Daily Papers

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.

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.

Recent research has demonstrated that Feed-Forward Networks (FFNs) in Large Language Models (LLMs) play a pivotal role in storing diverse linguistic and factual knowledge. Conventional methods frequently face challenges due to knowledge confusion stemming from their monolithic and redundant architectures, which calls for more efficient solutions with minimal computational overhead, particularly for LLMs. In this paper, we explore the FFN computation paradigm in LLMs and introduce FactorLLM, a novel approach that decomposes well-trained dense FFNs into sparse sub-networks without requiring any further modifications, while maintaining the same level of performance. Furthermore, we embed a router from the Mixture-of-Experts (MoE), combined with our devised Prior-Approximate (PA) loss term that facilitates the dynamic activation of experts and knowledge adaptation, thereby accelerating computational processes and enhancing performance using minimal training data and fine-tuning steps. FactorLLM thus enables efficient knowledge factorization and activates select groups of experts specifically tailored to designated tasks, emulating the interactive functional segmentation of the human brain. Extensive experiments across various benchmarks demonstrate the effectiveness of our proposed FactorLLM which achieves comparable performance to the source model securing up to 85% model performance while obtaining over a 30% increase in inference speed. Code: https://github.com/zhenwuweihe/FactorLLM.

Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can improve storage, compute, memory bandwidth, and energy usage. In this paper we propose a novel accurate pruning technique that allows precise control over the output network size. Our method uses an efficient optimal transportation scheme which we make end-to-end differentiable and which automatically tunes the exploration-exploitation behavior of the algorithm to find accurate sparse sub-networks. We show that our method achieves state-of-the-art performance compared to previous pruning methods on 3 different datasets, using 5 different models, across a wide range of pruning ratios, and with two types of sparsity budgets and pruning granularities.

The limited and dynamically varied resources on edge devices motivate us to deploy an optimized deep neural network that can adapt its sub-networks to fit in different resource constraints. However, existing works often build sub-networks through searching different network architectures in a hand-crafted sampling space, which not only can result in a subpar performance but also may cause on-device re-configuration overhead. In this paper, we propose a novel training algorithm, Dynamic REal-time Sparse Subnets (DRESS). DRESS samples multiple sub-networks from the same backbone network through row-based unstructured sparsity, and jointly trains these sub-networks in parallel with weighted loss. DRESS also exploits strategies including parameter reusing and row-based fine-grained sampling for efficient storage consumption and efficient on-device adaptation. Extensive experiments on public vision datasets show that DRESS yields significantly higher accuracy than state-of-the-art sub-networks.

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).

Sparse Mixture-of-Experts (MoE) has been a successful approach for scaling multilingual translation models to billions of parameters without a proportional increase in training computation. However, MoE models are prohibitively large and practitioners often resort to methods such as distillation for serving. In this work, we investigate routing strategies at different granularity (token, sentence, task) in MoE models to bypass distillation. Experiments on WMT and a web-scale dataset suggest that task-level routing (task-MoE) enables us to extract smaller, ready-to-deploy sub-networks from large sparse models. On WMT, our task-MoE with 32 experts (533M parameters) outperforms the best performing token-level MoE model (token-MoE) by +1.0 BLEU on average across 30 language pairs. The peak inference throughput is also improved by a factor of 1.9x when we route by tasks instead of tokens. While distilling a token-MoE to a smaller dense model preserves only 32% of the BLEU gains, our sub-network task-MoE, by design, preserves all the gains with the same inference cost as the distilled student model. Finally, when scaling up to 200 language pairs, our 128-expert task-MoE (13B parameters) performs competitively with a token-level counterpart, while improving the peak inference throughput by a factor of 2.6x.

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.

Spiking neural networks (SNNs) have shown their competence in handling spatial-temporal event-based data with low energy consumption. Similar to conventional artificial neural networks (ANNs), SNNs are also vulnerable to gradient-based adversarial attacks, wherein gradients are calculated by spatial-temporal back-propagation (STBP) and surrogate gradients (SGs). However, the SGs may be invisible for an inference-only model as they do not influence the inference results, and current gradient-based attacks are ineffective for binary dynamic images captured by the dynamic vision sensor (DVS). While some approaches addressed the issue of invisible SGs through universal SGs, their SGs lack a correlation with the victim model, resulting in sub-optimal performance. Moreover, the imperceptibility of existing SNN-based binary attacks is still insufficient. In this paper, we introduce an innovative potential-dependent surrogate gradient (PDSG) method to establish a robust connection between the SG and the model, thereby enhancing the adaptability of adversarial attacks across various models with invisible SGs. Additionally, we propose the sparse dynamic attack (SDA) to effectively attack binary dynamic images. Utilizing a generation-reduction paradigm, SDA can fully optimize the sparsity of adversarial perturbations. Experimental results demonstrate that our PDSG and SDA outperform state-of-the-art SNN-based attacks across various models and datasets. Specifically, our PDSG achieves 100% attack success rate on ImageNet, and our SDA obtains 82% attack success rate by modifying only 0.24% of the pixels on CIFAR10DVS. The code is available at https://github.com/ryime/PDSG-SDA .

Linear State Space Models (SSMs) have demonstrated strong performance in a variety of sequence modeling tasks due to their efficient encoding of the recurrent structure. However, in more comprehensive tasks like language modeling and machine translation, self-attention-based models still outperform SSMs. Hybrid models employing both SSM and self-attention generally show promising performance, but current approaches apply attention modules statically and uniformly to all elements in the input sequences, leading to sub-optimal quality-efficiency trade-offs. In this work, we introduce Sparse Modular Activation (SMA), a general mechanism enabling neural networks to sparsely and dynamically activate sub-modules for sequence elements in a differentiable manner. Through allowing each element to skip non-activated sub-modules, SMA reduces computation and memory consumption at both training and inference stages of sequence modeling. As a specific instantiation of SMA, we design a novel neural architecture, SeqBoat, which employs SMA to sparsely activate a Gated Attention Unit (GAU) based on the state representations learned from an SSM. By constraining the GAU to only conduct local attention on the activated inputs, SeqBoat can achieve linear inference complexity with theoretically infinite attention span, and provide substantially better quality-efficiency trade-off than the chunking-based models. With experiments on a wide range of tasks, including language modeling, speech classification and long-range arena, SeqBoat brings new state-of-the-art results among hybrid models with linear complexity and reveals the amount of attention needed for each task through the learned sparse activation patterns.

How to train a generalizable meta-policy by continually learning a sequence of tasks? It is a natural human skill yet challenging to achieve by current reinforcement learning: the agent is expected to quickly adapt to new tasks (plasticity) meanwhile retaining the common knowledge from previous tasks (stability). We address it by "Continual Task Allocation via Sparse Prompting (CoTASP)", which learns over-complete dictionaries to produce sparse masks as prompts extracting a sub-network for each task from a meta-policy network. CoTASP trains a policy for each task by optimizing the prompts and the sub-network weights alternatively. The dictionary is then updated to align the optimized prompts with tasks' embedding, thereby capturing tasks' semantic correlations. Hence, relevant tasks share more neurons in the meta-policy network due to similar prompts while cross-task interference causing forgetting is effectively restrained. Given a meta-policy and dictionaries trained on previous tasks, new task adaptation reduces to highly efficient sparse prompting and sub-network finetuning. In experiments, CoTASP achieves a promising plasticity-stability trade-off without storing or replaying any past tasks' experiences. It outperforms existing continual and multi-task RL methods on all seen tasks, forgetting reduction, and generalization to unseen tasks.

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.

Structured pruning is one of the most popular approaches to effectively compress the heavy deep neural networks (DNNs) into compact sub-networks while retaining performance. The existing methods suffer from multi-stage procedures along with significant engineering efforts and human expertise. The Only-Train-Once (OTO) series has been recently proposed to resolve the many pain points by streamlining the workflow by automatically conducting (i) search space generation, (ii) structured sparse optimization, and (iii) sub-network construction. However, the built-in sparse optimizers in the OTO series, i.e., the Half-Space Projected Gradient (HSPG) family, have limitations that require hyper-parameter tuning and the implicit controls of the sparsity exploration, consequently requires intervening by human expertise. To address such limitations, we propose a Hybrid Efficient Structured Sparse Optimizer (HESSO). HESSO could automatically and efficiently train a DNN to produce a high-performing subnetwork. Meanwhile, it is almost tuning-free and enjoys user-friendly integration for generic training applications. To address another common issue of irreversible performance collapse observed in pruning DNNs, we further propose a Corrective Redundant Identification Cycle (CRIC) for reliably identifying indispensable structures. We numerically demonstrate the efficacy of HESSO and its enhanced version HESSO-CRIC on a variety of applications ranging from computer vision to natural language processing, including large language model. The numerical results showcase that HESSO can achieve competitive even superior performance to varying state-of-the-arts and support most DNN architectures. Meanwhile, CRIC can effectively prevent the irreversible performance collapse and further enhance the performance of HESSO on certain applications. The code is available at https://github.com/microsoft/only_train_once.

