA offers a more flexible and adjustable sparsity rate, as well as a higher weight compression rate, and is efficiently compatible with weight-only quantization methods. Experimental results demonstrate that, under the GQSA W4S50% compression setting, the model's accuracy surpasses that of both 2:4 pruning and W2 quantization. Furthermore, at the inference level, GQSA outperforms W2 by 1.26times and 2:4 pruning by 2.35times in terms of speed.

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive embedding lengths, but it requires full model retraining and suffers from noticeable performance degradations at short lengths. In this paper, we show that sparse coding offers a compelling alternative for achieving adaptive representation with minimal overhead and higher fidelity. We propose Contrastive Sparse Representation (CSR), a method that sparsifies pre-trained embeddings into a high-dimensional but selectively activated feature space. By leveraging lightweight autoencoding and task-aware contrastive objectives, CSR preserves semantic quality while allowing flexible, cost-effective inference at different sparsity levels. Extensive experiments on image, text, and multimodal benchmarks demonstrate that CSR consistently outperforms MRL in terms of both accuracy and retrieval speed-often by large margins-while also cutting training time to a fraction of that required by MRL. Our results establish sparse coding as a powerful paradigm for adaptive representation learning in real-world applications where efficiency and fidelity are both paramount. Code is available at https://github.com/neilwen987/CSR_Adaptive_Rep

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

Sparse computation offers a compelling solution for the inference of Large Language Models (LLMs) in low-resource scenarios by dynamically skipping the computation of inactive neurons. While traditional approaches focus on ReLU-based LLMs, leveraging zeros in activation values, we broaden the scope of sparse LLMs beyond zero activation values. We introduce a general method that defines neuron activation through neuron output magnitudes and a tailored magnitude threshold, demonstrating that non-ReLU LLMs also exhibit sparse activation. To find the most efficient activation function for sparse computation, we propose a systematic framework to examine the sparsity of LLMs from three aspects: the trade-off between sparsity and performance, the predictivity of sparsity, and the hardware affinity. We conduct thorough experiments on LLMs utilizing different activation functions, including ReLU, SwiGLU, ReGLU, and ReLU^2. The results indicate that models employing ReLU^2 excel across all three evaluation aspects, highlighting its potential as an efficient activation function for sparse LLMs. We will release the code to facilitate future research.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling that solves an eOT problem. It is a relevant problem that can be used to infer unobserved/missing links, and to obtain meaningful information about the structure of the ground cost yielding the pairing. On one side, iOT benefits from convexity, but on the other side, being ill-posed, it requires regularization to handle the sampling noise. This work presents an in-depth theoretical study of the l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a far reaching generalization of the Lasso's celebrated Irrepresentability Condition. To provide additional insight into this condition, we work out in detail the Gaussian case. We show that as the entropic penalty varies, the iOT problem interpolates between a graphical Lasso and a classical Lasso, thereby establishing a connection between iOT and graph estimation, an important problem in ML.

Safety performance evaluation is critical for developing and deploying connected and automated vehicles (CAVs). One prevailing way is to design testing scenarios using prior knowledge of CAVs, test CAVs in these scenarios, and then evaluate their safety performances. However, significant differences between CAVs and prior knowledge could severely reduce the evaluation efficiency. Towards addressing this issue, most existing studies focus on the adaptive design of testing scenarios during the CAV testing process, but so far they cannot be applied to high-dimensional scenarios. In this paper, we focus on the adaptive safety performance evaluation by leveraging the testing results, after the CAV testing process. It can significantly improve the evaluation efficiency and be applied to high-dimensional scenarios. Specifically, instead of directly evaluating the unknown quantity (e.g., crash rates) of CAV safety performances, we evaluate the differences between the unknown quantity and known quantity (i.e., control variates). By leveraging the testing results, the control variates could be well designed and optimized such that the differences are close to zero, so the evaluation variance could be dramatically reduced for different CAVs. To handle the high-dimensional scenarios, we propose the sparse control variates method, where the control variates are designed only for the sparse and critical variables of scenarios. According to the number of critical variables in each scenario, the control variates are stratified into strata and optimized within each stratum using multiple linear regression techniques. We justify the proposed method's effectiveness by rigorous theoretical analysis and empirical study of high-dimensional overtaking scenarios.

Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and discuss the resulting conceptual insights. Surprisingly, this simple model achieves better ranking accuracy than various state-of-the-art collaborative-filtering approaches, including deep non-linear models, on most of the publicly available data-sets used in our experiments.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Sparse autoencoders (SAEs) are an unsupervised method for learning a sparse decomposition of a neural network's latent representations into seemingly interpretable features. Despite recent excitement about their potential, research applications outside of industry are limited by the high cost of training a comprehensive suite of SAEs. In this work, we introduce Gemma Scope, an open suite of JumpReLU SAEs trained on all layers and sub-layers of Gemma 2 2B and 9B and select layers of Gemma 2 27B base models. We primarily train SAEs on the Gemma 2 pre-trained models, but additionally release SAEs trained on instruction-tuned Gemma 2 9B for comparison. We evaluate the quality of each SAE on standard metrics and release these results. We hope that by releasing these SAE weights, we can help make more ambitious safety and interpretability research easier for the community. Weights and a tutorial can be found at https://huggingface.co/google/gemma-scope and an interactive demo can be found at https://www.neuronpedia.org/gemma-scope

An efficient attention implementation is essential for large models due to its quadratic time complexity. Fortunately, attention commonly exhibits sparsity, i.e., many values in the attention map are near zero, allowing for the omission of corresponding computations. Many studies have utilized the sparse pattern to accelerate attention. However, most existing works focus on optimizing attention within specific models by exploiting certain sparse patterns of the attention map. A universal sparse attention that guarantees both the speedup and end-to-end performance of diverse models remains elusive. In this paper, we propose SpargeAttn, a universal sparse and quantized attention for any model. Our method uses a two-stage online filter: in the first stage, we rapidly and accurately predict the attention map, enabling the skip of some matrix multiplications in attention. In the second stage, we design an online softmax-aware filter that incurs no extra overhead and further skips some matrix multiplications. Experiments show that our method significantly accelerates diverse models, including language, image, and video generation, without sacrificing end-to-end metrics. The codes are available at https://github.com/thu-ml/SpargeAttn.

We introduce Nerva, a fast neural network library under development in C++. It supports sparsity by using the sparse matrix operations of Intel's Math Kernel Library (MKL), which eliminates the need for binary masks. We show that Nerva significantly decreases training time and memory usage while reaching equivalent accuracy to PyTorch. We run static sparse experiments with an MLP on CIFAR-10. On high sparsity levels like 99%, the runtime is reduced by a factor of 4times compared to a PyTorch model using masks. Similar to other popular frameworks such as PyTorch and Keras, Nerva offers a Python interface for users to work with.

Non-uniformed 3D sparse data, e.g., point clouds or voxels in different spatial positions, make contribution to the task of 3D object detection in different ways. Existing basic components in sparse convolutional networks (Sparse CNNs) process all sparse data, regardless of regular or submanifold sparse convolution. In this paper, we introduce two new modules to enhance the capability of Sparse CNNs, both are based on making feature sparsity learnable with position-wise importance prediction. They are focal sparse convolution (Focals Conv) and its multi-modal variant of focal sparse convolution with fusion, or Focals Conv-F for short. The new modules can readily substitute their plain counterparts in existing Sparse CNNs and be jointly trained in an end-to-end fashion. For the first time, we show that spatially learnable sparsity in sparse convolution is essential for sophisticated 3D object detection. Extensive experiments on the KITTI, nuScenes and Waymo benchmarks validate the effectiveness of our approach. Without bells and whistles, our results outperform all existing single-model entries on the nuScenes test benchmark at the paper submission time. Code and models are at https://github.com/dvlab-research/FocalsConv.

