Daily Papers

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

The efficient compression of large language models (LLMs) is becoming increasingly popular. However, recovering the accuracy of compressed LLMs is still a major challenge. Structural pruning with standard Low-Rank Adaptation (LoRA) is a common technique in current LLM compression. In structural pruning, the model architecture is modified unevenly, resulting in suboptimal performance in various downstream tasks via standard LoRA with fixed rank. To address this problem, we introduce RankAdaptor, an efficient fine-tuning method with hierarchical dynamic rank scheduling for pruned LLMs. An end-to-end automatic optimization flow is developed that utilizes a lightweight performance model to determine the different ranks during fine-tuning. Comprehensive experiments on popular benchmarks show that RankAdaptor consistently outperforms standard LoRA with structural pruning over different pruning settings. Without increasing the trainable parameters, RankAdaptor further reduces the accuracy performance gap between the recovery of the pruned model and the original model compared to standard LoRA.

Modern Large Language Models (LLMs) are composed of matrices with billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Being significantly large, such matrices can often be expressed in low-rank format with potential to relax resource requirements. Unlike prior works which focus on developing novel matrix decomposition algorithms, in this work we first study the emergence of low-rank structures across matrices within different layers of LLMs and establish a consequential relationship between the gradient dynamics and emerging low-rank expressiveness of matrices. Our findings reveal that different layers exhibit varying levels of converged low-rank structure, necessitating a non-uniform rank reduction across them to minimize performance drop due to compression. In view of that, we present Weight Low-Rank Projection (WeLore) that unifies weight compression and memory-efficient fine-tuning as ONE, in a data-agnostic and one-shot way. WeLore capitalizes the heavy-tail distribution of singular values to identify a suitable rank reduction ratio for matrices within LLMs. Going beyond only as a compression technique, WeLore categorizes weight matrices into Low-rank Components (LRCs) and Non-Low-rank Components (N-LRCs) based on their ability to express themselves as low-rank. Our gradient perspective and extensive experiments illustrate that LRCs tend to have better finetuning capabilities and can closely mimic (sometimes outperform) the training loss trajectory and performance of full-finetuning with notable memory and compute footprint reduction. For example, finetuning a 50\% compressed LLaMa-2 7B model using only a fraction of parameters in LRCs (WeLore) can outperform its full finetuning with ~3x better throughput and ~0.6x GPU requirement. Our codes are available at https://github.com/VITA-Group/welore

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.

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of parameters and memory, either through low-rank adaptation or factorization. While effective for fine-tuning, low-rank structures are generally less suitable for pretraining because they restrict parameters to a low-dimensional subspace. In this work, we propose to parameterize the weights as a sum of low-rank and sparse matrices for pretraining, which we call SLTrain. The low-rank component is learned via matrix factorization, while for the sparse component, we employ a simple strategy of uniformly selecting the sparsity support at random and learning only the non-zero entries with the fixed support. While being simple, the random fixed-support sparse learning strategy significantly enhances pretraining when combined with low-rank learning. Our results show that SLTrain adds minimal extra parameters and memory costs compared to pretraining with low-rank parameterization, yet achieves substantially better performance, which is comparable to full-rank training. Remarkably, when combined with quantization and per-layer updates, SLTrain can reduce memory requirements by up to 73% when pretraining the LLaMA 7B model.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Deep Neural Networks (DNNs) have been a large driver and enabler for AI breakthroughs in recent years. These models have been getting larger in their attempt to become more accurate and tackle new upcoming use-cases, including AR/VR and intelligent assistants. However, the training process of such large models is a costly and time-consuming process, which typically yields a single model to fit all targets. To mitigate this, various techniques have been proposed in the literature, including pruning, sparsification or quantization of the model weights and updates. While able to achieve high compression rates, they often incur computational overheads or accuracy penalties. Alternatively, factorization methods have been leveraged to incorporate low-rank compression in the training process. Similarly, such techniques (e.g.,~SVD) frequently rely on the computationally expensive decomposition of layers and are potentially sub-optimal for non-linear models, such as DNNs. In this work, we take a further step in designing efficient low-rank models and propose Maestro, a framework for trainable low-rank layers. Instead of regularly applying a priori decompositions such as SVD, the low-rank structure is built into the training process through a generalized variant of Ordered Dropout. This method imposes an importance ordering via sampling on the decomposed DNN structure. Our theoretical analysis demonstrates that our method recovers the SVD decomposition of linear mapping on uniformly distributed data and PCA for linear autoencoders. We further apply our technique on DNNs and empirically illustrate that Maestro enables the extraction of lower footprint models that preserve model performance while allowing for graceful accuracy-latency tradeoff for the deployment to devices of different capabilities.

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

In this paper, we introduce Nested Low-Rank Adaptation (NoRA), a novel approach to parameter-efficient fine-tuning that extends the capabilities of Low-Rank Adaptation (LoRA) techniques. Vanilla LoRA overlooks pre-trained weight inheritance and still requires fine-tuning numerous parameters. To addresses these issues, our NoRA adopts a dual-layer nested structure with Singular Value Decomposition (SVD), effectively leveraging original matrix knowledge while reducing tunable parameters. Specifically, NoRA freezes the outer LoRA weights and utilizes an inner LoRA design, providing enhanced control over model optimization. This approach allows the model to more precisely adapt to specific tasks while maintaining a compact parameter space. By freezing outer LoRA weights and using an inner LoRA design, NoRA enables precise task adaptation with a compact parameter space. Evaluations on tasks including commonsense reasoning with large language models, fine-tuning vision-language models, and subject-driven generation demonstrate NoRA's superiority over LoRA and its variants. Code will be released upon acceptance.

In this paper, we propose the Hierarchical Document Transformer (HDT), a novel sparse Transformer architecture tailored for structured hierarchical documents. Such documents are extremely important in numerous domains, including science, law or medicine. However, most existing solutions are inefficient and fail to make use of the structure inherent to documents. HDT exploits document structure by introducing auxiliary anchor tokens and redesigning the attention mechanism into a sparse multi-level hierarchy. This approach facilitates information exchange between tokens at different levels while maintaining sparsity, thereby enhancing computational and memory efficiency while exploiting the document structure as an inductive bias. We address the technical challenge of implementing HDT's sample-dependent hierarchical attention pattern by developing a novel sparse attention kernel that considers the hierarchical structure of documents. As demonstrated by our experiments, utilizing structural information present in documents leads to faster convergence, higher sample efficiency and better performance on downstream tasks.

Document retrieval is a core component of question-answering systems, as it enables conditioning answer generation on new and large-scale corpora. While effective, the standard practice of encoding documents into high-dimensional embeddings for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. In this paper, we propose a tree-based method for organizing and representing reference documents at various granular levels, which offers the flexibility to balance cost and utility, and eases the inspection of the corpus content and retrieval operations. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches, hence directly optimizing for retrieval performance. Our evaluations show that ReTreever generally preserves full representation accuracy. Its hierarchical structure further provides strong coarse representations and enhances transparency by indirectly learning meaningful semantic groupings. Among hierarchical retrieval methods, ReTreever achieves the best retrieval accuracy at the lowest latency, proving that this family of techniques can be viable in practical applications.

Large language models (LLMs) show excellent performance in difficult tasks, but they often require massive memories and computational resources. How to reduce the parameter scale of LLMs has become research hotspots. In this study, we make an important observation that the multi-head self-attention (MHA) sub-layer of Transformer exhibits noticeable low-rank structure, while the feed-forward network (FFN) sub-layer does not. With this regard, we design a mixed compression model, which organically combines Low-Rank matrix approximation And structured Pruning (LoRAP). For the MHA sub-layer, we propose an input activation weighted singular value decomposition method to strengthen the low-rank characteristic. Furthermore, we discover that the weight matrices in MHA sub-layer have different low-rank degrees. Thus, a novel parameter allocation scheme according to the discrepancy of low-rank degrees is devised. For the FFN sub-layer, we propose a gradient-free structured channel pruning method. During the pruning, we get an interesting finding that the least important 1% of parameter actually play a vital role in model performance. Extensive evaluations on zero-shot perplexity and zero-shot task classification indicate that our proposal is superior to previous structured compression rivals under multiple compression ratios.

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.

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-of-the-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Many practical applications, such as recommender systems and learning to rank, involve solving multiple similar tasks. One example is learning of recommendation policies for users with similar movie preferences, where the users may still rank the individual movies slightly differently. Such tasks can be organized in a hierarchy, where similar tasks are related through a shared structure. In this work, we formulate this problem as a contextual off-policy optimization in a hierarchical graphical model from logged bandit feedback. To solve the problem, we propose a hierarchical off-policy optimization algorithm (HierOPO), which estimates the parameters of the hierarchical model and then acts pessimistically with respect to them. We instantiate HierOPO in linear Gaussian models, for which we also provide an efficient implementation and analysis. We prove per-task bounds on the suboptimality of the learned policies, which show a clear improvement over not using the hierarchical model. We also evaluate the policies empirically. Our theoretical and empirical results show a clear advantage of using the hierarchy over solving each task independently.

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank approximation and its application in adaptation can sometimes be obscure, leaving practitioners and researchers with questions about its true capabilities and limitations. This paper seeks to clarify low-rank approximation and adaptation by offering a comprehensive guide that reveals their inner workings and explains their utility in a clear and accessible way. Our focus here is to develop a solid intuition for how low-rank approximation and adaptation operate, and why they are so effective. We begin with basic concepts and gradually build up to the mathematical underpinnings, ensuring that readers of all backgrounds can gain a deeper understanding of low-rank approximation and adaptation. We strive to strike a balance between informal explanations and rigorous mathematics, ensuring that both newcomers and experienced experts can benefit from this survey. Additionally, we introduce new low-rank decomposition and adaptation algorithms that have not yet been explored in the field, hoping that future researchers will investigate their potential applicability.

Low-rank adaptation is a popular parameter-efficient fine-tuning method for large language models. In this paper, we analyze the impact of low-rank updating, as implemented in LoRA. Our findings suggest that the low-rank updating mechanism may limit the ability of LLMs to effectively learn and memorize new knowledge. Inspired by this observation, we propose a new method called MoRA, which employs a square matrix to achieve high-rank updating while maintaining the same number of trainable parameters. To achieve it, we introduce the corresponding non-parameter operators to reduce the input dimension and increase the output dimension for the square matrix. Furthermore, these operators ensure that the weight can be merged back into LLMs, which makes our method can be deployed like LoRA. We perform a comprehensive evaluation of our method across five tasks: instruction tuning, mathematical reasoning, continual pretraining, memory and pretraining. Our method outperforms LoRA on memory-intensive tasks and achieves comparable performance on other tasks.

The rapid expansion of Large Language Models (LLMs) has posed significant challenges regarding the computational resources required for fine-tuning and deployment. Recent advancements in low-rank adapters have demonstrated their efficacy in parameter-efficient fine-tuning (PEFT) of these models. This retrospective paper comprehensively discusses innovative approaches that synergize low-rank representations with Neural Architecture Search (NAS) techniques, particularly weight-sharing super-networks. Robust solutions for compressing and fine-tuning large pre-trained models are developed by integrating these methodologies. Our analysis highlights the potential of these combined strategies to democratize the use of LLMs, making them more accessible for deployment in resource-constrained environments. The resulting models exhibit reduced memory footprints and faster inference times, paving the way for more practical and scalable applications of LLMs. Models and code are available at https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning.