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.

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 develop an approach to growing deep network architectures over the course of training, driven by a principled combination of accuracy and sparsity objectives. Unlike existing pruning or architecture search techniques that operate on full-sized models or supernet architectures, our method can start from a small, simple seed architecture and dynamically grow and prune both layers and filters. By combining a continuous relaxation of discrete network structure optimization with a scheme for sampling sparse subnetworks, we produce compact, pruned networks, while also drastically reducing the computational expense of training. For example, we achieve 49.7% inference FLOPs and 47.4% training FLOPs savings compared to a baseline ResNet-50 on ImageNet, while maintaining 75.2% top-1 accuracy -- all without any dedicated fine-tuning stage. Experiments across CIFAR, ImageNet, PASCAL VOC, and Penn Treebank, with convolutional networks for image classification and semantic segmentation, and recurrent networks for language modeling, demonstrate that we both train faster and produce more efficient networks than competing architecture pruning or search methods.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

Traditional multi-task learning (MTL) methods use dense networks that use the same set of shared weights across several different tasks. This often creates interference where two or more tasks compete to pull model parameters in different directions. In this work, we study whether sparsely activated Mixture-of-Experts (MoE) improve multi-task learning by specializing some weights for learning shared representations and using the others for learning task-specific information. To this end, we devise task-aware gating functions to route examples from different tasks to specialized experts which share subsets of network weights conditioned on the task. This results in a sparsely activated multi-task model with a large number of parameters, but with the same computational cost as that of a dense model. We demonstrate such sparse networks to improve multi-task learning along three key dimensions: (i) transfer to low-resource tasks from related tasks in the training mixture; (ii) sample-efficient generalization to tasks not seen during training by making use of task-aware routing from seen related tasks; (iii) robustness to the addition of unrelated tasks by avoiding catastrophic forgetting of existing tasks.

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.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

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.

Utilizing pre-trained language models has achieved great success for neural document ranking. Limited by the computational and memory requirements, long document modeling becomes a critical issue. Recent works propose to modify the full attention matrix in Transformer by designing sparse attention patterns. However, most of them only focus on local connections of terms within a fixed-size window. How to build suitable remote connections between terms to better model document representation remains underexplored. In this paper, we propose the model Socialformer, which introduces the characteristics of social networks into designing sparse attention patterns for long document modeling in document ranking. Specifically, we consider several attention patterns to construct a graph like social networks. Endowed with the characteristic of social networks, most pairs of nodes in such a graph can reach with a short path while ensuring the sparsity. To facilitate efficient calculation, we segment the graph into multiple subgraphs to simulate friend circles in social scenarios. Experimental results confirm the effectiveness of our model on long document modeling.

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

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.

We aim to tackle the problem of point-based interactive segmentation, in which the key challenge is to propagate the user-provided annotations to unlabeled regions efficiently. Existing methods tackle this challenge by utilizing computationally expensive fully connected graphs or transformer architectures that sacrifice important fine-grained information required for accurate segmentation. To overcome these limitations, we propose a cascade sparse feature propagation network that learns a click-augmented feature representation for propagating user-provided information to unlabeled regions. The sparse design of our network enables efficient information propagation on high-resolution features, resulting in more detailed object segmentation. We validate the effectiveness of our method through comprehensive experiments on various benchmarks, and the results demonstrate the superior performance of our approach. Code is available at https://github.com/kleinzcy/CSFPN{https://github.com/kleinzcy/CSFPN}.

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

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.

Network pruning techniques, including weight pruning and filter pruning, reveal that most state-of-the-art neural networks can be accelerated without a significant performance drop. This work focuses on filter pruning which enables accelerated inference with any off-the-shelf deep learning library and hardware. We propose the concept of network pruning spaces that parametrize populations of subnetwork architectures. Based on this concept, we explore the structure aspect of subnetworks that result in minimal loss of accuracy in different pruning regimes and arrive at a series of observations by comparing subnetwork distributions. We conjecture through empirical studies that there exists an optimal FLOPs-to-parameter-bucket ratio related to the design of original network in a pruning regime. Statistically, the structure of a winning subnetwork guarantees an approximately optimal ratio in this regime. Upon our conjectures, we further refine the initial pruning space to reduce the cost of searching a good subnetwork architecture. Our experimental results on ImageNet show that the subnetwork we found is superior to those from the state-of-the-art pruning methods under comparable FLOPs.

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.

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.

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.

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.

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.

Recent advances in Neural Architecture Search (NAS) which extract specialized hardware-aware configurations (a.k.a. "sub-networks") from a hardware-agnostic "super-network" have become increasingly popular. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still largely under-explored. For example, some recent network morphism techniques allow a super-network to be trained once and then have hardware-specific networks extracted from it as needed. These methods decouple the super-network training from the sub-network search and thus decrease the computational burden of specializing to different hardware platforms. We propose a comprehensive system that automatically and efficiently finds sub-networks from a pre-trained super-network that are optimized to different performance metrics and hardware configurations. By combining novel search tactics and algorithms with intelligent use of predictors, we significantly decrease the time needed to find optimal sub-networks from a given super-network. Further, our approach does not require the super-network to be refined for the target task a priori, thus allowing it to interface with any super-network. We demonstrate through extensive experiments that our system works seamlessly with existing state-of-the-art super-network training methods in multiple domains. Moreover, we show how novel search tactics paired with evolutionary algorithms can accelerate the search process for ResNet50, MobileNetV3 and Transformer while maintaining objective space Pareto front diversity and demonstrate an 8x faster search result than the state-of-the-art Bayesian optimization WeakNAS approach.

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

We perform an empirical study of the behaviour of deep networks when fully linearizing some of its feature channels through a sparsity prior on the overall number of nonlinear units in the network. In experiments on image classification and machine translation tasks, we investigate how much we can simplify the network function towards linearity before performance collapses. First, we observe a significant performance gap when reducing nonlinearity in the network function early on as opposed to late in training, in-line with recent observations on the time-evolution of the data-dependent NTK. Second, we find that after training, we are able to linearize a significant number of nonlinear units while maintaining a high performance, indicating that much of a network's expressivity remains unused but helps gradient descent in early stages of training. To characterize the depth of the resulting partially linearized network, we introduce a measure called average path length, representing the average number of active nonlinearities encountered along a path in the network graph. Under sparsity pressure, we find that the remaining nonlinear units organize into distinct structures, forming core-networks of near constant effective depth and width, which in turn depend on task difficulty.

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.

The demand for efficient processing of deep neural networks (DNNs) on embedded devices is a significant challenge limiting their deployment. Exploiting sparsity in the network's feature maps is one of the ways to reduce its inference latency. It is known that unstructured sparsity results in lower accuracy degradation with respect to structured sparsity but the former needs extensive inference engine changes to get latency benefits. To tackle this challenge, we propose a solution to induce semi-structured activation sparsity exploitable through minor runtime modifications. To attain high speedup levels at inference time, we design a sparse training procedure with awareness of the final position of the activations while computing the General Matrix Multiplication (GEMM). We extensively evaluate the proposed solution across various models for image classification and object detection tasks. Remarkably, our approach yields a speed improvement of 1.25 times with a minimal accuracy drop of 1.1% for the ResNet18 model on the ImageNet dataset. Furthermore, when combined with a state-of-the-art structured pruning method, the resulting models provide a good latency-accuracy trade-off, outperforming models that solely employ structured pruning techniques.

The extensive need for computational resources poses a significant obstacle to deploying large-scale Deep Neural Networks (DNN) on devices with constrained resources. At the same time, studies have demonstrated that a significant number of these DNN parameters are redundant and extraneous. In this paper, we introduce a novel approach for learning structured sparse neural networks, aimed at bridging the DNN hardware deployment challenges. We develop a novel regularization technique, termed Weighted Group Sparse Envelope Function (WGSEF), generalizing the Sparse Envelop Function (SEF), to select (or nullify) neuron groups, thereby reducing redundancy and enhancing computational efficiency. The method speeds up inference time and aims to reduce memory demand and power consumption, thanks to its adaptability which lets any hardware specify group definitions, such as filters, channels, filter shapes, layer depths, a single parameter (unstructured), etc. The properties of the WGSEF enable the pre-definition of a desired sparsity level to be achieved at the training convergence. In the case of redundant parameters, this approach maintains negligible network accuracy degradation or can even lead to improvements in accuracy. Our method efficiently computes the WGSEF regularizer and its proximal operator, in a worst-case linear complexity relative to the number of group variables. Employing a proximal-gradient-based optimization technique, to train the model, it tackles the non-convex minimization problem incorporating the neural network loss and the WGSEF. Finally, we experiment and illustrate the efficiency of our proposed method in terms of the compression ratio, accuracy, and inference latency.