Sparse autoencoders provide a promising unsupervised approach for extracting interpretable features from a language model by reconstructing activations from a sparse bottleneck layer. Since language models learn many concepts, autoencoders need to be very large to recover all relevant features. However, studying the properties of autoencoder scaling is difficult due to the need to balance reconstruction and sparsity objectives and the presence of dead latents. We propose using k-sparse autoencoders [Makhzani and Frey, 2013] to directly control sparsity, simplifying tuning and improving the reconstruction-sparsity frontier. Additionally, we find modifications that result in few dead latents, even at the largest scales we tried. Using these techniques, we find clean scaling laws with respect to autoencoder size and sparsity. We also introduce several new metrics for evaluating feature quality based on the recovery of hypothesized features, the explainability of activation patterns, and the sparsity of downstream effects. These metrics all generally improve with autoencoder size. To demonstrate the scalability of our approach, we train a 16 million latent autoencoder on GPT-4 activations for 40 billion tokens. We release training code and autoencoders for open-source models, as well as a visualizer.

Network pruning is an effective approach to reduce network complexity with acceptable performance compromise. Existing studies achieve the sparsity of neural networks via time-consuming weight training or complex searching on networks with expanded width, which greatly limits the applications of network pruning. In this paper, we show that high-performing and sparse sub-networks without the involvement of weight training, termed "lottery jackpots", exist in pre-trained models with unexpanded width. Furthermore, we improve the efficiency for searching lottery jackpots from two perspectives. Firstly, we observe that the sparse masks derived from many existing pruning criteria have a high overlap with the searched mask of our lottery jackpot, among which, the magnitude-based pruning results in the most similar mask with ours. Consequently, our searched lottery jackpot removes 90% weights in ResNet-50, while it easily obtains more than 70% top-1 accuracy using only 5 searching epochs on ImageNet. In compliance with this insight, we initialize our sparse mask using the magnitude-based pruning, resulting in at least 3x cost reduction on the lottery jackpot searching while achieving comparable or even better performance. Secondly, we conduct an in-depth analysis of the searching process for lottery jackpots. Our theoretical result suggests that the decrease in training loss during weight searching can be disturbed by the dependency between weights in modern networks. To mitigate this, we propose a novel short restriction method to restrict change of masks that may have potential negative impacts on the training loss. Our code is available at https://github.com/zyxxmu/lottery-jackpots.

The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these tickets can be practically reused across a variety of tasks, hinting at some form of universality. We formalize this concept and theoretically prove that not only do such universal tickets exist but they also do not require further training. Our proofs introduce a couple of technical innovations related to pruning for strong lottery tickets, including extensions of subset sum results and a strategy to leverage higher amounts of depth. Our explicit sparse constructions of universal function families might be of independent interest, as they highlight representational benefits induced by univariate convolutional architectures.

Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.

We present a simple approach which can turn a ViT encoder into an efficient video model, which can seamlessly work with both image and video inputs. By sparsely sampling the inputs, the model is able to do training and inference from both inputs. The model is easily scalable and can be adapted to large-scale pre-trained ViTs without requiring full finetuning. The model achieves SOTA results and the code will be open-sourced.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Major complications arise from the recent increase in the amount of high-dimensional data, including high computational costs and memory requirements. Feature selection, which identifies the most relevant and informative attributes of a dataset, has been introduced as a solution to this problem. Most of the existing feature selection methods are computationally inefficient; inefficient algorithms lead to high energy consumption, which is not desirable for devices with limited computational and energy resources. In this paper, a novel and flexible method for unsupervised feature selection is proposed. This method, named QuickSelection, introduces the strength of the neuron in sparse neural networks as a criterion to measure the feature importance. This criterion, blended with sparsely connected denoising autoencoders trained with the sparse evolutionary training procedure, derives the importance of all input features simultaneously. We implement QuickSelection in a purely sparse manner as opposed to the typical approach of using a binary mask over connections to simulate sparsity. It results in a considerable speed increase and memory reduction. When tested on several benchmark datasets, including five low-dimensional and three high-dimensional datasets, the proposed method is able to achieve the best trade-off of classification and clustering accuracy, running time, and maximum memory usage, among widely used approaches for feature selection. Besides, our proposed method requires the least amount of energy among the state-of-the-art autoencoder-based feature selection methods.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