Despite large neural networks demonstrating remarkable abilities to complete different tasks, they require excessive memory usage to store the optimization states for training. To alleviate this, the low-rank adaptation (LoRA) is proposed to reduce the optimization states by training fewer parameters. However, LoRA restricts overall weight update matrices to be low-rank, limiting the model performance. In this work, we investigate the dynamics of LoRA and identify that it can be approximated by a random projection. Based on this observation, we propose Flora, which is able to achieve high-rank updates by resampling the projection matrices while enjoying the sublinear space complexity of optimization states. We conduct experiments across different tasks and model architectures to verify the effectiveness of our approach.

Applying a pre-trained large model to downstream tasks is prohibitive under resource-constrained conditions. Recent dominant approaches for addressing efficiency issues involve adding a few learnable parameters to the fixed backbone model. This strategy, however, leads to more challenges in loading large models for downstream fine-tuning with limited resources. In this paper, we propose a novel method for increasing the parameter efficiency of pre-trained models by introducing an intermediate pre-training stage. To this end, we first employ low-rank approximation to compress the original large model and then devise a feature distillation module and a weight perturbation regularization module. These modules are specifically designed to enhance the low-rank model. In particular, we update only the low-rank model while freezing the backbone parameters during pre-training. This allows for direct and efficient utilization of the low-rank model for downstream fine-tuning tasks. The proposed method achieves both efficiencies in terms of required parameters and computation time while maintaining comparable results with minimal modifications to the backbone architecture. Specifically, when applied to three vision-only and one vision-language Transformer models, our approach often demonstrates a merely sim0.6 point decrease in performance while reducing the original parameter size by 1/3 to 2/3.

Large Language Models (LLMs) have recently gained popularity due to their impressive few-shot performance across various downstream tasks. However, fine-tuning all parameters and storing a unique model for each downstream task or domain becomes impractical because of the massive size of checkpoints (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank modifications to the original weights of an LLM, enabling efficient adaptation and storage for task-specific models. These methods can reduce the number of parameters needed to fine-tune an LLM by several orders of magnitude. Yet, these methods face two primary limitations: 1) the parameter reduction is lower-bounded by the rank one decomposition, and 2) the extent of reduction is heavily influenced by both the model architecture and the chosen rank. For instance, in larger models, even a rank one decomposition might exceed the number of parameters truly needed for adaptation. In this paper, we introduce NOLA, which overcomes the rank one lower bound present in LoRA. It achieves this by re-parameterizing the low-rank matrices in LoRA using linear combinations of randomly generated matrices (basis) and optimizing the linear mixture coefficients only. This approach allows us to decouple the number of trainable parameters from both the choice of rank and the network architecture. We present adaptation results using GPT-2 and ViT in natural language and computer vision tasks. NOLA performs as well as, or better than models with equivalent parameter counts. Furthermore, we demonstrate that we can halve the parameters in larger models compared to LoRA with rank one, without sacrificing performance.

Low-Rank Adaptation (LoRA) has emerged as a popular technique for fine-tuning large language models (LLMs) to various domains due to its modular design and widespread availability on platforms like Huggingface. This modularity has sparked interest in combining multiple LoRAs to enhance LLM capabilities. However, existing methods for LoRA composition primarily focus on task-specific adaptations that require additional training, and current model merging techniques often fail to fully leverage LoRA's modular nature, leading to parameter interference and performance degradation. In this paper, we investigate the feasibility of disassembling and reassembling multiple LoRAs at a finer granularity, analogous to assembling LEGO blocks. We introduce the concept of Minimal Semantic Units (MSUs), where the parameters corresponding to each rank in LoRA function as independent units. These MSUs demonstrate permutation invariance and concatenation-summation equivalence properties, enabling flexible combinations to create new LoRAs. Building on these insights, we propose the LoRA-LEGO framework. This framework conducts rank-wise parameter clustering by grouping MSUs from different LoRAs into k clusters. The centroid of each cluster serves as a representative MSU, enabling the assembly of a merged LoRA with an adjusted rank of k. Additionally, we apply a dual reweighting strategy to optimize the scale of the merged LoRA. Experiments across various benchmarks demonstrate that our method outperforms existing approaches in LoRA merging.

Modeling long range dependencies in sequential data is a fundamental step towards attaining human-level performance in many modalities such as text, vision, audio and video. While attention-based models are a popular and effective choice in modeling short-range interactions, their performance on tasks requiring long range reasoning has been largely inadequate. In an exciting result, Gu et al. (ICLR 2022) proposed the Structured State Space (S4) architecture delivering large gains over state-of-the-art models on several long-range tasks across various modalities. The core proposition of S4 is the parameterization of state matrices via a diagonal plus low rank structure, allowing efficient computation. In this work, we show that one can match the performance of S4 even without the low rank correction and thus assuming the state matrices to be diagonal. Our Diagonal State Space (DSS) model matches the performance of S4 on Long Range Arena tasks, speech classification on Speech Commands dataset, while being conceptually simpler and straightforward to implement.

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular neural network models is obscure in most cases and may vary from layer to layer even in the same network. Prior structured matrices proposed for efficient DNNs were mostly hand-crafted without a generalized framework to systematically learn them. To address this issue, we propose a generalized and differentiable framework to learn efficient structures of weight matrices by gradient descent. We first define a new class of structured matrices that covers a wide range of structured matrices in the literature by adjusting the structural parameters. Then, the frequency-domain differentiable parameterization scheme based on the Gaussian-Dirichlet kernel is adopted to learn the structural parameters by proximal gradient descent. On the image and language tasks, our method learns efficient DNNs with structured matrices, achieving lower complexity and/or higher performance than prior approaches that employ low-rank, block-sparse, or block-low-rank matrices.

The rapid growth of large models has raised concerns about their environmental impact and equity in accessibility due to significant computational costs. Low-Rank Adapters (LoRA) offer a lightweight solution for finetuning large models, resulting in an abundance of publicly available adapters tailored to diverse domains. We ask: Can these pretrained adapters be leveraged to further streamline adaptation to new tasks while addressing these challenges? We introduce EigenLoRAx, a parameter-efficient finetuning method that recycles existing adapters to create a principal subspace aligned with their shared domain knowledge which can be further augmented with orthogonal basis vectors in low-resource scenarios. This enables rapid adaptation to new tasks by learning only lightweight coefficients on the principal components of the subspace - eliminating the need to finetune entire adapters. EigenLoRAx requires significantly fewer parameters and memory, improving efficiency for both training and inference. Our method demonstrates strong performance across diverse domains and tasks, offering a scalable for edge-based applications, personalization, and equitable deployment of large models in resource-constrained environments.

With the ever-growing size of pretrained models (PMs), fine-tuning them has become more expensive and resource-hungry. As a remedy, low-rank adapters (LoRA) keep the main pretrained weights of the model frozen and just introduce some learnable truncated SVD modules (so-called LoRA blocks) to the model. While LoRA blocks are parameter-efficient, they suffer from two major problems: first, the size of these blocks is fixed and cannot be modified after training (for example, if we need to change the rank of LoRA blocks, then we need to re-train them from scratch); second, optimizing their rank requires an exhaustive search and effort. In this work, we introduce a dynamic low-rank adaptation (DyLoRA) technique to address these two problems together. Our DyLoRA method trains LoRA blocks for a range of ranks instead of a single rank by sorting the representation learned by the adapter module at different ranks during training. We evaluate our solution on different natural language understanding (GLUE benchmark) and language generation tasks (E2E, DART and WebNLG) using different pretrained models such as RoBERTa and GPT with different sizes. Our results show that we can train dynamic search-free models with DyLoRA at least 4 to 7 times (depending to the task) faster than LoRA without significantly compromising performance. Moreover, our models can perform consistently well on a much larger range of ranks compared to LoRA.

Low-rank adaptation (LoRA) and its variants have recently gained much interest due to their ability to avoid excessive inference costs. However, LoRA still encounters the following challenges: (1) Limitation of low-rank assumption; and (2) Its initialization method may be suboptimal. To this end, we propose PMSS(Pre-trained Matrices Skeleton Selection), which enables high-rank updates with low costs while leveraging semantic and linguistic information inherent in pre-trained weight. It achieves this by selecting skeletons from the pre-trained weight matrix and only learning a small matrix instead. Experiments demonstrate that PMSS outperforms LoRA and other fine-tuning methods across tasks with much less trainable parameters. We demonstrate its effectiveness, especially in handling complex tasks such as DROP benchmark(+3.4%/+5.9% on LLaMA2-7B/13B) and math reasoning(+12.89%/+5.61%/+3.11% on LLaMA2-7B, Mistral-7B and Gemma-7B of GSM8K). The code and model will be released soon.

Continual learning (CL) enables models to adapt to new tasks and environments without forgetting previously learned knowledge. While current CL setups have ignored the relationship between labels in the past task and the new task with or without small task overlaps, real-world scenarios often involve hierarchical relationships between old and new tasks, posing another challenge for traditional CL approaches. To address this challenge, we propose a novel multi-level hierarchical class incremental task configuration with an online learning constraint, called hierarchical label expansion (HLE). Our configuration allows a network to first learn coarse-grained classes, with data labels continually expanding to more fine-grained classes in various hierarchy depths. To tackle this new setup, we propose a rehearsal-based method that utilizes hierarchy-aware pseudo-labeling to incorporate hierarchical class information. Additionally, we propose a simple yet effective memory management and sampling strategy that selectively adopts samples of newly encountered classes. Our experiments demonstrate that our proposed method can effectively use hierarchy on our HLE setup to improve classification accuracy across all levels of hierarchies, regardless of depth and class imbalance ratio, outperforming prior state-of-the-art works by significant margins while also outperforming them on the conventional disjoint, blurry and i-Blurry CL setups.

In this paper we generalize and extend an idea of low-rank adaptation (LoRA) of large language models (LLMs) based on Transformer architecture. Widely used LoRA-like methods of fine-tuning LLMs are based on matrix factorization of gradient update. We introduce LoTR, a novel approach for parameter-efficient fine-tuning of LLMs which represents a gradient update to parameters in a form of tensor decomposition. Low-rank adapter for each layer is constructed as a product of three matrices, and tensor structure arises from sharing left and right multipliers of this product among layers. Simultaneous compression of a sequence of layers with low-rank tensor representation allows LoTR to archive even better parameter efficiency then LoRA especially for deep models. Moreover, the core tensor does not depend on original weight dimension and can be made arbitrary small, which allows for extremely cheap and fast downstream fine-tuning.

State-of-the-art LLMs often rely on scale with high computational costs, which has sparked a research agenda to reduce parameter counts and costs without significantly impacting performance. Our study focuses on Transformer-based LLMs, specifically applying low-rank parametrization to the computationally intensive feedforward networks (FFNs), which are less studied than attention blocks. In contrast to previous works, (i) we explore low-rank parametrization at scale, up to 1.3B parameters; (ii) within Transformer language models rather than convolutional architectures; and (iii) starting from training from scratch. Experiments on the large RefinedWeb dataset show that low-rank parametrization is both efficient (e.g., 2.6times FFN speed-up with 32\% parameters) and effective during training. Interestingly, these structured FFNs exhibit steeper scaling curves than the original models. Motivated by this finding, we develop the wide and structured networks surpassing the current medium-sized and large-sized Transformer in perplexity and throughput performance. Our code is available at https://github.com/CLAIRE-Labo/StructuredFFN/tree/main.