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

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.

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.

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.

In the past few years, neural networks have evolved from simple Feedforward Neural Networks to more complex neural networks, such as Convolutional Neural Networks and Recurrent Neural Networks. Where CNNs are a perfect fit for tasks where the sequence is not important such as image recognition, RNNs are useful when order is important such as machine translation. An increasing number of layers in a neural network is one way to improve its performance, but it also increases its complexity making it much more time and power-consuming to train. One way to tackle this problem is to introduce sparsity in the architecture of the neural network. Pruning is one of the many methods to make a neural network architecture sparse by clipping out weights below a certain threshold while keeping the performance near to the original. Another way is to generate arbitrary structures using random graphs and embed them between an input and output layer of an Artificial Neural Network. Many researchers in past years have focused on pruning mainly CNNs, while hardly any research is done for the same in RNNs. The same also holds in creating sparse architectures for RNNs by generating and embedding arbitrary structures. Therefore, this thesis focuses on investigating the effects of the before-mentioned two techniques on the performance of RNNs. We first describe the pruning of RNNs, its impact on the performance of RNNs, and the number of training epochs required to regain accuracy after the pruning is performed. Next, we continue with the creation and training of Sparse Recurrent Neural Networks and identify the relation between the performance and the graph properties of its underlying arbitrary structure. We perform these experiments on RNN with Tanh nonlinearity (RNN-Tanh), RNN with ReLU nonlinearity (RNN-ReLU), GRU, and LSTM. Finally, we analyze and discuss the results achieved from both the experiments.

Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to O(n n). We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.

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.

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.

As a deep learning model typically contains millions of trainable weights, there has been a growing demand for a more efficient network structure with reduced storage space and improved run-time efficiency. Pruning is one of the most popular network compression techniques. In this paper, we propose a novel unstructured pruning pipeline, Attention-based Simultaneous sparse structure and Weight Learning (ASWL). Unlike traditional channel-wise or weight-wise attention mechanism, ASWL proposed an efficient algorithm to calculate the pruning ratio through layer-wise attention for each layer, and both weights for the dense network and the sparse network are tracked so that the pruned structure is simultaneously learned from randomly initialized weights. Our experiments on MNIST, Cifar10, and ImageNet show that ASWL achieves superior pruning results in terms of accuracy, pruning ratio and operating efficiency when compared with state-of-the-art network pruning methods.

Recent advances in Neural Architecture Search (NAS) such as one-shot NAS offer the ability to extract specialized hardware-aware sub-network configurations from a task-specific super-network. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still under-explored. Popular methods decouple the super-network training from the sub-network search and use performance predictors to reduce the computational burden of searching on different hardware platforms. We propose a flexible search framework that automatically and efficiently finds optimal sub-networks that are optimized for different performance metrics and hardware configurations. Specifically, we show how evolutionary algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate architecture search in a multi-objective setting for various modalities including machine translation and image classification.

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.

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

Transformers use the dense self-attention mechanism which gives a lot of flexibility for long-range connectivity. Over multiple layers of a deep transformer, the number of possible connectivity patterns increases exponentially. However, very few of these contribute to the performance of the network, and even fewer are essential. We hypothesize that there are sparsely connected sub-networks within a transformer, called information pathways which can be trained independently. However, the dynamic (i.e., input-dependent) nature of these pathways makes it difficult to prune dense self-attention during training. But the overall distribution of these pathways is often predictable. We take advantage of this fact to propose Stochastically Subsampled self-Attention (SSA) - a general-purpose training strategy for transformers that can reduce both the memory and computational cost of self-attention by 4 to 8 times during training while also serving as a regularization method - improving generalization over dense training. We show that an ensemble of sub-models can be formed from the subsampled pathways within a network, which can achieve better performance than its densely attended counterpart. We perform experiments on a variety of NLP, computer vision and graph learning tasks in both generative and discriminative settings to provide empirical evidence for our claims and show the effectiveness of the proposed method.

State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond just a few layers, two fundamental challenges emerge: 1. degraded expressivity due to oversmoothing, and 2. expensive computation due to neighborhood explosion. We propose a design principle to decouple the depth and scope of GNNs -- to generate representation of a target entity (i.e., a node or an edge), we first extract a localized subgraph as the bounded-size scope, and then apply a GNN of arbitrary depth on top of the subgraph. A properly extracted subgraph consists of a small number of critical neighbors, while excluding irrelevant ones. The GNN, no matter how deep it is, smooths the local neighborhood into informative representation rather than oversmoothing the global graph into "white noise". Theoretically, decoupling improves the GNN expressive power from the perspectives of graph signal processing (GCN), function approximation (GraphSAGE) and topological learning (GIN). Empirically, on seven graphs (with up to 110M nodes) and six backbone GNN architectures, our design achieves significant accuracy improvement with orders of magnitude reduction in computation and hardware cost.

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.

Sequential models achieve state-of-the-art results in audio, visual and textual domains with respect to both estimating the data distribution and generating high-quality samples. Efficient sampling for this class of models has however remained an elusive problem. With a focus on text-to-speech synthesis, we describe a set of general techniques for reducing sampling time while maintaining high output quality. We first describe a single-layer recurrent neural network, the WaveRNN, with a dual softmax layer that matches the quality of the state-of-the-art WaveNet model. The compact form of the network makes it possible to generate 24kHz 16-bit audio 4x faster than real time on a GPU. Second, we apply a weight pruning technique to reduce the number of weights in the WaveRNN. We find that, for a constant number of parameters, large sparse networks perform better than small dense networks and this relationship holds for sparsity levels beyond 96%. The small number of weights in a Sparse WaveRNN makes it possible to sample high-fidelity audio on a mobile CPU in real time. Finally, we propose a new generation scheme based on subscaling that folds a long sequence into a batch of shorter sequences and allows one to generate multiple samples at once. The Subscale WaveRNN produces 16 samples per step without loss of quality and offers an orthogonal method for increasing sampling efficiency.

We present an approach to modifying Transformer architectures by integrating graph-aware relational reasoning into the attention mechanism, merging concepts from graph neural networks and language modeling. Building on the inherent connection between attention and graph theory, we reformulate the Transformer's attention mechanism as a graph operation and propose Graph-Aware Isomorphic Attention. This method leverages advanced graph modeling strategies, including Graph Isomorphism Networks (GIN) and Principal Neighborhood Aggregation (PNA), to enrich the representation of relational structures. Our approach captures complex dependencies and generalizes across tasks, as evidenced by a reduced generalization gap and improved learning performance. Additionally, we expand the concept of graph-aware attention to introduce Sparse GIN-Attention, a fine-tuning approach that employs sparse GINs. By interpreting attention matrices as sparse adjacency graphs, this technique enhances the adaptability of pre-trained foundational models with minimal computational overhead, endowing them with graph-aware capabilities. Sparse GIN-Attention fine-tuning achieves improved training dynamics and better generalization compared to alternative methods like low-rank adaption (LoRA). We discuss latent graph-like structures within traditional attention mechanisms, offering a new lens through which Transformers can be understood. By evolving Transformers as hierarchical GIN models for relational reasoning. This perspective suggests profound implications for foundational model development, enabling the design of architectures that dynamically adapt to both local and global dependencies. Applications in bioinformatics, materials science, language modeling, and beyond could benefit from this synthesis of relational and sequential data modeling, setting the stage for interpretable and generalizable modeling strategies.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

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 present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

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.

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.

Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. However, prevailing SR models suffer from prohibitive memory footprint and intensive computations, which limits further deployment on edge devices. This work investigates the potential of network pruning for super-resolution to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. Two main challenges remain in applying pruning methods for SR. First, the widely-used filter pruning technique reflects limited granularity and restricted adaptability to diverse network structures. Second, existing pruning methods generally operate upon a pre-trained network for the sparse structure determination, hard to get rid of dense model training in the traditional SR paradigm. To address these challenges, we adopt unstructured pruning with sparse models directly trained from scratch. Specifically, we propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly initialized network at each iteration and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly. We observe that the proposed ISS-P can dynamically learn sparse structures adapting to the optimization process and preserve the sparse model's trainability by yielding a more regularized gradient throughput. Experiments on benchmark datasets demonstrate the effectiveness of the proposed ISS-P over diverse network architectures. Code is available at https://github.com/Jiamian-Wang/Iterative-Soft-Shrinkage-SR

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.

Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g. sparsity, scale-freeness), we argue that (contrary to general practice) artificial neural networks, too, should not have fully-connected layers. Here we propose sparse evolutionary training of artificial neural networks, an algorithm which evolves an initial sparse topology (Erdos-R\'enyi random graph) of two consecutive layers of neurons into a scale-free topology, during learning. Our method replaces artificial neural networks fully-connected layers with sparse ones before training, reducing quadratically the number of parameters, with no decrease in accuracy. We demonstrate our claims on restricted Boltzmann machines, multi-layer perceptrons, and convolutional neural networks for unsupervised and supervised learning on 15 datasets. Our approach has the potential to enable artificial neural networks to scale up beyond what is currently possible.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

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 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.