In this paper, we derive a novel bound on the generalization error of Magnitude-Based pruning of overparameterized neural networks. Our work builds on the bounds in Arora et al. [2018] where the error depends on one, the approximation induced by pruning, and two, the number of parameters in the pruned model, and improves upon standard norm-based generalization bounds. The pruned estimates obtained using our new Magnitude-Based compression algorithm are close to the unpruned functions with high probability, which improves the first criteria. Using Sparse Matrix Sketching, the space of the pruned matrices can be efficiently represented in the space of dense matrices of much smaller dimensions, thereby lowering the second criterion. This leads to stronger generalization bound than many state-of-the-art methods, thereby breaking new ground in the algorithm development for pruning and bounding generalization error of overparameterized models. Beyond this, we extend our results to obtain generalization bound for Iterative Pruning [Frankle and Carbin, 2018]. We empirically verify the success of this new method on ReLU-activated Feed Forward Networks on the MNIST and CIFAR10 datasets.

Continual learning (CL) refers to the ability of an intelligent system to sequentially acquire and retain knowledge from a stream of data with as little computational overhead as possible. To this end; regularization, replay, architecture, and parameter isolation approaches were introduced to the literature. Parameter isolation using a sparse network which enables to allocate distinct parts of the neural network to different tasks and also allows to share of parameters between tasks if they are similar. Dynamic Sparse Training (DST) is a prominent way to find these sparse networks and isolate them for each task. This paper is the first empirical study investigating the effect of different DST components under the CL paradigm to fill a critical research gap and shed light on the optimal configuration of DST for CL if it exists. Therefore, we perform a comprehensive study in which we investigate various DST components to find the best topology per task on well-known CIFAR100 and miniImageNet benchmarks in a task-incremental CL setup since our primary focus is to evaluate the performance of various DST criteria, rather than the process of mask selection. We found that, at a low sparsity level, Erdos-Renyi Kernel (ERK) initialization utilizes the backbone more efficiently and allows to effectively learn increments of tasks. At a high sparsity level, however, uniform initialization demonstrates more reliable and robust performance. In terms of growth strategy; performance is dependent on the defined initialization strategy, and the extent of sparsity. Finally, adaptivity within DST components is a promising way for better continual learners.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely many steps under a (preconditioned) restricted isometry condition. In this paper, we present a new perspective to analyze the algorithm, which turns out that the efficiency of the algorithm can be further elaborated by an estimate of the number of iterations for the guaranteed convergence. The convergence condition of NST+HT+FB is also improved. Moreover, an adaptive scheme (AdptNST+HT+FB) without the knowledge of the sparsity level is proposed with its convergence guarantee. The number of iterations for the finite step of convergence of the AdptNST+HT+FB scheme is also derived. It is further shown that the number of iterations can be significantly reduced by exploiting the structure of the specific sparse signal or the random measurement matrix.

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

Since the pioneering work on the lottery ticket hypothesis for graph neural networks (GNNs) was proposed in Chen et al. (2021), the study on finding graph lottery tickets (GLT) has become one of the pivotal focus in the GNN community, inspiring researchers to discover sparser GLT while achieving comparable performance to original dense networks. In parallel, the graph structure has gained substantial attention as a crucial factor in GNN training dynamics, also elucidated by several recent studies. Despite this, contemporary studies on GLT, in general, have not fully exploited inherent pathways in the graph structure and identified tickets in an iterative manner, which is time-consuming and inefficient. To address these limitations, we introduce TEDDY, a one-shot edge sparsification framework that leverages structural information by incorporating edge-degree information. Following edge sparsification, we encourage the parameter sparsity during training via simple projected gradient descent on the ell_0 ball. Given the target sparsity levels for both the graph structure and the model parameters, our TEDDY facilitates efficient and rapid realization of GLT within a single training. Remarkably, our experimental results demonstrate that TEDDY significantly surpasses conventional iterative approaches in generalization, even when conducting one-shot sparsification that solely utilizes graph structures, without taking feature information into account.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