With the proliferation of large pre-trained language models (PLMs), fine-tuning all model parameters becomes increasingly inefficient, particularly when dealing with numerous downstream tasks that entail substantial training and storage costs. Several approaches aimed at achieving parameter-efficient fine-tuning (PEFT) have been proposed. Among them, Low-Rank Adaptation (LoRA) stands out as an archetypal method, incorporating trainable rank decomposition matrices into each target module. Nevertheless, LoRA does not consider the varying importance of each layer. To address these challenges, we introduce PRILoRA, which linearly allocates a different rank for each layer, in an increasing manner, and performs pruning throughout the training process, considering both the temporary magnitude of weights and the accumulated statistics of the input to any given layer. We validate the effectiveness of PRILoRA through extensive experiments on eight GLUE benchmarks, setting a new state of the art.

Despite the dominance and effectiveness of scaling, resulting in large networks with hundreds of billions of parameters, the necessity to train overparametrized models remains poorly understood, and alternative approaches do not necessarily make it cheaper to train high-performance models. In this paper, we explore low-rank training techniques as an alternative approach to training large neural networks. We introduce a novel method called ReLoRA, which utilizes low-rank updates to train high-rank networks. We apply ReLoRA to pre-training transformer language models with up to 350M parameters and demonstrate comparable performance to regular neural network training. Furthermore, we observe that the efficiency of ReLoRA increases with model size, making it a promising approach for training multi-billion-parameter networks efficiently. Our findings shed light on the potential of low-rank training techniques and their implications for scaling laws.

In this work, we study how well the learned weights of a neural network utilize the space available to them. This notion is related to capacity, but additionally incorporates the interaction of the network architecture with the dataset. Most learned weights appear to be full rank, and are therefore not amenable to low rank decomposition. This deceptively implies that the weights are utilizing the entire space available to them. We propose a simple data-driven transformation that projects the weights onto the subspace where the data and the weight interact. This preserves the functional mapping of the layer and reveals its low rank structure. In our findings, we conclude that most models utilize a fraction of the available space. For instance, for ViTB-16 and ViTL-16 trained on ImageNet, the mean layer utilization is 35% and 20% respectively. Our transformation results in reducing the parameters to 50% and 25% respectively, while resulting in less than 0.2% accuracy drop after fine-tuning. We also show that self-supervised pre-training drives this utilization up to 70%, justifying its suitability for downstream tasks.

Large pre-trained models (LPMs) have demonstrated exceptional performance in diverse natural language processing and computer vision tasks. However, fully fine-tuning these models poses substantial memory challenges, particularly in resource-constrained environments. Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, mitigate this issue by adjusting only a small subset of parameters. Nevertheless, these methods typically employ random initialization for low-rank matrices, which can lead to inefficiencies in gradient descent and diminished generalizability due to suboptimal starting points. To address these limitations, we propose SVFit, a novel PEFT approach that leverages singular value decomposition (SVD) to initialize low-rank matrices using critical singular values as trainable parameters. Specifically, SVFit performs SVD on the pre-trained weight matrix to obtain the best rank-r approximation matrix, emphasizing the most critical singular values that capture over 99% of the matrix's information. These top-r singular values are then used as trainable parameters to scale the fundamental subspaces of the matrix, facilitating rapid domain adaptation. Extensive experiments across various pre-trained models in natural language understanding, text-to-image generation, and image classification tasks reveal that SVFit outperforms LoRA while requiring 16 times fewer trainable parameters.

Fine-tuning pre-trained large language models in a parameter-efficient manner is widely studied for its effectiveness and efficiency. The popular method of low-rank adaptation (LoRA) offers a notable approach, hypothesizing that the adaptation process is intrinsically low-dimensional. Although LoRA has demonstrated commendable performance, it is implemented with a fixed and unalterable intrinsic rank that might not always be the ideal choice. Recognizing the need for more flexible adaptation, we extend the methodology of LoRA to an innovative approach we call sparse low-rank adaptation (SoRA) that enables dynamic adjustments to the intrinsic rank during the adaptation process. We achieve this through the incorporation of a gate unit optimized with proximal gradient method in the training stage, controlling the cardinality of rank under the sparsity of the gate. In the subsequent inference stage, we eliminate the parameter blocks corresponding to the zeroed-out ranks, to reduce each SoRA module back to a concise yet rank-optimal LoRA. Our approach strengthens the representation power of LoRA by initializing it with a higher rank, while efficiently taming a temporarily increased number of parameters via updating in a sparse way. We further introduce a sparsifying scheduler for SoRA, aiming to examine the impact of the number of non-zero parameters on the model's memorization and generalization. Our experimental results demonstrate that SoRA can outperform other baselines even with 70% retained parameters and 70% training time.

Open vocabulary models (e.g. CLIP) have shown strong performance on zero-shot classification through their ability generate embeddings for each class based on their (natural language) names. Prior work has focused on improving the accuracy of these models through prompt engineering or by incorporating a small amount of labeled downstream data (via finetuning). However, there has been little focus on improving the richness of the class names themselves, which can pose issues when class labels are coarsely-defined and are uninformative. We propose Classification with Hierarchical Label Sets (or CHiLS), an alternative strategy for zero-shot classification specifically designed for datasets with implicit semantic hierarchies. CHiLS proceeds in three steps: (i) for each class, produce a set of subclasses, using either existing label hierarchies or by querying GPT-3; (ii) perform the standard zero-shot CLIP procedure as though these subclasses were the labels of interest; (iii) map the predicted subclass back to its parent to produce the final prediction. Across numerous datasets with underlying hierarchical structure, CHiLS leads to improved accuracy in situations both with and without ground-truth hierarchical information. CHiLS is simple to implement within existing zero-shot pipelines and requires no additional training cost. Code is available at: https://github.com/acmi-lab/CHILS.

Low-Rank Adaptation (LoRA), a parameter-efficient fine-tuning method that leverages low-rank adaptation of weight matrices, has emerged as a prevalent technique for fine-tuning pre-trained models such as large language models and diffusion models. Despite its huge success in practice, the theoretical underpinnings of LoRA have largely remained unexplored. This paper takes the first step to bridge this gap by theoretically analyzing the expressive power of LoRA. We prove that, for fully connected neural networks, LoRA can adapt any model f to accurately represent any smaller target model f if LoRA-rank geq(width of f) times text{depth of f}{depth of f}. We also quantify the approximation error when LoRA-rank is lower than the threshold. For Transformer networks, we show any model can be adapted to a target model of the same size with rank-(text{embedding size}{2}) LoRA adapters.

As large language models (LLMs) have become increasingly compute and memory intensive, parameter-efficient fine-tuning (PEFT) methods are now a common strategy to fine-tune LLMs. A popular PEFT method is Low-Rank Adapters (LoRA), which adds trainable low-rank "adapters" to selected layers. Each adapter consists of a low-rank matrix product, multiplicatively scaled by a rank-dependent factor. This scaling factor, which divides adapters by a factor of the rank, results in slowed learning and stunted performance for LoRA with higher-rank adapters. Consequently, the use of LoRA in practice has generally been limited to very low ranks. In this work, we study the impact of the scaling factor on the learning process and prove that LoRA adapters should be divided by a factor of the square root of the rank. Modifying LoRA with the appropriate scaling factor, which we call the rank-stabilized LoRA (rsLoRA) method, easily provides for a fine-tuning compute/performance trade-off, where larger ranks can be used to trade off increased computational resources during training for better fine-tuning performance, with no change in inference computing cost.

Low-rank approximation techniques have become the de facto standard for fine-tuning Large Language Models (LLMs) due to their reduced computational and memory requirements. This paper investigates the effectiveness of these methods in capturing the shift of fine-tuning datasets from the initial pre-trained data distribution. Our findings reveal that there are cases in which low-rank fine-tuning falls short in learning such shifts. This, in turn, produces non-negligible side effects, especially when fine-tuning is adopted for toxicity mitigation in pre-trained models, or in scenarios where it is important to provide fair models. Through comprehensive empirical evidence on several models, datasets, and tasks, we show that low-rank fine-tuning inadvertently preserves undesirable biases and toxic behaviors. We also show that this extends to sequential decision-making tasks, emphasizing the need for careful evaluation to promote responsible LLMs development.

Universally modeling all typical information extraction tasks (UIE) with one generative language model (GLM) has revealed great potential by the latest study, where various IE predictions are unified into a linearized hierarchical expression under a GLM. Syntactic structure information, a type of effective feature which has been extensively utilized in IE community, should also be beneficial to UIE. In this work, we propose a novel structure-aware GLM, fully unleashing the power of syntactic knowledge for UIE. A heterogeneous structure inductor is explored to unsupervisedly induce rich heterogeneous structural representations by post-training an existing GLM. In particular, a structural broadcaster is devised to compact various latent trees into explicit high-order forests, helping to guide a better generation during decoding. We finally introduce a task-oriented structure fine-tuning mechanism, further adjusting the learned structures to most coincide with the end-task's need. Over 12 IE benchmarks across 7 tasks our system shows significant improvements over the baseline UIE system. Further in-depth analyses show that our GLM learns rich task-adaptive structural bias that greatly resolves the UIE crux, the long-range dependence issue and boundary identifying. Source codes are open at https://github.com/ChocoWu/LasUIE.

With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training costs, a prominent line of work uses low-rank matrix factorizations to represent the network weights. Although able to retain accuracy, we observe that low-rank methods tend to compromise model robustness against adversarial perturbations. By modeling robustness in terms of the condition number of the neural network, we argue that this loss of robustness is due to the exploding singular values of the low-rank weight matrices. Thus, we introduce a robust low-rank training algorithm that maintains the network's weights on the low-rank matrix manifold while simultaneously enforcing approximate orthonormal constraints. The resulting model reduces both training and inference costs while ensuring well-conditioning and thus better adversarial robustness, without compromising model accuracy. This is shown by extensive numerical evidence and by our main approximation theorem that shows the computed robust low-rank network well-approximates the ideal full model, provided a highly performing low-rank sub-network exists.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

The recent trend in scaling language models has led to a growing demand for parameter-efficient tuning (PEFT) methods such as LoRA (Low-Rank Adaptation). LoRA consistently matches or surpasses the full fine-tuning baseline with fewer parameters. However, handling numerous task-specific or user-specific LoRA modules on top of a base model still presents significant storage challenges. To address this, we introduce LoRA-XS (Low-Rank Adaptation with eXtremely Small number of parameters), a novel approach leveraging Singular Value Decomposition (SVD) for parameter-efficient fine-tuning. LoRA-XS introduces a small r x r weight matrix between frozen LoRA matrices, which are constructed by SVD of the original weight matrix. Training only r x r weight matrices ensures independence from model dimensions, enabling more parameter-efficient fine-tuning, especially for larger models. LoRA-XS achieves a remarkable reduction of trainable parameters by over 100x in 7B models compared to LoRA. Our benchmarking across various scales, including GLUE, GSM8k, and MATH benchmarks, shows that our approach outperforms LoRA and recent state-of-the-art approaches like VeRA in terms of parameter efficiency while maintaining competitive performance.

Recent low-rank training methods, such as GaLore, have significantly reduced the memory required to optimize large language models (LLMs). However, these methods often suffer from time-consuming low-rank projection estimations. In particular, the singular value decomposition (SVD) in GaLore can consume more than 80\% of the total training time. To address this issue, we propose GaLore+, which uses cross-head low-rank projection to reduce the substantial time consumption in estimating low-rank projections for multi-head attention. In addition, we employ randomized subspace iteration to achieve fast SVD. To further enhance performance, we propose sparsely coded residuals to reduce the errors caused by low-rank approximation on the first- and second-order moments of the optimizers and weight updates. We evaluate GaLore+ on arithmetic reasoning and natural language generation datasets. Our experiments demonstrate that GaLore+ delivers superior performance while achieving approximately 4times fine-tuning speed compared to vanilla GaLore.