Due to the over-parameterization of neural networks, many model compression methods based on pruning and quantization have emerged. They are remarkable in reducing the size, parameter number, and computational complexity of the model. However, most of the models compressed by such methods need the support of special hardware and software, which increases the deployment cost. Moreover, these methods are mainly used in classification tasks, and rarely directly used in detection tasks. To address these issues, for the object detection network we introduce a three-stage model compression method: dynamic sparse training, group channel pruning, and spatial attention distilling. Firstly, to select out the unimportant channels in the network and maintain a good balance between sparsity and accuracy, we put forward a dynamic sparse training method, which introduces a variable sparse rate, and the sparse rate will change with the training process of the network. Secondly, to reduce the effect of pruning on network accuracy, we propose a novel pruning method called group channel pruning. In particular, we divide the network into multiple groups according to the scales of the feature layer and the similarity of module structure in the network, and then we use different pruning thresholds to prune the channels in each group. Finally, to recover the accuracy of the pruned network, we use an improved knowledge distillation method for the pruned network. Especially, we extract spatial attention information from the feature maps of specific scales in each group as knowledge for distillation. In the experiments, we use YOLOv4 as the object detection network and PASCAL VOC as the training dataset. Our method reduces the parameters of the model by 64.7 % and the calculation by 34.9%.

Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (Han et al., 2015; Narang et al., 2017) prune deep networks at the cost of only a marginal loss in accuracy and achieve a sizable reduction in model size. This hints at the possibility that the baseline models in these experiments are perhaps severely over-parameterized at the outset and a viable alternative for model compression might be to simply reduce the number of hidden units while maintaining the model's dense connection structure, exposing a similar trade-off in model size and accuracy. We investigate these two distinct paths for model compression within the context of energy-efficient inference in resource-constrained environments and propose a new gradual pruning technique that is simple and straightforward to apply across a variety of models/datasets with minimal tuning and can be seamlessly incorporated within the training process. We compare the accuracy of large, but pruned models (large-sparse) and their smaller, but dense (small-dense) counterparts with identical memory footprint. Across a broad range of neural network architectures (deep CNNs, stacked LSTM, and seq2seq LSTM models), we find large-sparse models to consistently outperform small-dense models and achieve up to 10x reduction in number of non-zero parameters with minimal loss in accuracy.

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.

Subgraphs of a larger global graph may be distributed across multiple devices, and only locally accessible due to privacy restrictions, although there may be links between subgraphs. Recently proposed subgraph Federated Learning (FL) methods deal with those missing links across local subgraphs while distributively training Graph Neural Networks (GNNs) on them. However, they have overlooked the inevitable heterogeneity between subgraphs comprising different communities of a global graph, consequently collapsing the incompatible knowledge from local GNN models. To this end, we introduce a new subgraph FL problem, personalized subgraph FL, which focuses on the joint improvement of the interrelated local GNNs rather than learning a single global model, and propose a novel framework, FEDerated Personalized sUBgraph learning (FED-PUB), to tackle it. Since the server cannot access the subgraph in each client, FED-PUB utilizes functional embeddings of the local GNNs using random graphs as inputs to compute similarities between them, and use the similarities to perform weighted averaging for server-side aggregation. Further, it learns a personalized sparse mask at each client to select and update only the subgraph-relevant subset of the aggregated parameters. We validate our FED-PUB for its subgraph FL performance on six datasets, considering both non-overlapping and overlapping subgraphs, on which it significantly outperforms relevant baselines. Our code is available at https://github.com/JinheonBaek/FED-PUB.

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.

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNNs evaluation. Experimental results show that SSL achieves on average 5.1x and 3.1x speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%, which is still slightly higher than that of original ResNet with 32 layers. For AlexNet, structure regularization by SSL also reduces the error by around ~1%. Open source code is in https://github.com/wenwei202/caffe/tree/scnn

The Multi-Prize Lottery Ticket Hypothesis posits that randomly initialized neural networks contain several subnetworks that achieve comparable accuracy to fully trained models of the same architecture. However, current methods require that the network is sufficiently overparameterized. In this work, we propose a modification to two state-of-the-art algorithms (Edge-Popup and Biprop) that finds high-accuracy subnetworks with no additional storage cost or scaling. The algorithm, Iterative Weight Recycling, identifies subsets of important weights within a randomly initialized network for intra-layer reuse. Empirically we show improvements on smaller network architectures and higher prune rates, finding that model sparsity can be increased through the "recycling" of existing weights. In addition to Iterative Weight Recycling, we complement the Multi-Prize Lottery Ticket Hypothesis with a reciprocal finding: high-accuracy, randomly initialized subnetwork's produce diverse masks, despite being generated with the same hyperparameter's and pruning strategy. We explore the landscapes of these masks, which show high variability.

We explore a key architectural aspect of deep convolutional neural networks: the pattern of internal skip connections used to aggregate outputs of earlier layers for consumption by deeper layers. Such aggregation is critical to facilitate training of very deep networks in an end-to-end manner. This is a primary reason for the widespread adoption of residual networks, which aggregate outputs via cumulative summation. While subsequent works investigate alternative aggregation operations (e.g. concatenation), we focus on an orthogonal question: which outputs to aggregate at a particular point in the network. We propose a new internal connection structure which aggregates only a sparse set of previous outputs at any given depth. Our experiments demonstrate this simple design change offers superior performance with fewer parameters and lower computational requirements. Moreover, we show that sparse aggregation allows networks to scale more robustly to 1000+ layers, thereby opening future avenues for training long-running visual processes.

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.

Sparse training is one of the promising techniques to reduce the computational cost of DNNs while retaining high accuracy. In particular, N:M fine-grained structured sparsity, where only N out of consecutive M elements can be nonzero, has attracted attention due to its hardware-friendly pattern and capability of achieving a high sparse ratio. However, the potential to accelerate N:M sparse DNN training has not been fully exploited, and there is a lack of efficient hardware supporting N:M sparse training. To tackle these challenges, this paper presents a computation-efficient training scheme for N:M sparse DNNs using algorithm, architecture, and dataflow co-design. At the algorithm level, a bidirectional weight pruning method, dubbed BDWP, is proposed to leverage the N:M sparsity of weights during both forward and backward passes of DNN training, which can significantly reduce the computational cost while maintaining model accuracy. At the architecture level, a sparse accelerator for DNN training, namely SAT, is developed to neatly support both the regular dense operations and the computation-efficient N:M sparse operations. At the dataflow level, multiple optimization methods ranging from interleave mapping, pre-generation of N:M sparse weights, and offline scheduling, are proposed to boost the computational efficiency of SAT. Finally, the effectiveness of our training scheme is evaluated on a Xilinx VCU1525 FPGA card using various DNN models and datasets. Experimental results show the SAT accelerator with the BDWP sparse training method under 2:8 sparse ratio achieves an average speedup of 1.75x over that with the dense training, accompanied by a negligible accuracy loss of 0.56% on average. Furthermore, our proposed training scheme significantly improves the training throughput by 2.97~25.22x and the energy efficiency by 1.36~3.58x over prior FPGA-based accelerators.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

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.

Grokking is one of the most surprising puzzles in neural network generalization: a network first reaches a memorization solution with perfect training accuracy and poor generalization, but with further training, it reaches a perfectly generalized solution. We aim to analyze the mechanism of grokking from the lottery ticket hypothesis, identifying the process to find the lottery tickets (good sparse subnetworks) as the key to describing the transitional phase between memorization and generalization. We refer to these subnetworks as ''Grokking tickets'', which is identified via magnitude pruning after perfect generalization. First, using ''Grokking tickets'', we show that the lottery tickets drastically accelerate grokking compared to the dense networks on various configurations (MLP and Transformer, and an arithmetic and image classification tasks). Additionally, to verify that ''Grokking ticket'' are a more critical factor than weight norms, we compared the ''good'' subnetworks with a dense network having the same L1 and L2 norms. Results show that the subnetworks generalize faster than the controlled dense model. In further investigations, we discovered that at an appropriate pruning rate, grokking can be achieved even without weight decay. We also show that speedup does not happen when using tickets identified at the memorization solution or transition between memorization and generalization or when pruning networks at the initialization (Random pruning, Grasp, SNIP, and Synflow). The results indicate that the weight norm of network parameters is not enough to explain the process of grokking, but the importance of finding good subnetworks to describe the transition from memorization to generalization. The implementation code can be accessed via this link: https://github.com/gouki510/Grokking-Tickets.