In the era of foundation models with huge pre-training budgets, the downstream tasks have been shifted to the narrative of efficient and fast adaptation. For classification-based tasks in the domain of computer vision, the two most efficient approaches have been linear probing (LP) and visual prompting/reprogramming (VP); the former aims to learn a classifier in the form of a linear head on the features extracted by the pre-trained model, while the latter maps the input data to the domain of the source data on which the model was originally pre-trained on. Although extensive studies have demonstrated the differences between LP and VP in terms of downstream performance, we explore the capabilities of the two aforementioned methods via the sparsity axis: (a) Data sparsity: the impact of few-shot adaptation and (b) Model sparsity: the impact of lottery tickets (LT). We demonstrate that LT are not universal reprogrammers, i.e., for certain target datasets, reprogramming an LT yields significantly lower performance than the reprogrammed dense model although their corresponding upstream performance is similar. Further, we demonstrate that the calibration of dense models is always superior to that of their lottery ticket counterparts under both LP and VP regimes. Our empirical study opens a new avenue of research into VP for sparse models and encourages further understanding of the performance beyond the accuracy achieved by VP under constraints of sparsity. Code and logs can be accessed at https://github.com/landskape-ai/Reprogram_LT.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

When the performance of a machine learning model varies over groups defined by sensitive attributes (e.g., gender or ethnicity), the performance disparity can be expressed in terms of the probability distributions of the input and output variables over each group. In this paper, we exploit this fact to reduce the disparate impact of a fixed classification model over a population of interest. Given a black-box classifier, we aim to eliminate the performance gap by perturbing the distribution of input variables for the disadvantaged group. We refer to the perturbed distribution as a counterfactual distribution, and characterize its properties for common fairness criteria. We introduce a descent algorithm to learn a counterfactual distribution from data. We then discuss how the estimated distribution can be used to build a data preprocessor that can reduce disparate impact without training a new model. We validate our approach through experiments on real-world datasets, showing that it can repair different forms of disparity without a significant drop in accuracy.

In neural Information Retrieval, ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. In this work, we present a new first-stage ranker based on explicit sparsity regularization and a log-saturation effect on term weights, leading to highly sparse representations and competitive results with respect to state-of-the-art dense and sparse methods. Our approach is simple, trained end-to-end in a single stage. We also explore the trade-off between effectiveness and efficiency, by controlling the contribution of the sparsity regularization.

With the latest advances in deep learning, there has been a lot of focus on the online learning paradigm due to its relevance in practical settings. Although many methods have been investigated for optimal learning settings in scenarios where the data stream is continuous over time, sparse networks training in such settings have often been overlooked. In this paper, we explore the problem of training a neural network with a target sparsity in a particular case of online learning: the anytime learning at macroscale paradigm (ALMA). We propose a novel way of progressive pruning, referred to as Anytime Progressive Pruning (APP); the proposed approach significantly outperforms the baseline dense and Anytime OSP models across multiple architectures and datasets under short, moderate, and long-sequence training. Our method, for example, shows an improvement in accuracy of approx 7% and a reduction in the generalization gap by approx 22%, while being approx 1/3 rd the size of the dense baseline model in few-shot restricted imagenet training. We further observe interesting nonmonotonic transitions in the generalization gap in the high number of megabatches-based ALMA. The code and experiment dashboards can be accessed at https://github.com/landskape-ai/Progressive-Pruning and https://wandb.ai/landskape/APP, respectively.