Parameter-efficient fine-tuning (PEFT) is a popular method for tailoring pre-trained large language models (LLMs), especially as the models' scale and the diversity of tasks increase. Low-rank adaptation (LoRA) is based on the idea that the adaptation process is intrinsically low-dimensional, i.e., significant model changes can be represented with relatively few parameters. However, decreasing the rank encounters challenges with generalization errors for specific tasks when compared to full-parameter fine-tuning. We present MELoRA, a mini-ensemble low-rank adapters that uses fewer trainable parameters while maintaining a higher rank, thereby offering improved performance potential. The core idea is to freeze original pretrained weights and train a group of mini LoRAs with only a small number of parameters. This can capture a significant degree of diversity among mini LoRAs, thus promoting better generalization ability. We conduct a theoretical analysis and empirical studies on various NLP tasks. Our experimental results show that, compared to LoRA, MELoRA achieves better performance with 8 times fewer trainable parameters on natural language understanding tasks and 36 times fewer trainable parameters on instruction following tasks, which demonstrates the effectiveness of MELoRA.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Training Large Language Models (LLMs) presents significant memory challenges, predominantly due to the growing size of weights and optimizer states. Common memory-reduction approaches, such as low-rank adaptation (LoRA), add a trainable low-rank matrix to the frozen pre-trained weight in each layer, reducing trainable parameters and optimizer states. However, such approaches typically underperform training with full-rank weights in both pre-training and fine-tuning stages since they limit the parameter search to a low-rank subspace and alter the training dynamics, and further, may require full-rank warm start. In this work, we propose Gradient Low-Rank Projection (GaLore), a training strategy that allows full-parameter learning but is more memory-efficient than common low-rank adaptation methods such as LoRA. Our approach reduces memory usage by up to 65.5% in optimizer states while maintaining both efficiency and performance for pre-training on LLaMA 1B and 7B architectures with C4 dataset with up to 19.7B tokens, and on fine-tuning RoBERTa on GLUE tasks. Our 8-bit GaLore further reduces optimizer memory by up to 82.5% and total training memory by 63.3%, compared to a BF16 baseline. Notably, we demonstrate, for the first time, the feasibility of pre-training a 7B model on consumer GPUs with 24GB memory (e.g., NVIDIA RTX 4090) without model parallel, checkpointing, or offloading strategies.

Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern hardware. Moreover, unlike quantization, the compressed linear layers remain fully differentiable and all the parameters trainable, while being able to leverage the existing highly efficient kernels over floating point matrices. We study the potential to compress Large Language Models (LLMs) for monolingual Code generation via Low Rank Decomposition (LoRD) and observe that ranks for the linear layers in these models can be reduced by upto 39.58% with less than 1% increase in perplexity. We then use Low Rank Decomposition (LoRD) to compress StarCoder 16B to 13.2B parameter with no drop and to 12.3B with minimal drop in HumanEval Pass@1 score, in less than 10 minutes on a single A100. The compressed models speeds up inference by up to 22.35% with just a single line of change in code over huggingface's implementation with pytorch backend. Low Rank Decomposition (LoRD) models remain compatible with state of the art near-lossless quantization method such as SpQR, which allows leveraging further compression gains of quantization. Lastly, QLoRA over Low Rank Decomposition (LoRD) model further reduces memory requirements by as much as 21.2% over vanilla QLoRA while offering similar gains from parameter efficient fine tuning. Our work shows Low Rank Decomposition (LoRD) as a promising new paradigm for LLM compression.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

Low-rank adapters have become standard for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a learnable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90 times fewer learnable parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

The continually increasing number of documents produced each year necessitates ever improving information processing methods for searching, retrieving, and organizing text. Central to these information processing methods is document classification, which has become an important application for supervised learning. Recently the performance of these traditional classifiers has degraded as the number of documents has increased. This is because along with this growth in the number of documents has come an increase in the number of categories. This paper approaches this problem differently from current document classification methods that view the problem as multi-class classification. Instead we perform hierarchical classification using an approach we call Hierarchical Deep Learning for Text classification (HDLTex). HDLTex employs stacks of deep learning architectures to provide specialized understanding at each level of the document hierarchy.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

While recent vision-and-language models (VLMs) like CLIP are a powerful tool for analyzing text and images in a shared semantic space, they do not explicitly model the hierarchical nature of the set of texts which may describe an image. Conversely, existing multimodal hierarchical representation learning methods require costly training from scratch, failing to leverage the knowledge encoded by state-of-the-art multimodal foundation models. In this work, we study the knowledge of existing foundation models, finding that they exhibit emergent understanding of visual-semantic hierarchies despite not being directly trained for this purpose. We propose the Radial Embedding (RE) framework for probing and optimizing hierarchical understanding, and contribute the HierarCaps dataset, a benchmark facilitating the study of hierarchical knowledge in image--text representations, constructed automatically via large language models. Our results show that foundation VLMs exhibit zero-shot hierarchical understanding, surpassing the performance of prior models explicitly designed for this purpose. Furthermore, we show that foundation models may be better aligned to hierarchical reasoning via a text-only fine-tuning phase, while retaining pretraining knowledge.

Recommending novel content, which expands user horizons by introducing them to new interests, has been shown to improve users' long-term experience on recommendation platforms chen2021values. Users however are not constantly looking to explore novel content. It is therefore crucial to understand their novelty-seeking intent and adjust the recommendation policy accordingly. Most existing literature models a user's propensity to choose novel content or to prefer a more diverse set of recommendations at individual interactions. Hierarchical structure, on the other hand, exists in a user's novelty-seeking intent, which is manifested as a static and intrinsic user preference for seeking novelty along with a dynamic session-based propensity. To this end, we propose a novel hierarchical reinforcement learning-based method to model the hierarchical user novelty-seeking intent, and to adapt the recommendation policy accordingly based on the extracted user novelty-seeking propensity. We further incorporate diversity and novelty-related measurement in the reward function of the hierarchical RL (HRL) agent to encourage user exploration chen2021values. We demonstrate the benefits of explicitly modeling hierarchical user novelty-seeking intent in recommendations through extensive experiments on simulated and real-world datasets. In particular, we demonstrate that the effectiveness of our proposed hierarchical RL-based method lies in its ability to capture such hierarchically-structured intent. As a result, the proposed HRL model achieves superior performance on several public datasets, compared with state-of-art baselines.

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to match the performance of fully fine-tuned models on various tasks with an extreme reduction in the number of trainable parameters. Even in settings where both methods learn similarly accurate models, are their learned solutions really equivalent? We study how different fine-tuning methods change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that full fine-tuning and LoRA yield weight matrices whose singular value decompositions exhibit very different structure; moreover, the fine-tuned models themselves show distinct generalization behaviors when tested outside the adaptation task's distribution. More specifically, we first show that the weight matrices trained with LoRA have new, high-ranking singular vectors, which we call intruder dimensions. Intruder dimensions do not appear during full fine-tuning. Second, we show that LoRA models with intruder dimensions, despite achieving similar performance to full fine-tuning on the target task, become worse models of the pre-training distribution and adapt less robustly to multiple tasks sequentially. Higher-rank, rank-stabilized LoRA models closely mirror full fine-tuning, even when performing on par with lower-rank LoRA models on the same tasks. These results suggest that models updated with LoRA and full fine-tuning access different parts of parameter space, even when they perform equally on the fine-tuned distribution. We conclude by examining why intruder dimensions appear in LoRA fine-tuned models, why they are undesirable, and how their effects can be minimized.

The recent surge in large-scale foundation models has spurred the development of efficient methods for adapting these models to various downstream tasks. Low-rank adaptation methods, such as LoRA, have gained significant attention due to their outstanding parameter efficiency and no additional inference latency. This paper investigates a more general form of adapter module based on the analysis that parallel and sequential adaptation branches learn novel and general features during fine-tuning, respectively. The proposed method, named Hydra, due to its multi-head computational branches, combines parallel and sequential branch to integrate capabilities, which is more expressive than existing single branch methods and enables the exploration of a broader range of optimal points in the fine-tuning process. In addition, the proposed adaptation method explicitly leverages the pre-trained weights by performing a linear combination of the pre-trained features. It allows the learned features to have better generalization performance across diverse downstream tasks. Furthermore, we perform a comprehensive analysis of the characteristics of each adaptation branch with empirical evidence. Through an extensive range of experiments, encompassing comparisons and ablation studies, we substantiate the efficiency and demonstrate the superior performance of Hydra. This comprehensive evaluation underscores the potential impact and effectiveness of Hydra in a variety of applications. Our code is available on https://github.com/extremebird/Hydra

Graph contrastive learning (GCL) has become a powerful tool for learning graph data, but its scalability remains a significant challenge. In this work, we propose a simple yet effective training framework called Structural Compression (StructComp) to address this issue. Inspired by a sparse low-rank approximation on the diffusion matrix, StructComp trains the encoder with the compressed nodes. This allows the encoder not to perform any message passing during the training stage, and significantly reduces the number of sample pairs in the contrastive loss. We theoretically prove that the original GCL loss can be approximated with the contrastive loss computed by StructComp. Moreover, StructComp can be regarded as an additional regularization term for GCL models, resulting in a more robust encoder. Empirical studies on seven benchmark datasets show that StructComp greatly reduces the time and memory consumption while improving model performance compared to the vanilla GCL models and scalable training methods.

As far as Scene Graph Generation (SGG), coarse and fine predicates mix in the dataset due to the crowd-sourced labeling, and the long-tail problem is also pronounced. Given this tricky situation, many existing SGG methods treat the predicates equally and learn the model under the supervision of mixed-granularity predicates in one stage, leading to relatively coarse predictions. In order to alleviate the negative impact of the suboptimum mixed-granularity annotation and long-tail effect problems, this paper proposes a novel Hierarchical Memory Learning (HML) framework to learn the model from simple to complex, which is similar to the human beings' hierarchical memory learning process. After the autonomous partition of coarse and fine predicates, the model is first trained on the coarse predicates and then learns the fine predicates. In order to realize this hierarchical learning pattern, this paper, for the first time, formulates the HML framework using the new Concept Reconstruction (CR) and Model Reconstruction (MR) constraints. It is worth noticing that the HML framework can be taken as one general optimization strategy to improve various SGG models, and significant improvement can be achieved on the SGG benchmark (i.e., Visual Genome).

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.

Deep Click-Through Rate (CTR) prediction models play an important role in modern industrial recommendation scenarios. However, high memory overhead and computational costs limit their deployment in resource-constrained environments. Low-rank approximation is an effective method for computer vision and natural language processing models, but its application in compressing CTR prediction models has been less explored. Due to the limited memory and computing resources, compression of CTR prediction models often confronts three fundamental challenges, i.e., (1). How to reduce the model sizes to adapt to edge devices? (2). How to speed up CTR prediction model inference? (3). How to retain the capabilities of original models after compression? Previous low-rank compression research mostly uses tensor decomposition, which can achieve a high parameter compression ratio, but brings in AUC degradation and additional computing overhead. To address these challenges, we propose a unified low-rank decomposition framework for compressing CTR prediction models. We find that even with the most classic matrix decomposition SVD method, our framework can achieve better performance than the original model. To further improve the effectiveness of our framework, we locally compress the output features instead of compressing the model weights. Our unified low-rank compression framework can be applied to embedding tables and MLP layers in various CTR prediction models. Extensive experiments on two academic datasets and one real industrial benchmark demonstrate that, with 3-5x model size reduction, our compressed models can achieve both faster inference and higher AUC than the uncompressed original models. Our code is at https://github.com/yuhao318/Atomic_Feature_Mimicking.