Neural network pruning reduces the computational cost of an over-parameterized network to improve its efficiency. Popular methods vary from ell_1-norm sparsification to Neural Architecture Search (NAS). In this work, we propose a novel pruning method that optimizes the final accuracy of the pruned network and distills knowledge from the over-parameterized parent network's inner layers. To enable this approach, we formulate the network pruning as a Knapsack Problem which optimizes the trade-off between the importance of neurons and their associated computational cost. Then we prune the network channels while maintaining the high-level structure of the network. The pruned network is fine-tuned under the supervision of the parent network using its inner network knowledge, a technique we refer to as the Inner Knowledge Distillation. Our method leads to state-of-the-art pruning results on ImageNet, CIFAR-10 and CIFAR-100 using ResNet backbones. To prune complex network structures such as convolutions with skip-links and depth-wise convolutions, we propose a block grouping approach to cope with these structures. Through this we produce compact architectures with the same FLOPs as EfficientNet-B0 and MobileNetV3 but with higher accuracy, by 1% and 0.3% respectively on ImageNet, and faster runtime on GPU.

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.

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.

As the size of deep learning models continues to grow, finding optimal models under memory and computation constraints becomes increasingly more important. Although usually the architecture and constituent building blocks of neural networks allow them to be used in a modular way, their training process is not aware of this modularity. Consequently, conventional neural network training lacks the flexibility to adapt the computational load of the model during inference. This paper proposes SortedNet, a generalized and scalable solution to harness the inherent modularity of deep neural networks across various dimensions for efficient dynamic inference. Our training considers a nested architecture for the sub-models with shared parameters and trains them together with the main model in a sorted and probabilistic manner. This sorted training of sub-networks enables us to scale the number of sub-networks to hundreds using a single round of training. We utilize a novel updating scheme during training that combines random sampling of sub-networks with gradient accumulation to improve training efficiency. Furthermore, the sorted nature of our training leads to a search-free sub-network selection at inference time; and the nested architecture of the resulting sub-networks leads to minimal storage requirement and efficient switching between sub-networks at inference. Our general dynamic training approach is demonstrated across various architectures and tasks, including large language models and pre-trained vision models. Experimental results show the efficacy of the proposed approach in achieving efficient sub-networks while outperforming state-of-the-art dynamic training approaches. Our findings demonstrate the feasibility of training up to 160 different sub-models simultaneously, showcasing the extensive scalability of our proposed method while maintaining 96% of the model performance.

The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their inefficiency. Sparse representations, either in symbolic or latent form, are more efficient with an inverted index. Taking the merits of the sparse and dense representations, we propose an ultra-high dimensional (UHD) representation scheme equipped with directly controllable sparsity. UHD's large capacity and minimal noise and interference among the dimensions allow for binarized representations, which are highly efficient for storage and search. Also proposed is a bucketing method, where the embeddings from multiple layers of BERT are selected/merged to represent diverse linguistic aspects. We test our models with MS MARCO and TREC CAR, showing that our models outperforms other sparse 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.

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive generative capabilities that have been used to correct corruptions in images, and the similarities between "in-painting" and filling in missing nodes and edges conditioned on the observed graph, we propose a novel graph generative framework, SGDM, which is based on subgraph diffusion. Our framework not only improves the scalability and fidelity of graph diffusion models, but also leverages the reverse process to perform novel, conditional generation tasks. In particular, through extensive empirical analysis and a set of novel metrics, we demonstrate that our proposed model effectively supports the following refinement tasks for partially observable networks: T1: denoising extraneous subgraphs, T2: expanding existing subgraphs and T3: performing "style" transfer by regenerating a particular subgraph to match the characteristics of a different node or subgraph.

With the increasing number of new neural architecture designs and substantial existing neural architectures, it becomes difficult for the researchers to situate their contributions compared with existing neural architectures or establish the connections between their designs and other relevant ones. To discover similar neural architectures in an efficient and automatic manner, we define a new problem Neural Architecture Retrieval which retrieves a set of existing neural architectures which have similar designs to the query neural architecture. Existing graph pre-training strategies cannot address the computational graph in neural architectures due to the graph size and motifs. To fulfill this potential, we propose to divide the graph into motifs which are used to rebuild the macro graph to tackle these issues, and introduce multi-level contrastive learning to achieve accurate graph representation learning. Extensive evaluations on both human-designed and synthesized neural architectures demonstrate the superiority of our algorithm. Such a dataset which contains 12k real-world network architectures, as well as their embedding, is built for neural architecture retrieval.

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.

Temporal networks have been widely used to model real-world complex systems such as financial systems and e-commerce systems. In a temporal network, the joint neighborhood of a set of nodes often provides crucial structural information useful for predicting whether they may interact at a certain time. However, recent representation learning methods for temporal networks often fail to extract such information or depend on online construction of structural features, which is time-consuming. To address the issue, this work proposes Neighborhood-Aware Temporal network model (NAT). For each node in the network, NAT abandons the commonly-used one-single-vector-based representation while adopting a novel dictionary-type neighborhood representation. Such a dictionary representation records a downsampled set of the neighboring nodes as keys, and allows fast construction of structural features for a joint neighborhood of multiple nodes. We also design a dedicated data structure termed N-cache to support parallel access and update of those dictionary representations on GPUs. NAT gets evaluated over seven real-world large-scale temporal networks. NAT not only outperforms all cutting-edge baselines by averaged 1.2% and 4.2% in transductive and inductive link prediction accuracy, respectively, but also keeps scalable by achieving a speed-up of 4.1-76.7x against the baselines that adopt joint structural features and achieves a speed-up of 1.6-4.0x against the baselines that cannot adopt those features. The link to the code: https: //github.com/Graph-COM/Neighborhood-Aware-Temporal-Network.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

The sparse Mixture-of-Experts (Sparse-MoE) framework efficiently scales up model capacity in various domains, such as natural language processing and vision. Sparse-MoEs select a subset of the "experts" (thus, only a portion of the overall network) for each input sample using a sparse, trainable gate. Existing sparse gates are prone to convergence and performance issues when training with first-order optimization methods. In this paper, we introduce two improvements to current MoE approaches. First, we propose a new sparse gate: COMET, which relies on a novel tree-based mechanism. COMET is differentiable, can exploit sparsity to speed up computation, and outperforms state-of-the-art gates. Second, due to the challenging combinatorial nature of sparse expert selection, first-order methods are typically prone to low-quality solutions. To deal with this challenge, we propose a novel, permutation-based local search method that can complement first-order methods in training any sparse gate, e.g., Hash routing, Top-k, DSelect-k, and COMET. We show that local search can help networks escape bad initializations or solutions. We performed large-scale experiments on various domains, including recommender systems, vision, and natural language processing. On standard vision and recommender systems benchmarks, COMET+ (COMET with local search) achieves up to 13% improvement in ROC AUC over popular gates, e.g., Hash routing and Top-k, and up to 9% over prior differentiable gates e.g., DSelect-k. When Top-k and Hash gates are combined with local search, we see up to 100times reduction in the budget needed for hyperparameter tuning. Moreover, for language modeling, our approach improves over the state-of-the-art MoEBERT model for distilling BERT on 5/7 GLUE benchmarks as well as SQuAD 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 introduce DLSIA (Deep Learning for Scientific Image Analysis), a Python-based machine learning library that empowers scientists and researchers across diverse scientific domains with a range of customizable convolutional neural network (CNN) architectures for a wide variety of tasks in image analysis to be used in downstream data processing, or for experiment-in-the-loop computing scenarios. DLSIA features easy-to-use architectures such as autoencoders, tunable U-Nets, and parameter-lean mixed-scale dense networks (MSDNets). Additionally, we introduce sparse mixed-scale networks (SMSNets), generated using random graphs and sparse connections. As experimental data continues to grow in scale and complexity, DLSIA provides accessible CNN construction and abstracts CNN complexities, allowing scientists to tailor their machine learning approaches, accelerate discoveries, foster interdisciplinary collaboration, and advance research in scientific image analysis.

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of these neighborhood aggregation methods only consider immediate neighbors, and the performance decreases when going deeper to enable larger receptive fields. Several recent studies attribute this performance deterioration to the over-smoothing issue, which states that repeated propagation makes node representations of different classes indistinguishable. In this work, we study this observation systematically and develop new insights towards deeper graph neural networks. First, we provide a systematical analysis on this issue and argue that the key factor compromising the performance significantly is the entanglement of representation transformation and propagation in current graph convolution operations. After decoupling these two operations, deeper graph neural networks can be used to learn graph node representations from larger receptive fields. We further provide a theoretical analysis of the above observation when building very deep models, which can serve as a rigorous and gentle description of the over-smoothing issue. Based on our theoretical and empirical analysis, we propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields. A set of experiments on citation, co-authorship, and co-purchase datasets have confirmed our analysis and insights and demonstrated the superiority of our proposed methods.