Large Language Models (LLMs) have achieved remarkable success in various fields, prompting several studies to explore their potential in recommendation systems. However, these attempts have so far resulted in only modest improvements over traditional recommendation models. Moreover, three critical questions remain under-explored: firstly, the real value of LLMs' pre-trained weights, often considered to encapsulate world knowledge; secondly, the necessity of fine-tuning for recommendation tasks; lastly, whether LLMs can exhibit the same scalability benefits in recommendation systems as they do in other domains. In this paper, we propose a novel Hierarchical Large Language Model (HLLM) architecture designed to enhance sequential recommendation systems. Our approach employs a two-tier model: the first Item LLM extracts rich content features from the detailed text description of the item, while the second User LLM utilizes these features to predict users' future interests based on their interaction history. Extensive experiments demonstrate that our method effectively leverages the pre-trained capabilities of open-source LLMs, and further fine-tuning leads to significant performance boosts. Additionally, HLLM achieves excellent scalability, with the largest configuration utilizing 7B parameters for both item feature extraction and user interest modeling. Moreover, HLLM offers excellent training and serving efficiency, making it practical in real-world applications. Evaluations on two large-scale datasets, PixelRec and Amazon Reviews, show that HLLM achieves state-of-the-art results, outperforming traditional ID-based models by a wide margin. In online A/B testing, HLLM showcases notable gains, validating its practical impact in real-world recommendation scenarios. Codes are available at https://github.com/bytedance/HLLM.

We propose a novel theoretical framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks (e.g., SimCLR). First, we prove that in each SGD update of SimCLR with various loss functions, including simple contrastive loss, soft Triplet loss and InfoNCE loss, the weights at each layer are updated by a covariance operator that specifically amplifies initial random selectivities that vary across data samples but survive averages over data augmentations. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a hierarchical latent tree model (HLTM) and prove that the hidden neurons of deep ReLU networks can learn the latent variables in HLTM, despite the fact that the network receives no direct supervision from these unobserved latent variables. This leads to a provable emergence of hierarchical features through the amplification of initially random selectivities through contrastive SSL. Extensive numerical studies justify our theoretical findings. Code is released in https://github.com/facebookresearch/luckmatters/tree/master/ssl.

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pretrained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. As a result, performance usually drops significantly and a sophisticated effort on fine-tuning is required to recover accuracy. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training process. We propose Trained Rank Pruning (TRP), which alternates between low rank approximation and training. TRP maintains the capacity of the original network while imposing low-rank constraints during training. A nuclear regularization optimized by stochastic sub-gradient descent is utilized to further promote low rank in TRP. The TRP trained network inherently has a low-rank structure, and is approximated with negligible performance loss, thus eliminating the fine-tuning process after low rank decomposition. The proposed method is comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation.

Low-Rank Adaptation (LoRA) is the bread and butter of Large Language Model (LLM) finetuning. LoRA learns an additive low-rank perturbation, AB, of a pretrained matrix parameter W to align the model to a new task or dataset with W+AB. We identify three core limitations to LoRA for finetuning--a setting that employs limited amount of data and training steps. First, LoRA employs Dropout to prevent overfitting. We prove that Dropout is only suitable for long training episodes but fails to converge to a reliable regularizer for short training episodes. Second, LoRA's initialization of B at 0 creates a slow training dynamic between A and B. That dynamic is also exacerbated by Dropout that further slows the escape from 0 for B which is particularly harmful for short training episodes. Third, the scaling factor multiplying each LoRA additive perturbation creates ``short-sighted'' interactions between the LoRA modules of different layers. Motivated by principled analysis of those limitations, we find an elegant solution: a Dropout-free, scaling-free, LoRA with Adaptive Learning rate--coined ALLoRA. By scaling the per sample and per parameter gradients with a coefficient inversely proportional to parameters' ell_2 norm, ALLoRA alleviates those three limitations. As a by-product, ALLoRA removes two hyper-parameters from LoRA: the scaling factor and the dropout rate. Empirical results show that ALLoRA admits better accuracy than LoRA on various settings, including against recent LoRA variants such as Weight-Decomposed Low-Rank Adaptation (DoRA). Ablation studies show our solution is the optimal in a family of weight-dependent / output-dependent approaches on various LLMs including the latest Llama3.

Large Language Models (LLMs) have significantly advanced natural language processing with exceptional task generalization capabilities. Low-Rank Adaption (LoRA) offers a cost-effective fine-tuning solution, freezing the original model parameters and training only lightweight, low-rank adapter matrices. However, the memory footprint of LoRA is largely dominated by the original model parameters. To mitigate this, we propose LoRAM, a memory-efficient LoRA training scheme founded on the intuition that many neurons in over-parameterized LLMs have low training utility but are essential for inference. LoRAM presents a unique twist: it trains on a pruned (small) model to obtain pruned low-rank matrices, which are then recovered and utilized with the original (large) model for inference. Additionally, minimal-cost continual pre-training, performed by the model publishers in advance, aligns the knowledge discrepancy between pruned and original models. Our extensive experiments demonstrate the efficacy of LoRAM across various pruning strategies and downstream tasks. For a model with 70 billion parameters, LoRAM enables training on a GPU with only 20G HBM, replacing an A100-80G GPU for LoRA training and 15 GPUs for full fine-tuning. Specifically, QLoRAM implemented by structured pruning combined with 4-bit quantization, for LLaMA-3.1-70B (LLaMA-2-70B), reduces the parameter storage cost that dominates the memory usage in low-rank matrix training by 15.81times (16.95times), while achieving dominant performance gains over both the original LLaMA-3.1-70B (LLaMA-2-70B) and LoRA-trained LLaMA-3.1-8B (LLaMA-2-13B).

Recent research has shown that training low-rank neural networks can effectively reduce the total number of trainable parameters without sacrificing predictive accuracy, resulting in end-to-end speedups. However, low-rank model training necessitates adjusting several additional factorization hyperparameters, such as the rank of the factorization at each layer. In this paper, we tackle this challenge by introducing Cuttlefish, an automated low-rank training approach that eliminates the need for tuning factorization hyperparameters. Cuttlefish leverages the observation that after a few epochs of full-rank training, the stable rank (i.e., an approximation of the true rank) of each layer stabilizes at a constant value. Cuttlefish switches from full-rank to low-rank training once the stable ranks of all layers have converged, setting the dimension of each factorization to its corresponding stable rank. Our results show that Cuttlefish generates models up to 5.6 times smaller than full-rank models, and attains up to a 1.2 times faster end-to-end training process while preserving comparable accuracy. Moreover, Cuttlefish outperforms state-of-the-art low-rank model training methods and other prominent baselines. The source code for our implementation can be found at: https://github.com/hwang595/Cuttlefish.

Image classification is one of the most important areas in computer vision. Hierarchical multi-label classification applies when a multi-class image classification problem is arranged into smaller ones based upon a hierarchy or taxonomy. Thus, hierarchical classification modes generally provide multiple class predictions on each instance, whereby these are expected to reflect the structure of image classes as related to one another. In this paper, we propose a multi-label capsule network (ML-CapsNet) for hierarchical classification. Our ML-CapsNet predicts multiple image classes based on a hierarchical class-label tree structure. To this end, we present a loss function that takes into account the multi-label predictions of the network. As a result, the training approach for our ML-CapsNet uses a coarse to fine paradigm while maintaining consistency with the structure in the classification levels in the label-hierarchy. We also perform experiments using widely available datasets and compare the model with alternatives elsewhere in the literature. In our experiments, our ML-CapsNet yields a margin of improvement with respect to these alternative methods.

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of k+1 reference points. As this definition relies on points and not on tangent vectors, it can also be extended to geodesic spaces which are not Riemannian. For instance, in stratified spaces, it naturally allows principal subspaces that span several strata, which is impossible in previous generalizations of PCA. We show that barycentric subspaces locally define a submanifold of dimension k which generalizes geodesic subspaces.Second, we rephrase PCA in Euclidean spaces as an optimization on flags of linear subspaces (a hierarchy of properly embedded linear subspaces of increasing dimension). We show that the Euclidean PCA minimizes the Accumulated Unexplained Variances by all the subspaces of the flag (AUV). Barycentric subspaces are naturally nested, allowing the construction of hierarchically nested subspaces. Optimizing the AUV criterion to optimally approximate data points with flags of affine spans in Riemannian manifolds lead to a particularly appealing generalization of PCA on manifolds called Barycentric Subspaces Analysis (BSA).

With the commercialization of large language models (LLMs), weight-activation quantization has emerged to compress and accelerate LLMs, achieving high throughput while reducing inference costs. However, existing post-training quantization (PTQ) techniques for quantizing weights and activations of LLMs still suffer from non-negligible accuracy drops, especially on massive multitask language understanding. To address this issue, we propose Low-Rank Quantization (LRQ) - a simple yet effective post-training weight quantization method for LLMs that reconstructs the outputs of an intermediate Transformer block by leveraging low-rank weight-scaling matrices, replacing the conventional full weight-scaling matrices that entail as many learnable scales as their associated weights. Thanks to parameter sharing via low-rank structure, LRQ only needs to learn significantly fewer parameters while enabling the individual scaling of weights, thus boosting the generalization capability of quantized LLMs. We show the superiority of LRQ over prior LLM PTQ works under (i) 8-bit weight and per-tensor activation quantization, (ii) 4-bit weight and 8-bit per-token activation quantization, and (iii) low-bit weight-only quantization schemes. Our code is available at https://github.com/onliwad101/FlexRound_LRQ to inspire LLM researchers and engineers.

Large-scale pretraining followed by task-specific finetuning has achieved great success in various NLP tasks. Since finetuning all parameters of large pretrained models poses substantial computational and memory challenges, several efficient finetuning methods have been developed. Among them, low-rank adaptation (LoRA), which finetunes low-rank incremental update matrices on top of frozen pretrained weights, has proven particularly effective. Nonetheless, LoRA's uniform rank assignment across all layers, along with its reliance on an exhaustive search to find the best rank, leads to high computation costs and suboptimal finetuning performance. To address these limitations, we introduce AutoLoRA, a meta learning based framework for automatically identifying the optimal rank of each LoRA layer. AutoLoRA associates each rank-1 matrix in a low-rank update matrix with a selection variable, which determines whether the rank-1 matrix should be discarded. A meta learning based method is developed to learn these selection variables. The optimal rank is determined by thresholding the values of these variables. Our comprehensive experiments on natural language understanding, generation, and sequence labeling demonstrate the effectiveness of AutoLoRA.

As the adoption of large language models increases and the need for per-user or per-task model customization grows, the parameter-efficient fine-tuning (PEFT) methods, such as low-rank adaptation (LoRA) and its variants, incur substantial storage and transmission costs. To further reduce stored parameters, we introduce a "divide-and-share" paradigm that breaks the barriers of low-rank decomposition across matrix dimensions, modules and layers by sharing parameters globally via a vector bank. As an instantiation of the paradigm to LoRA, our proposed VB-LoRA composites all the low-rank matrices of LoRA from a shared vector bank with a differentiable top-k admixture module. VB-LoRA achieves extreme parameter efficiency while maintaining comparable or better performance compared to state-of-the-art PEFT methods. Extensive experiments demonstrate the effectiveness of VB-LoRA on natural language understanding, natural language generation, and instruction tuning tasks. When fine-tuning the Llama2-13B model, VB-LoRA only uses 0.4% of LoRA's stored parameters, yet achieves superior results. Our source code is available at https://github.com/leo-yangli/VB-LoRA.

In this paper, we show that Low Rank Adaptation (LoRA) as originally introduced in Hu et al. (2021) leads to suboptimal finetuning of models with large width (embedding dimension). This is due to the fact that adapter matrices A and B in LoRA are updated with the same learning rate. Using scaling arguments for large width networks, we demonstrate that using the same learning rate for A and B does not allow efficient feature learning. We then show that this suboptimality of LoRA can be corrected simply by setting different learning rates for the LoRA adapter matrices A and B with a well-chosen ratio. We call this proposed algorithm LoRA+. In our extensive experiments, LoRA+ improves performance (1-2 % improvements) and finetuning speed (up to sim 2X SpeedUp), at the same computational cost as LoRA.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Ranking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and Web3 protocols deliberately eschew centralized databases and computational architectures when designing services and features. As such, robust search-and-rank algorithms designed for such domains must be engineered specifically for decentralized networks, and must be lightweight enough to operate on consumer-grade personal devices such as a smartphone or laptop computer. We introduce G-Rank, an unsupervised ranking algorithm designed exclusively for decentralized networks. We demonstrate that accurate, relevant ranking results can be achieved in fully decentralized networks without any centralized data aggregation, feature engineering, or model training. Furthermore, we show that such results are obtainable with minimal data preprocessing and computational overhead, and can still return highly relevant results even when a user's device is disconnected from the network. G-Rank is highly modular in design, is not limited to categorical data, and can be implemented in a variety of domains with minimal modification. The results herein show that unsupervised ranking models designed for decentralized p2p networks are not only viable, but worthy of further research.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Structure information is critical for understanding the semantics of text-rich images, such as documents, tables, and charts. Existing Multimodal Large Language Models (MLLMs) for Visual Document Understanding are equipped with text recognition ability but lack general structure understanding abilities for text-rich document images. In this work, we emphasize the importance of structure information in Visual Document Understanding and propose the Unified Structure Learning to boost the performance of MLLMs. Our Unified Structure Learning comprises structure-aware parsing tasks and multi-grained text localization tasks across 5 domains: document, webpage, table, chart, and natural image. To better encode structure information, we design a simple and effective vision-to-text module H-Reducer, which can not only maintain the layout information but also reduce the length of visual features by merging horizontal adjacent patches through convolution, enabling the LLM to understand high-resolution images more efficiently. Furthermore, by constructing structure-aware text sequences and multi-grained pairs of texts and bounding boxes for publicly available text-rich images, we build a comprehensive training set DocStruct4M to support structure learning. Finally, we construct a small but high-quality reasoning tuning dataset DocReason25K to trigger the detailed explanation ability in the document domain. Our model DocOwl 1.5 achieves state-of-the-art performance on 10 visual document understanding benchmarks, improving the SOTA performance of MLLMs with a 7B LLM by more than 10 points in 5/10 benchmarks. Our codes, models, and datasets are publicly available at https://github.com/X-PLUG/mPLUG-DocOwl/tree/main/DocOwl1.5.

In natural language processing (NLP), lexical function is a concept to unambiguously represent semantic and syntactic features of words and phrases in text first crafted in the Meaning-Text Theory. Hierarchical classification of lexical functions involves organizing these features into a tree-like hierarchy of categories or labels. This is a challenging task as it requires a good understanding of the context and the relationships among words and phrases in text. It also needs large amounts of labeled data to train language models effectively. In this paper, we present a dataset of most frequent Spanish verb-noun collocations and sentences where they occur, each collocation is assigned to one of 37 lexical functions defined as classes for a hierarchical classification task. Each class represents a relation between the noun and the verb in a collocation involving their semantic and syntactic features. We combine the classes in a tree-based structure, and introduce classification objectives for each level of the structure. The dataset was created by dependency tree parsing and matching of the phrases in Spanish news. We provide baselines and data splits for each objective.

Low-rank training has emerged as a promising approach for reducing memory usage in training Large Language Models (LLMs). Previous methods either rely on decomposing weight matrices (e.g., LoRA), or seek to decompose gradient matrices (e.g., GaLore) to ensure reduced memory consumption. However, both of them constrain the training in a low-rank subspace, thus inevitably leading to sub-optimal performance. This raises a question: whether it is possible to consistently preserve the low-rank constraint for memory efficiency, while achieving full-rank training (i.e., training with full-rank gradients of full-rank weights) to avoid inferior outcomes? In this paper, we propose a new plug-and-play training framework for LLMs called Fira, as the first attempt to achieve this goal. First, we observe an interesting phenomenon during LLM training: the scaling impact of adaptive optimizers (e.g., Adam) on the gradient norm remains similar from low-rank to full-rank training. Based on this observation, we propose a norm-based scaling method, which utilizes the scaling impact of low-rank optimizers as substitutes for that of original full-rank optimizers to enable full-rank training. In this way, we can preserve the low-rank constraint in the optimizer while achieving full-rank training for better performance. Moreover, we find that there are sudden gradient rises during the optimization process, potentially causing loss spikes. To address this, we further put forward a norm-growth limiter to smooth the gradient via regulating the relative increase of gradient norms. Extensive experiments on the pre-training and fine-tuning of LLMs show that Fira outperforms both LoRA and GaLore, achieving performance that is comparable to or even better than full-rank training.

With the increasing size of pre-trained language models (PLMs), fine-tuning all the parameters in the model is not efficient, especially when there are a large number of downstream tasks, which incur significant training and storage costs. Many parameter-efficient fine-tuning (PEFT) approaches have been proposed, among which, Low-Rank Adaptation (LoRA) is a representative approach that injects trainable rank decomposition matrices into every target module. Yet LoRA ignores the importance of parameters in different modules. To address this problem, many works have been proposed to prune the parameters of LoRA. However, under limited training conditions, the upper bound of the rank of the pruned parameter matrix is still affected by the preset values. We, therefore, propose IncreLoRA, an incremental parameter allocation method that adaptively adds trainable parameters during training based on the importance scores of each module. This approach is different from the pruning method as it is not limited by the initial number of training parameters, and each parameter matrix has a higher rank upper bound for the same training overhead. We conduct extensive experiments on GLUE to demonstrate the effectiveness of IncreLoRA. The results show that our method owns higher parameter efficiency, especially when under the low-resource settings where our method significantly outperforms the baselines. Our code is publicly available.

Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with N data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank rlesssim N; (ii) using LoRA with rank rgtrsim N eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA generalizes well.

We investigate LoRA in federated learning through the lens of the asymmetry analysis of the learned A and B matrices. In doing so, we uncover that A matrices are responsible for learning general knowledge, while B matrices focus on capturing client-specific knowledge. Based on this finding, we introduce Federated Share-A Low-Rank Adaptation (FedSA-LoRA), which employs two low-rank trainable matrices A and B to model the weight update, but only A matrices are shared with the server for aggregation. Moreover, we delve into the relationship between the learned A and B matrices in other LoRA variants, such as rsLoRA and VeRA, revealing a consistent pattern. Consequently, we extend our FedSA-LoRA method to these LoRA variants, resulting in FedSA-rsLoRA and FedSA-VeRA. In this way, we establish a general paradigm for integrating LoRA with FL, offering guidance for future work on subsequent LoRA variants combined with FL. Extensive experimental results on natural language understanding and generation tasks demonstrate the effectiveness of the proposed method.

Low-Rank Adaptation (LoRA) and its variants have shown impressive results in reducing the number of trainable parameters and memory requirements of large transformer networks while maintaining fine-tuning performance. However, the low-rank nature of the weight update inherently limits the representation power of fine-tuned models, potentially compromising performance on complex tasks. This raises a critical question: when a performance gap between LoRA and standard fine-tuning is observed, is it due to the reduced number of trainable parameters or the rank deficiency? This paper aims to answer this question by introducing RandLoRA, a parameter-efficient method that performs full-rank updates using a learned linear combinations of low-rank, non-trainable random matrices. Our method limits the number of trainable parameters by restricting optimization to diagonal scaling matrices applied to the fixed random matrices. This allows us to effectively overcome the low-rank limitations while maintaining parameter and memory efficiency during training. Through extensive experimentation across vision, language, and vision-language benchmarks, we systematically evaluate the limitations of LoRA and existing random basis methods. Our findings reveal that full-rank updates are beneficial across vision and language tasks individually, and even more so for vision-language tasks, where RandLoRA significantly reduces -- and sometimes eliminates -- the performance gap between standard fine-tuning and LoRA, demonstrating its efficacy.

Low-rank adaptation (LoRA) is a popular method for fine-tuning large-scale pre-trained models in downstream tasks by learning low-rank incremental matrices. Though LoRA and its variants effectively reduce the number of trainable parameters compared to full fine-tuning methods, they often overfit training data, resulting in sub-optimal generalization on test data. To address this problem, we introduce BiLoRA, an overfitting-alleviating fine-tuning approach based on bi-level optimization (BLO). BiLoRA employs pseudo singular value decomposition to parameterize low-rank incremental matrices and splits the training of pseudo singular vectors and values across two different subsets of training data. This division, embedded within separate levels of the BLO framework, mitigates the risk of overfitting to a single dataset. Tested on ten datasets covering natural language understanding and generation tasks and applied to various well-known large pre-trained models, BiLoRA significantly outperforms LoRA methods and other fine-tuning approaches, with similar amounts of trainable parameters.

A good initialization of deep learning models is essential since it can help them converge better and faster. However, pretraining large models is unaffordable for many researchers, which makes a desired prediction for initial parameters more necessary nowadays. Graph HyperNetworks (GHNs), one approach to predicting model parameters, have recently shown strong performance in initializing large vision models. Unfortunately, predicting parameters of very wide networks relies on copying small chunks of parameters multiple times and requires an extremely large number of parameters to support full prediction, which greatly hinders its adoption in practice. To address this limitation, we propose LoGAH (Low-rank GrAph Hypernetworks), a GHN with a low-rank parameter decoder that expands to significantly wider networks without requiring as excessive increase of parameters as in previous attempts. LoGAH allows us to predict the parameters of 774-million large neural networks in a memory-efficient manner. We show that vision and language models (i.e., ViT and GPT-2) initialized with LoGAH achieve better performance than those initialized randomly or using existing hypernetworks. Furthermore, we show promising transfer learning results w.r.t. training LoGAH on small datasets and using the predicted parameters to initialize for larger tasks. We provide the codes in https://github.com/Blackzxy/LoGAH .

Weak supervision (WS) frameworks are a popular way to bypass hand-labeling large datasets for training data-hungry models. These approaches synthesize multiple noisy but cheaply-acquired estimates of labels into a set of high-quality pseudolabels for downstream training. However, the synthesis technique is specific to a particular kind of label, such as binary labels or sequences, and each new label type requires manually designing a new synthesis algorithm. Instead, we propose a universal technique that enables weak supervision over any label type while still offering desirable properties, including practical flexibility, computational efficiency, and theoretical guarantees. We apply this technique to important problems previously not tackled by WS frameworks including learning to rank, regression, and learning in hyperbolic space. Theoretically, our synthesis approach produces a consistent estimators for learning some challenging but important generalizations of the exponential family model. Experimentally, we validate our framework and show improvement over baselines in diverse settings including real-world learning-to-rank and regression problems along with learning on hyperbolic manifolds.