The ever-increasing large language models (LLMs), though opening a potential path for the upcoming artificial general intelligence, sadly drops a daunting obstacle on the way towards their on-device deployment. As one of the most well-established pre-LLMs approaches in reducing model complexity, network pruning appears to lag behind in the era of LLMs, due mostly to its costly fine-tuning (or re-training) necessity under the massive volumes of model parameter and training data. To close this industry-academia gap, we introduce Dynamic Sparse No Training (DSnoT), a training-free fine-tuning approach that slightly updates sparse LLMs without the expensive backpropagation and any weight updates. Inspired by the Dynamic Sparse Training, DSnoT minimizes the reconstruction error between the dense and sparse LLMs, in the fashion of performing iterative weight pruning-and-growing on top of sparse LLMs. To accomplish this purpose, DSnoT particularly takes into account the anticipated reduction in reconstruction error for pruning and growing, as well as the variance w.r.t. different input data for growing each weight. This practice can be executed efficiently in linear time since its obviates the need of backpropagation for fine-tuning LLMs. Extensive experiments on LLaMA-V1/V2, Vicuna, and OPT across various benchmarks demonstrate the effectiveness of DSnoT in enhancing the performance of sparse LLMs, especially at high sparsity levels. For instance, DSnoT is able to outperform the state-of-the-art Wanda by 26.79 perplexity at 70% sparsity with LLaMA-7B. Our paper offers fresh insights into how to fine-tune sparse LLMs in an efficient training-free manner and open new venues to scale the great potential of sparsity to LLMs. Codes are available at https://github.com/zyxxmu/DSnoT.

We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks contain interacting subpaths of different lengths, but do not include any pass-through or residual connections; every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. In experiments, fractal networks match the excellent performance of standard residual networks on both CIFAR and ImageNet classification tasks, thereby demonstrating that residual representations may not be fundamental to the success of extremely deep convolutional neural networks. Rather, the key may be the ability to transition, during training, from effectively shallow to deep. We note similarities with student-teacher behavior and develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. Such regularization allows extraction of high-performance fixed-depth subnetworks. Additionally, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.

Graph Neural Networks (GNNs) are popular models for machine learning on graphs that typically follow the message-passing paradigm, whereby the feature of a node is updated recursively upon aggregating information over its neighbors. While exchanging messages over the input graph endows GNNs with a strong inductive bias, it can also make GNNs susceptible to over-squashing, thereby preventing them from capturing long-range interactions in the given graph. To rectify this issue, graph rewiring techniques have been proposed as a means of improving information flow by altering the graph connectivity. In this work, we identify three desiderata for graph-rewiring: (i) reduce over-squashing, (ii) respect the locality of the graph, and (iii) preserve the sparsity of the graph. We highlight fundamental trade-offs that occur between spatial and spectral rewiring techniques; while the former often satisfy (i) and (ii) but not (iii), the latter generally satisfy (i) and (iii) at the expense of (ii). We propose a novel rewiring framework that satisfies all of (i)--(iii) through a locality-aware sequence of rewiring operations. We then discuss a specific instance of such rewiring framework and validate its effectiveness on several real-world benchmarks, showing that it either matches or significantly outperforms existing rewiring approaches.

Self-attention has recently been adopted for a wide range of sequence modeling problems. Despite its effectiveness, self-attention suffers from quadratic compute and memory requirements with respect to sequence length. Successful approaches to reduce this complexity focused on attending to local sliding windows or a small set of locations independent of content. Our work proposes to learn dynamic sparse attention patterns that avoid allocating computation and memory to attend to content unrelated to the query of interest. This work builds upon two lines of research: it combines the modeling flexibility of prior work on content-based sparse attention with the efficiency gains from approaches based on local, temporal sparse attention. Our model, the Routing Transformer, endows self-attention with a sparse routing module based on online k-means while reducing the overall complexity of attention to Oleft(n^{1.5}dright) from Oleft(n^2dright) for sequence length n and hidden dimension d. We show that our model outperforms comparable sparse attention models on language modeling on Wikitext-103 (15.8 vs 18.3 perplexity) as well as on image generation on ImageNet-64 (3.43 vs 3.44 bits/dim) while using fewer self-attention layers. Additionally, we set a new state-of-the-art on the newly released PG-19 data-set, obtaining a test perplexity of 33.2 with a 22 layer Routing Transformer model trained on sequences of length 8192.

Pruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters. However, relatively little work has gone into characterising the small pruned networks obtained, beyond a measure of their accuracy. In this paper, we use the sparse double descent approach to identify univocally and characterise pruned models associated with classification tasks. We observe empirically that, for a given task, iterative magnitude pruning (IMP) tends to converge to networks of comparable sizes even when starting from full networks with sizes ranging over orders of magnitude. We analyse the best pruned models in a controlled experimental setup and show that their number of parameters reflects task difficulty and that they are much better than full networks at capturing the true conditional probability distribution of the labels. On real data, we similarly observe that pruned models are less prone to overconfident predictions. Our results suggest that pruned models obtained via IMP not only have advantageous computational properties but also provide a better representation of uncertainty in learning.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

Contrastive learning has recently achieved remarkable success in many domains including graphs. However contrastive loss, especially for graphs, requires a large number of negative samples which is unscalable and computationally prohibitive with a quadratic time complexity. Sub-sampling is not optimal and incorrect negative sampling leads to sampling bias. In this work, we propose a meta-node based approximation technique that can (a) proxy all negative combinations (b) in quadratic cluster size time complexity, (c) at graph level, not node level, and (d) exploit graph sparsity. By replacing node-pairs with additive cluster-pairs, we compute the negatives in cluster-time at graph level. The resulting Proxy approximated meta-node Contrastive (PamC) loss, based on simple optimized GPU operations, captures the full set of negatives, yet is efficient with a linear time complexity. By avoiding sampling, we effectively eliminate sample bias. We meet the criterion for larger number of samples, thus achieving block-contrastiveness, which is proven to outperform pair-wise losses. We use learnt soft cluster assignments for the meta-node constriction, and avoid possible heterophily and noise added during edge creation. Theoretically, we show that real world graphs easily satisfy conditions necessary for our approximation. Empirically, we show promising accuracy gains over state-of-the-art graph clustering on 6 benchmarks. Importantly, we gain substantially in efficiency; up to 3x in training time, 1.8x in inference time and over 5x in GPU memory reduction.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

We address the challenging problem of efficient inference across many devices and resource constraints, especially on edge devices. Conventional approaches either manually design or use neural architecture search (NAS) to find a specialized neural network and train it from scratch for each case, which is computationally prohibitive (causing CO_2 emission as much as 5 cars' lifetime) thus unscalable. In this work, we propose to train a once-for-all (OFA) network that supports diverse architectural settings by decoupling training and search, to reduce the cost. We can quickly get a specialized sub-network by selecting from the OFA network without additional training. To efficiently train OFA networks, we also propose a novel progressive shrinking algorithm, a generalized pruning method that reduces the model size across many more dimensions than pruning (depth, width, kernel size, and resolution). It can obtain a surprisingly large number of sub-networks (> 10^{19}) that can fit different hardware platforms and latency constraints while maintaining the same level of accuracy as training independently. On diverse edge devices, OFA consistently outperforms state-of-the-art (SOTA) NAS methods (up to 4.0% ImageNet top1 accuracy improvement over MobileNetV3, or same accuracy but 1.5x faster than MobileNetV3, 2.6x faster than EfficientNet w.r.t measured latency) while reducing many orders of magnitude GPU hours and CO_2 emission. In particular, OFA achieves a new SOTA 80.0% ImageNet top-1 accuracy under the mobile setting (<600M MACs). OFA is the winning solution for the 3rd Low Power Computer Vision Challenge (LPCVC), DSP classification track and the 4th LPCVC, both classification track and detection track. Code and 50 pre-trained models (for many devices & many latency constraints) are released at https://github.com/mit-han-lab/once-for-all.

We present STanHop-Net (Sparse Tandem Hopfield Network) for multivariate time series prediction with memory-enhanced capabilities. At the heart of our approach is STanHop, a novel Hopfield-based neural network block, which sparsely learns and stores both temporal and cross-series representations in a data-dependent fashion. In essence, STanHop sequentially learn temporal representation and cross-series representation using two tandem sparse Hopfield layers. In addition, StanHop incorporates two additional external memory modules: a Plug-and-Play module and a Tune-and-Play module for train-less and task-aware memory-enhancements, respectively. They allow StanHop-Net to swiftly respond to certain sudden events. Methodologically, we construct the StanHop-Net by stacking STanHop blocks in a hierarchical fashion, enabling multi-resolution feature extraction with resolution-specific sparsity. Theoretically, we introduce a sparse extension of the modern Hopfield model (Generalized Sparse Modern Hopfield Model) and show that it endows a tighter memory retrieval error compared to the dense counterpart without sacrificing memory capacity. Empirically, we validate the efficacy of our framework on both synthetic and real-world settings.