Large language models (LLMs) excel in language tasks, especially with supervised fine-tuning after pre-training. However, their substantial memory and computational requirements hinder practical applications. Structural pruning, which reduces less significant weight dimensions, is one solution. Yet, traditional post-hoc pruning often leads to significant performance loss, with limited recovery from further fine-tuning due to reduced capacity. Since the model fine-tuning refines the general and chaotic knowledge in pre-trained models, we aim to incorporate structural pruning with the fine-tuning, and propose the Pruning-Aware Tuning (PAT) paradigm to eliminate model redundancy while preserving the model performance to the maximum extend. Specifically, we insert the innovative Hybrid Sparsification Modules (HSMs) between the Attention and FFN components to accordingly sparsify the upstream and downstream linear modules. The HSM comprises a lightweight operator and a globally shared trainable mask. The lightweight operator maintains a training overhead comparable to that of LoRA, while the trainable mask unifies the channels to be sparsified, ensuring structural pruning. Additionally, we propose the Identity Loss which decouples the transformation and scaling properties of the HSMs to enhance training robustness. Extensive experiments demonstrate that PAT excels in both performance and efficiency. For example, our Llama2-7b model with a 25\% pruning ratio achieves 1.33times speedup while outperforming the LoRA-finetuned model by up to 1.26\% in accuracy with a similar training cost. Code: https://github.com/kriskrisliu/PAT_Pruning-Aware-Tuning

Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of downstream tasks. Existing parameter-efficient fine-tuning (PEFT) methods such as Low-Rank Adaptation (LoRA) rely on a bypass framework that ignores the differential parameter budget requirements across weight matrices, which may lead to suboptimal fine-tuning outcomes. To address this issue, we introduce the Dynamic Low-Rank Adaptation (DoRA) method. DoRA decomposes high-rank LoRA layers into structured single-rank components, allowing for dynamic pruning of parameter budget based on their importance to specific tasks during training, which makes the most of the limited parameter budget. Experimental results demonstrate that DoRA can achieve competitive performance compared with LoRA and full model fine-tuning, and outperform various strong baselines with the same storage parameter budget. Our code is available at https://github.com/MIkumikumi0116/DoRA

Low-Rank Adaptation (LoRA) has recently gained attention for fine-tuning foundation models by incorporating trainable low-rank matrices, thereby reducing the number of trainable parameters. While LoRA offers numerous advantages, its applicability for real-time serving to a diverse and global user base is constrained by its incapability to handle multiple task-specific adapters efficiently. This imposes a performance bottleneck in scenarios requiring personalized, task-specific adaptations for each incoming request. To mitigate this constraint, we introduce Fast LoRA (FLoRA), a framework in which each input example in a minibatch can be associated with its unique low-rank adaptation weights, allowing for efficient batching of heterogeneous requests. We empirically demonstrate that FLoRA retains the performance merits of LoRA, showcasing competitive results on the MultiPL-E code generation benchmark spanning over 8 languages and a multilingual speech recognition task across 6 languages.

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.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as Low-Rank Adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning. However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning. To address these issues, we propose LoLDU, a Parameter-Efficient Fine-Tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages Lower-Diag-Upper Decomposition (LDU) to initialize low-rank matrices for faster convergence and orthogonality. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, 6 natural language understanding (NLU) datasets, 8 image classification datasets, and image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and Stable Diffusion), providing a comprehensive and detailed analysis. Our open-source code can be accessed at https://github.com/SKDDJ/LoLDU{https://github.com/SKDDJ/LoLDU}.

Recently, recommender systems have been able to emit substantially improved recommendations by leveraging user-provided reviews. Existing methods typically merge all reviews of a given user or item into a long document, and then process user and item documents in the same manner. In practice, however, these two sets of reviews are notably different: users' reviews reflect a variety of items that they have bought and are hence very heterogeneous in their topics, while an item's reviews pertain only to that single item and are thus topically homogeneous. In this work, we develop a novel neural network model that properly accounts for this important difference by means of asymmetric attentive modules. The user module learns to attend to only those signals that are relevant with respect to the target item, whereas the item module learns to extract the most salient contents with regard to properties of the item. Our multi-hierarchical paradigm accounts for the fact that neither are all reviews equally useful, nor are all sentences within each review equally pertinent. Extensive experimental results on a variety of real datasets demonstrate the effectiveness of our method.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation. Code is available: https://github.com/yuhuixu1993/Trained-Rank-Pruning

Recent efforts to scale Transformer models have demonstrated rapid progress across a wide range of tasks (Wei et al., 2022). However, fine-tuning these models for downstream tasks is expensive due to their large parameter counts. Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable alternative by allowing us to fine-tune models by updating only a small number of parameters. In this work, we propose a general framework for parameter efficient fine-tuning (PEFT), based on structured unrestricted-rank matrices (SURM) which can serve as a drop-in replacement for popular approaches such as Adapters and LoRA. Unlike other methods like LoRA, SURMs provides more flexibility in finding the right balance between compactness and expressiveness. This is achieved by using low displacement rank matrices (LDRMs), which hasn't been used in this context before. SURMs remain competitive with baselines, often providing significant quality improvements while using a smaller parameter budget. SURMs achieve 5-7% accuracy gains on various image classification tasks while replacing low-rank matrices in LoRA. It also results in up to 12x reduction of the number of parameters in adapters (with virtually no loss in quality) on the GLUE benchmark.

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

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

Low-Rank Adaptation (LoRA) is widely used for adapting large language models (LLMs) to specific domains due to its efficiency and modularity. Meanwhile, vanilla LoRA struggles with task conflicts in multi-task scenarios. Recent works adopt Mixture of Experts (MoE) by treating each LoRA module as an expert, thereby mitigating task interference through multiple specialized LoRA modules. While effective, these methods often isolate knowledge within individual tasks, failing to fully exploit the shared knowledge across related tasks. In this paper, we establish a connection between single LoRA and multi-LoRA MoE, integrating them into a unified framework. We demonstrate that the dynamic routing of multiple LoRAs is functionally equivalent to rank partitioning and block-level activation within a single LoRA. We further empirically demonstrate that finer-grained LoRA partitioning, within the same total and activated parameter constraints, leads to better performance gains across heterogeneous tasks. Building on these findings, we propose Single-ranked Mixture of Experts LoRA (SMoRA), which embeds MoE into LoRA by treating each rank as an independent expert. With a dynamic rank-wise activation mechanism, SMoRA promotes finer-grained knowledge sharing while mitigating task conflicts. Experiments demonstrate that SMoRA activates fewer parameters yet achieves better performance in multi-task scenarios.

There is a recently discovered and intriguing phenomenon called Neural Collapse: at the terminal phase of training a deep neural network for classification, the within-class penultimate feature means and the associated classifier vectors of all flat classes collapse to the vertices of a simplex Equiangular Tight Frame (ETF). Recent work has tried to exploit this phenomenon by fixing the related classifier weights to a pre-computed ETF to induce neural collapse and maximize the separation of the learned features when training with imbalanced data. In this work, we propose to fix the linear classifier of a deep neural network to a Hierarchy-Aware Frame (HAFrame), instead of an ETF, and use a cosine similarity-based auxiliary loss to learn hierarchy-aware penultimate features that collapse to the HAFrame. We demonstrate that our approach reduces the mistake severity of the model's predictions while maintaining its top-1 accuracy on several datasets of varying scales with hierarchies of heights ranging from 3 to 12. Code: https://github.com/ltong1130ztr/HAFrame

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.

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.

Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.

While Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning for Large Language Models (LLMs), its performance often falls short of Full Fine-Tuning (Full FT). Current methods optimize LoRA by initializing with static singular value decomposition (SVD) subsets, leading to suboptimal leveraging of pre-trained knowledge. Another path for improving LoRA is incorporating a Mixture-of-Experts (MoE) architecture. However, weight misalignment and complex gradient dynamics make it challenging to adopt SVD prior to the LoRA MoE architecture. To mitigate these issues, we propose Great LoRA Mixture-of-Expert (GOAT), a framework that (1) adaptively integrates relevant priors using an SVD-structured MoE, and (2) aligns optimization with full fine-tuned MoE by deriving a theoretical scaling factor. We demonstrate that proper scaling, without modifying the architecture or training algorithms, boosts LoRA MoE's efficiency and performance. Experiments across 25 datasets, including natural language understanding, commonsense reasoning, image classification, and natural language generation, demonstrate GOAT's state-of-the-art performance, closing the gap with Full FT.

The growing computational demands posed by increasingly number of neural network's parameters necessitate low-memory-consumption training approaches. Previous memory reduction techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, suffer from the limitation of low rank and saddle point issues, particularly during intensive tasks like pre-training. In this paper, we propose Sparse Spectral Training (SST), an advanced training methodology that updates all singular values and selectively updates singular vectors of network weights, thereby optimizing resource usage while closely approximating full-rank training. SST refines the training process by employing a targeted updating strategy for singular vectors, which is determined by a multinomial sampling method weighted by the significance of the singular values, ensuring both high performance and memory reduction. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, including natural language generation, machine translation, node classification and link prediction, SST demonstrates its capability to outperform existing memory reduction training methods and is comparable with full-rank training in some cases. On OPT-125M, with rank equating to 8.3% of embedding dimension, SST reduces the perplexity gap to full-rank training by 67.6%, demonstrating a significant reduction of the performance loss with prevalent low-rank methods. This approach offers a strong alternative to traditional training techniques, paving the way for more efficient and scalable neural network training solutions.

Low-rank adapation (LoRA) is a popular method that reduces the number of trainable parameters when finetuning large language models, but still faces acute storage challenges when scaling to even larger models or deploying numerous per-user or per-task adapted models. In this work, we present Vector-based Random Matrix Adaptation (VeRA), which reduces the number of trainable parameters by 10x compared to LoRA, yet maintains the same performance. It achieves this by using a single pair of low-rank matrices shared across all layers and learning small scaling vectors instead. We demonstrate its effectiveness on the GLUE and E2E benchmarks, and show its application in instruction-following with just 1.4M parameters using the Llama2 7B model.

Parameter-efficient fine-tuning (PEFT) is essential for adapting large language models (LLMs), with low-rank adaptation (LoRA) being the most popular approach. However, LoRA suffers from slow convergence, and some recent LoRA variants, such as PiSSA, primarily rely on Singular Value Decomposition (SVD) for initialization, leading to expensive computation. To mitigate these problems, we use the Nystr\"om method, which follows a three-matrix manipulation. We first introduce StructuredLoRA (SLoRA), which investigates adding a small intermediate matrix between the low-rank matrices A and B. Secondly, we propose Nystr\"omLoRA (NLoRA), which leverages Nystr\"om-based initialization for SLoRA to improve its effectiveness and efficiency. Finally, we propose IntermediateTune (IntTune), which explores fine-tuning exclusively on the intermediate matrix of NLoRA to further boost LLM efficiency. We evaluate our methods on five natural language generation (NLG) tasks and eight natural language understanding (NLU) tasks. On GSM8K, SLoRA and NLoRA achieve accuracies of 56.48% and 57.70%, surpassing LoRA by 33.52% and 36.41%, with only 3.67 million additional trainable parameters. IntTune improves average NLG performance over LoRA by 7.45% while using only 1.25% of its parameters. These results demonstrate the efficiency and effectiveness of our approach in enhancing model performance with minimal parameter overhead.

Hierarchical text classification (HTC) is the task of assigning labels to a text within a structured space organized as a hierarchy. Recent works treat HTC as a conventional multilabel classification problem, therefore evaluating it as such. We instead propose to evaluate models based on specifically designed hierarchical metrics and we demonstrate the intricacy of metric choice and prediction inference method. We introduce a new challenging dataset and we evaluate fairly, recent sophisticated models, comparing them with a range of simple but strong baselines, including a new theoretically motivated loss. Finally, we show that those baselines are very often competitive with the latest models. This highlights the importance of carefully considering the evaluation methodology when proposing new methods for HTC. Code implementation and dataset are available at https://github.com/RomanPlaud/revisitingHTC.