It has been shown that a message passing neural networks (MPNNs), a popular family of neural networks for graph-structured data, are at most as expressive as the first-order Weisfeiler-Leman (1-WL) graph isomorphism test, which has motivated the development of more expressive architectures. In this work, we analyze if the limited expressiveness is actually a limiting factor for MPNNs and other WL-based models in standard graph datasets. Interestingly, we find that the expressiveness of WL is sufficient to identify almost all graphs in most datasets. Moreover, we find that the classification accuracy upper bounds are often close to 100\%. Furthermore, we find that simple WL-based neural networks and several MPNNs can be fitted to several datasets. In sum, we conclude that the performance of WL/MPNNs is not limited by their expressiveness in practice.

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.

In this paper, we present a new MTL framework that searches for structures optimized for multiple tasks with diverse graph topologies and shares features among tasks. We design a restricted DAG-based central network with read-in/read-out layers to build topologically diverse task-adaptive structures while limiting search space and time. We search for a single optimized network that serves as multiple task adaptive sub-networks using our three-stage training process. To make the network compact and discretized, we propose a flow-based reduction algorithm and a squeeze loss used in the training process. We evaluate our optimized network on various public MTL datasets and show ours achieves state-of-the-art performance. An extensive ablation study experimentally validates the effectiveness of the sub-module and schemes in our framework.

Neural networks have achieved remarkable performance in various application domains. Nevertheless, a large number of weights in pre-trained deep neural networks prohibit them from being deployed on smartphones and embedded systems. It is highly desirable to obtain lightweight versions of neural networks for inference in edge devices. Many cost-effective approaches were proposed to prune dense and convolutional layers that are common in deep neural networks and dominant in the parameter space. However, a unified theoretical foundation for the problem mostly is missing. In this paper, we identify the close connection between matrix spectrum learning and neural network training for dense and convolutional layers and argue that weight pruning is essentially a matrix sparsification process to preserve the spectrum. Based on the analysis, we also propose a matrix sparsification algorithm tailored for neural network pruning that yields better pruning result. We carefully design and conduct experiments to support our arguments. Hence we provide a consolidated viewpoint for neural network pruning and enhance the interpretability of deep neural networks by identifying and preserving the critical neural weights.

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.

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

With the growth of neural network size, model compression has attracted increasing interest in recent research. As one of the most common techniques, pruning has been studied for a long time. By exploiting the structured sparsity of the neural network, existing methods can prune neurons instead of individual weights. However, in most existing pruning methods, surviving neurons are randomly connected in the neural network without any structure, and the non-zero weights within each neuron are also randomly distributed. Such irregular sparse structure can cause very high control overhead and irregular memory access for the hardware and even increase the neural network computational complexity. In this paper, we propose a three-layer hierarchical prior to promote a more regular sparse structure during pruning. The proposed three-layer hierarchical prior can achieve per-neuron weight-level structured sparsity and neuron-level structured sparsity. We derive an efficient Turbo-variational Bayesian inferencing (Turbo-VBI) algorithm to solve the resulting model compression problem with the proposed prior. The proposed Turbo-VBI algorithm has low complexity and can support more general priors than existing model compression algorithms. Simulation results show that our proposed algorithm can promote a more regular structure in the pruned neural networks while achieving even better performance in terms of compression rate and inferencing accuracy compared with the baselines.

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.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

Overparameterized Neural Networks (NN) display state-of-the-art performance. However, there is a growing need for smaller, energy-efficient, neural networks tobe able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained NN (LeCun et al.,1990; Hassibi et al., 1993), recent work by Lee et al. (2018) has shown promising results when pruning at initialization. However, for Deep NNs, such procedures remain unsatisfactory as the resulting pruned networks can be difficult to train and, for instance, they do not prevent one layer from being fully pruned. In this paper, we provide a comprehensive theoretical analysis of Magnitude and Gradient based pruning at initialization and training of sparse architectures. This allows us to propose novel principled approaches which we validate experimentally on a variety of NN architectures.

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

The sparsely-activated models have achieved great success in natural language processing through large-scale parameters and relatively low computational cost, and gradually become a feasible technique for training and implementing extremely large models. Due to the limit of communication cost, activating multiple experts is hardly affordable during training and inference. Therefore, previous work usually activate just one expert at a time to alleviate additional communication cost. Such routing mechanism limits the upper bound of model performance. In this paper, we first investigate a phenomenon that increasing the number of activated experts can boost the model performance with higher sparse ratio. To increase the number of activated experts without an increase in computational cost, we propose SAM (Switch and Mixture) routing, an efficient hierarchical routing mechanism that activates multiple experts in a same device (GPU). Our methods shed light on the training of extremely large sparse models and experiments prove that our models can achieve significant performance gain with great efficiency improvement.

We investigate the problem of producing structured graph representations of visual scenes. Our work analyzes the role of motifs: regularly appearing substructures in scene graphs. We present new quantitative insights on such repeated structures in the Visual Genome dataset. Our analysis shows that object labels are highly predictive of relation labels but not vice-versa. We also find that there are recurring patterns even in larger subgraphs: more than 50% of graphs contain motifs involving at least two relations. Our analysis motivates a new baseline: given object detections, predict the most frequent relation between object pairs with the given labels, as seen in the training set. This baseline improves on the previous state-of-the-art by an average of 3.6% relative improvement across evaluation settings. We then introduce Stacked Motif Networks, a new architecture designed to capture higher order motifs in scene graphs that further improves over our strong baseline by an average 7.1% relative gain. Our code is available at github.com/rowanz/neural-motifs.

Neural architecture search (NAS) for Graph neural networks (GNNs), called NAS-GNNs, has achieved significant performance over manually designed GNN architectures. However, these methods inherit issues from the conventional NAS methods, such as high computational cost and optimization difficulty. More importantly, previous NAS methods have ignored the uniqueness of GNNs, where GNNs possess expressive power without training. With the randomly-initialized weights, we can then seek the optimal architecture parameters via the sparse coding objective and derive a novel NAS-GNNs method, namely neural architecture coding (NAC). Consequently, our NAC holds a no-update scheme on GNNs and can efficiently compute in linear time. Empirical evaluations on multiple GNN benchmark datasets demonstrate that our approach leads to state-of-the-art performance, which is up to 200times faster and 18.8% more accurate than the strong baselines.

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor.

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.

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

Pruning generates sparse networks by setting parameters to zero. In this work we improve one-shot pruning methods, applied before training, without adding any additional storage costs while preserving the sparse gradient computations. The main difference to pruning is that we do not sparsify the network's weights but learn just a few key parameters and keep the other ones fixed at their random initialized value. This mechanism is called freezing the parameters. Those frozen weights can be stored efficiently with a single 32bit random seed number. The parameters to be frozen are determined one-shot by a single for- and backward pass applied before training starts. We call the introduced method FreezeNet. In our experiments we show that FreezeNets achieve good results, especially for extreme freezing rates. Freezing weights preserves the gradient flow throughout the network and consequently, FreezeNets train better and have an increased capacity compared to their pruned counterparts. On the classification tasks MNIST and CIFAR-10/100 we outperform SNIP, in this setting the best reported one-shot pruning method, applied before training. On MNIST, FreezeNet achieves 99.2% performance of the baseline LeNet-5-Caffe architecture, while compressing the number of trained and stored parameters by a factor of x 157.

Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods. However, they suffer from exponential computational costs or searching the matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we first prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. We can then yield an implementation of linear time complexity by the built-in tree-structured aggregation mechanism on graph neural networks. Moreover, circle structures and node attributes can be easily incorporated in D2Match to boost the matching performance. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed exploits the subtrees and differs from existing GNNs-based subgraph matching methods that depend on memorizing the data distribution divergence

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is still on primary stage. In this paper, we move towards this goal from the perspective of generalization. To be specific, we first establish high probability bounds of generalization gap and gradients in transductive learning with consideration of stochastic optimization. After that, we provide high probability bounds of generalization gap for popular GNNs. The theoretical results reveal the architecture specific factors affecting the generalization gap. Experimental results on benchmark datasets show the consistency between theoretical results and empirical evidence. Our results provide new insights in understanding the generalization of GNNs.

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 mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, effective training of SMoE has proven to be challenging due to the representation collapse issue, which causes parameter redundancy and limited representation potentials. In this work, we propose a competition mechanism to address this fundamental challenge of representation collapse. By routing inputs only to experts with the highest neural response, we show that, under mild assumptions, competition enjoys the same convergence rate as the optimal estimator. We further propose CompeteSMoE, an effective and efficient algorithm to train large language models by deploying a simple router that predicts the competition outcomes. Consequently, CompeteSMoE enjoys strong performance gains from the competition routing policy while having low computation overheads. Our extensive empirical evaluations on two transformer architectures and a wide range of tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies.

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 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.

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

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.

Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroactively on small vision tasks. However, IMP fails on deeper networks, and proposed methods to prune before training or train pruned networks encounter similar scaling limitations. In this paper, we argue that these efforts have struggled on deeper networks because they have focused on pruning precisely at initialization. We modify IMP to search for subnetworks that could have been obtained by pruning early in training (0.1% to 7% through) rather than at iteration 0. With this change, it finds small subnetworks of deeper networks (e.g., 80% sparsity on Resnet-50) that can complete the training process to match the accuracy of the original network on more challenging tasks (e.g., ImageNet). In situations where IMP fails at iteration 0, the accuracy benefits of delaying pruning accrue rapidly over the earliest iterations of training. To explain these behaviors, we study subnetwork "stability," finding that - as accuracy improves in this fashion - IMP subnetworks train to parameters closer to those of the full network and do so with improved consistency in the face of gradient noise. These results offer new insights into the opportunity to prune large-scale networks early in training and the behaviors underlying the lottery ticket hypothesis

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adopting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.

Graph Neural Networks (GNNs) have already been widely applied in various graph mining tasks. However, they suffer from the shallow architecture issue, which is the key impediment that hinders the model performance improvement. Although several relevant approaches have been proposed, none of the existing studies provides an in-depth understanding of the root causes of performance degradation in deep GNNs. In this paper, we conduct the first systematic experimental evaluation to present the fundamental limitations of shallow architectures. Based on the experimental results, we answer the following two essential questions: (1) what actually leads to the compromised performance of deep GNNs; (2) when we need and how to build deep GNNs. The answers to the above questions provide empirical insights and guidelines for researchers to design deep and well-performed GNNs. To show the effectiveness of our proposed guidelines, we present Deep Graph Multi-Layer Perceptron (DGMLP), a powerful approach (a paradigm in its own right) that helps guide deep GNN designs. Experimental results demonstrate three advantages of DGMLP: 1) high accuracy -- it achieves state-of-the-art node classification performance on various datasets; 2) high flexibility -- it can flexibly choose different propagation and transformation depths according to graph size and sparsity; 3) high scalability and efficiency -- it supports fast training on large-scale graphs. Our code is available in https://github.com/zwt233/DGMLP.

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.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Training large, deep neural networks to convergence can be prohibitively expensive. As a result, often only a small selection of popular, dense models are reused across different contexts and tasks. Increasingly, sparsely activated models, which seek to decouple model size from computation costs, are becoming an attractive alternative to dense models. Although more efficient in terms of quality and computation cost, sparse models remain data-hungry and costly to train from scratch in the large scale regime. In this work, we propose sparse upcycling -- a simple way to reuse sunk training costs by initializing a sparsely activated Mixture-of-Experts model from a dense checkpoint. We show that sparsely upcycled T5 Base, Large, and XL language models and Vision Transformer Base and Large models, respectively, significantly outperform their dense counterparts on SuperGLUE and ImageNet, using only ~50% of the initial dense pretraining sunk cost. The upcycled models also outperform sparse models trained from scratch on 100% of the initial dense pretraining computation budget.

Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while still relying on the same backbone architecture. In the meantime, sparse representation learning fueled by traditional inverted indexing techniques has seen a growing interest, inheriting from desirable IR priors such as explicit lexical matching. While some architectural variants have been proposed, a lesser effort has been put in the training of such models. In this work, we build on SPLADE -- a sparse expansion-based retriever -- and show to which extent it is able to benefit from the same training improvements as dense models, by studying the effect of distillation, hard-negative mining as well as the Pre-trained Language Model initialization. We furthermore study the link between effectiveness and efficiency, on in-domain and zero-shot settings, leading to state-of-the-art results in both scenarios for sufficiently expressive models.

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not environmental-friendly with much power cost. In this paper, we focus on low-rank optimization for efficient deep learning techniques. In the space domain, deep neural networks are compressed by low rank approximation of the network parameters, which directly reduces the storage requirement with a smaller number of network parameters. In the time domain, the network parameters can be trained in a few subspaces, which enables efficient training for fast convergence. The model compression in the spatial domain is summarized into three categories as pre-train, pre-set, and compression-aware methods, respectively. With a series of integrable techniques discussed, such as sparse pruning, quantization, and entropy coding, we can ensemble them in an integration framework with lower computational complexity and storage. Besides of summary of recent technical advances, we have two findings for motivating future works: one is that the effective rank outperforms other sparse measures for network compression. The other is a spatial and temporal balance for tensorized neural networks.

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of 2, and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

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.

The sheer size of modern neural networks makes model serving a serious computational challenge. A popular class of compression techniques overcomes this challenge by pruning or sparsifying the weights of pretrained networks. While useful, these techniques often face serious tradeoffs between computational requirements and compression quality. In this work, we propose a novel optimization-based pruning framework that considers the combined effect of pruning (and updating) multiple weights subject to a sparsity constraint. Our approach, CHITA, extends the classical Optimal Brain Surgeon framework and results in significant improvements in speed, memory, and performance over existing optimization-based approaches for network pruning. CHITA's main workhorse performs combinatorial optimization updates on a memory-friendly representation of local quadratic approximation(s) of the loss function. On a standard benchmark of pretrained models and datasets, CHITA leads to significantly better sparsity-accuracy tradeoffs than competing methods. For example, for MLPNet with only 2% of the weights retained, our approach improves the accuracy by 63% relative to the state of the art. Furthermore, when used in conjunction with fine-tuning SGD steps, our method achieves significant accuracy gains over the state-of-the-art approaches.

Attention mechanisms have been widely used to capture long-range dependencies among nodes in Graph Transformers. Bottlenecked by the quadratic computational cost, attention mechanisms fail to scale in large graphs. Recent improvements in computational efficiency are mainly achieved by attention sparsification with random or heuristic-based graph subsampling, which falls short in data-dependent context reasoning. State space models (SSMs), such as Mamba, have gained prominence for their effectiveness and efficiency in modeling long-range dependencies in sequential data. However, adapting SSMs to non-sequential graph data presents a notable challenge. In this work, we introduce Graph-Mamba, the first attempt to enhance long-range context modeling in graph networks by integrating a Mamba block with the input-dependent node selection mechanism. Specifically, we formulate graph-centric node prioritization and permutation strategies to enhance context-aware reasoning, leading to a substantial improvement in predictive performance. Extensive experiments on ten benchmark datasets demonstrate that Graph-Mamba outperforms state-of-the-art methods in long-range graph prediction tasks, with a fraction of the computational cost in both FLOPs and GPU memory consumption. The code and models are publicly available at https://github.com/bowang-lab/Graph-Mamba.

In neural Information Retrieval (IR), 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. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than 9\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

Recent advances in Graph Neural Networks (GNNs) and Graph Transformers (GTs) have been driven by innovations in architectures and Positional Encodings (PEs), which are critical for augmenting node features and capturing graph topology. PEs are essential for GTs, where topological information would otherwise be lost without message-passing. However, PEs are often tested alongside novel architectures, making it difficult to isolate their effect on established models. To address this, we present a comprehensive benchmark of PEs in a unified framework that includes both message-passing GNNs and GTs. We also establish theoretical connections between MPNNs and GTs and introduce a sparsified GRIT attention mechanism to examine the influence of global connectivity. Our findings demonstrate that previously untested combinations of GNN architectures and PEs can outperform existing methods and offer a more comprehensive picture of the state-of-the-art. To support future research and experimentation in our framework, we make the code publicly available.

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.

While Graph Neural Networks have gained popularity in multiple domains, graph-structured input remains a major challenge due to (a) over-smoothing, (b) noisy neighbours (heterophily), and (c) the suspended animation problem. To address all these problems simultaneously, we propose a novel graph neural network FDGATII, inspired by attention mechanism's ability to focus on selective information supplemented with two feature preserving mechanisms. FDGATII combines Initial Residuals and Identity Mapping with the more expressive dynamic self-attention to handle noise prevalent from the neighbourhoods in heterophilic data sets. By using sparse dynamic attention, FDGATII is inherently parallelizable in design, whist efficient in operation; thus theoretically able to scale to arbitrary graphs with ease. Our approach has been extensively evaluated on 7 datasets. We show that FDGATII outperforms GAT and GCN based benchmarks in accuracy and performance on fully supervised tasks, obtaining state-of-the-art results on Chameleon and Cornell datasets with zero domain-specific graph pre-processing, and demonstrate its versatility and fairness.

Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years. However, these models often lack guarantees of existence and uniqueness, raising stability, performance, and reproducibility issues. In this paper, we present a new analysis of the existence and uniqueness of fixed points for implicit-depth neural networks based on the concept of subhomogeneous operators and the nonlinear Perron-Frobenius theory. Compared to previous similar analyses, our theory allows for weaker assumptions on the parameter matrices, thus yielding a more flexible framework for well-defined implicit networks. We illustrate the performance of the resulting subhomogeneous networks on feedforward, convolutional, and graph neural network examples.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.