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into "supervertices" which are arranged according to a d-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.

The advent of large language models (LLMs) has revolutionized natural language processing, enabling unprecedented capabilities in understanding and generating human-like text. However, the computational cost and convergence times associated with fine-tuning these models remain significant challenges. Low-Rank Adaptation (LoRA) has emerged as a promising method to mitigate these issues by introducing efficient fine-tuning techniques with a reduced number of trainable parameters. In this paper, we present OLoRA, an enhancement to the LoRA method that leverages orthonormal matrix initialization through QR decomposition. OLoRA significantly accelerates the convergence of LLM training while preserving the efficiency benefits of LoRA, such as the number of trainable parameters and GPU memory footprint. Our empirical evaluations demonstrate that OLoRA not only converges faster but also exhibits improved performance compared to standard LoRA across a variety of language modeling tasks. This advancement opens new avenues for more efficient and accessible fine-tuning of LLMs, potentially enabling broader adoption and innovation in natural language applications.

Low-rank adapters (LoRA) and their variants are popular parameter-efficient fine-tuning (PEFT) techniques that closely match full model fine-tune performance while requiring only a small number of additional parameters. These additional LoRA parameters are specific to the base model being adapted. When the base model needs to be deprecated and replaced with a new one, all the associated LoRA modules need to be re-trained. Such re-training requires access to the data used to train the LoRA for the original base model. This is especially problematic for commercial cloud applications where the LoRA modules and the base models are hosted by service providers who may not be allowed to host proprietary client task data. To address this challenge, we propose Trans-LoRA -- a novel method for lossless, nearly data-free transfer of LoRAs across base models. Our approach relies on synthetic data to transfer LoRA modules. Using large language models, we design a synthetic data generator to approximate the data-generating process of the observed task data subset. Training on the resulting synthetic dataset transfers LoRA modules to new models. We show the effectiveness of our approach using both LLama and Gemma model families. Our approach achieves lossless (mostly improved) LoRA transfer between models within and across different base model families, and even between different PEFT methods, on a wide variety of tasks.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

The rapid advancements in large language models (LLMs) have revolutionized natural language processing, creating an increased need for efficient, task-specific fine-tuning methods. Traditional fine-tuning of LLMs involves updating a large number of parameters, which is computationally expensive and memory-intensive. Low-Rank Adaptation (LoRA) has emerged as a promising solution, enabling parameter-efficient fine-tuning by reducing the number of trainable parameters. However, while LoRA reduces the number of trainable parameters, LoRA modules still create significant storage challenges. We propose LoRA-Mini, an optimized adaptation of LoRA that improves parameter efficiency by splitting low-rank matrices into four parts, with only the two inner matrices being trainable. This approach achieves upto a 20x reduction compared to standard LoRA in the number of trainable parameters while preserving performance levels comparable to standard LoRA, addressing both computational and storage efficiency in LLM fine-tuning.

Existing low-rank adaptation (LoRA) methods face challenges on sparse large language models (LLMs) due to the inability to maintain sparsity. Recent works introduced methods that maintain sparsity by augmenting LoRA techniques with additional masking mechanisms. Despite these successes, such approaches suffer from an increased memory and computation overhead, which affects efficiency of LoRA methods. In response to this limitation, we introduce LoRS, an innovative method designed to achieve both memory and computation efficiency when fine-tuning sparse LLMs. To mitigate the substantial memory and computation demands associated with preserving sparsity, our approach incorporates strategies of weight recompute and computational graph rearrangement. In addition, we also improve the effectiveness of LoRS through better adapter initialization. These innovations lead to a notable reduction in memory and computation consumption during the fine-tuning phase, all while achieving performance levels that outperform existing LoRA approaches.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the first convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating the projection matrix with eigenvectors, Online Subspace Descent updates the projection matrix with online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We show that for the task of pretraining LLaMA models ranging from 60M to 7B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity and better downstream tasks performance than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

Pre-trained language models, trained on large-scale corpora, demonstrate strong generalizability across various NLP tasks. Fine-tuning these models for specific tasks typically involves updating all parameters, which is resource-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as the popular LoRA family, introduce low-rank matrices to learn only a few parameters efficiently. However, during inference, the product of these matrices updates all pre-trained parameters, complicating tasks like knowledge editing that require selective updates. We propose a novel PEFT method, which conducts row and column-wise sparse low-rank adaptation (RoseLoRA), to address this challenge. RoseLoRA identifies and updates only the most important parameters for a specific task, maintaining efficiency while preserving other model knowledge. By adding a sparsity constraint on the product of low-rank matrices and converting it to row and column-wise sparsity, we ensure efficient and precise model updates. Our theoretical analysis guarantees the lower bound of the sparsity with respective to the matrix product. Extensive experiments on five benchmarks across twenty datasets demonstrate that RoseLoRA outperforms baselines in both general fine-tuning and knowledge editing tasks.

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the effective rank of the weight updates remains low-rank, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce FRUGAL (Full-Rank Updates with GrAdient spLitting), a new memory-efficient optimization framework. FRUGAL leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

Large Language Models (LLMs) have reshaped the landscape of artificial intelligence by demonstrating exceptional performance across various tasks. However, substantial computational requirements make their deployment challenging on devices with limited resources. Recently, compression methods using low-rank matrix techniques have shown promise, yet these often lead to degraded accuracy or introduce significant overhead in parameters and inference latency. This paper introduces Modular Decomposition (MoDeGPT), a novel structured compression framework that does not need recovery fine-tuning while resolving the above drawbacks. MoDeGPT partitions the Transformer block into modules comprised of matrix pairs and reduces the hidden dimensions via reconstructing the module-level outputs. MoDeGPT is developed based on a theoretical framework that utilizes three well-established matrix decomposition algorithms -- Nystr\"om approximation, CR decomposition, and SVD -- and applies them to our redefined transformer modules. Our comprehensive experiments show MoDeGPT, without backward propagation, matches or surpasses previous structured compression methods that rely on gradient information, and saves 98% of compute costs on compressing a 13B model. On Llama-2/3 and OPT models, MoDeGPT maintains 90-95% zero-shot performance with 25-30% compression rates. Moreover, the compression can be done on a single GPU within a few hours and increases the inference throughput by up to 46%.

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

Large-scale foundation models have demonstrated exceptional performance in language and vision tasks. However, the numerous dense matrix-vector operations involved in these large networks pose significant computational challenges during inference. To address these challenges, we introduce the Block-Level Adaptive STructured (BLAST) matrix, designed to learn and leverage efficient structures prevalent in the weight matrices of linear layers within deep learning models. Compared to existing structured matrices, the BLAST matrix offers substantial flexibility, as it can represent various types of structures that are either learned from data or computed from pre-existing weight matrices. We demonstrate the efficiency of using the BLAST matrix for compressing both language and vision tasks, showing that (i) for medium-sized models such as ViT and GPT-2, training with BLAST weights boosts performance while reducing complexity by 70% and 40%, respectively; and (ii) for large foundation models such as Llama-7B and DiT-XL, the BLAST matrix achieves a 2x compression while exhibiting the lowest performance degradation among all tested structured matrices. Our code is available at https://github.com/changwoolee/BLAST.

We investigate whether the pre-trained knowledge of vision-language models (VLMs), such as CLIP, can be retained or even enhanced during continual learning (CL) while absorbing knowledge from a data stream. Existing methods often rely on additional reference data, isolated components for distribution or domain predictions, leading to high training costs, increased inference complexity, and limited improvement potential for pre-trained models. To address these challenges, we first comprehensively analyze the effects of parameter update locations and ranks on downstream adaptation and knowledge retention. Based on these insights, we propose Dynamic Rank-Selective Low Rank Adaptation (LoRA), a universal and efficient CL approach that adaptively assigns ranks to LoRA modules based on their relevance to the current data. Unlike prior methods, our approach continually enhances the pre-trained VLM by retaining both the pre-trained knowledge and the knowledge acquired during CL. Our approach eliminates the need for explicit domain or distribution prediction and additional reference data, enabling seamless integration of new tasks while preserving pre-trained capabilities. It also maintains the original architecture and deployment pipeline of the pre-trained model without incurring any additional inference overhead. Extensive experiments and analyses demonstrate that our method outperforms state-of-the-art approaches in continually absorbing knowledge of downstream tasks while retaining pre-trained knowledge.

Low-Rank Adaptation (LoRA) is a widely-used parameter-efficient finetuning method for large language models. LoRA saves memory by training only low rank perturbations to selected weight matrices. In this work, we compare the performance of LoRA and full finetuning on two target domains, programming and mathematics. We consider both the instruction finetuning (approx100K prompt-response pairs) and continued pretraining (approx10B unstructured tokens) data regimes. Our results show that, in most settings, LoRA substantially underperforms full finetuning. Nevertheless, LoRA exhibits a desirable form of regularization: it better maintains the base model's performance on tasks outside the target domain. We show that LoRA provides stronger regularization compared to common techniques such as weight decay and dropout; it also helps maintain more diverse generations. We show that full finetuning learns perturbations with a rank that is 10-100X greater than typical LoRA configurations, possibly explaining some of the reported gaps. We conclude by proposing best practices for finetuning with LoRA.

Low-Rank Adaptation (LoRA) has achieved remarkable training results by freezing the original weights and training only low-rank matrices, establishing itself as the predominant fine-tuning method for LLMs. In pursuit of performance closer to full-parameter training, a series of LoRA variants have emerged, such as LoRA+, PISSA, Olora, and LoRA-GA. However, these improvements complicate the initial setup of model training and increase initialization time. More importantly, they overlook the internal interactions of the original weight information. To address these issues, we introduce a novel theory, ``Weight Guide'' aimed at continuously guiding trainable matrices through the original weights during training to enhance the utilization of weight information. Based on this theory, we designed a new PEFT technique called Bone (Block Affine), which not only enhances the utilization of original weight information but also emphasizes the internal connections between weights, leading to faster convergence and better data fitting. Experimental comparisons across two different LLM architectures (LLaMA2, RWKV6) and various parameter scales demonstrate that the Bone structure can achieve rapid convergence and superior data fitting without the need for complex initialization. For example, when fine-tuning LLaMA2-7B on the MetaMathQA dataset and validating on GSM8k and math benchmarks, Bone achieved fine-tuning scores of 49.36 and 8.8, respectively, outperforming PISSA by 5.84\% and 1.96\%.

Low-Rank Adaptation (LoRA) is extensively utilized in text-to-image models for the accurate rendition of specific elements like distinct characters or unique styles in generated images. Nonetheless, existing methods face challenges in effectively composing multiple LoRAs, especially as the number of LoRAs to be integrated grows, thus hindering the creation of complex imagery. In this paper, we study multi-LoRA composition through a decoding-centric perspective. We present two training-free methods: LoRA Switch, which alternates between different LoRAs at each denoising step, and LoRA Composite, which simultaneously incorporates all LoRAs to guide more cohesive image synthesis. To evaluate the proposed approaches, we establish ComposLoRA, a new comprehensive testbed as part of this research. It features a diverse range of LoRA categories with 480 composition sets. Utilizing an evaluation framework based on GPT-4V, our findings demonstrate a clear improvement in performance with our methods over the prevalent baseline, particularly evident when increasing the number of LoRAs in a composition.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Low-rank adaptation (LoRA) reduces the computational and memory demands of fine-tuning large language models (LLMs) by approximating updates with low-rank matrices. However, low-rank approximation in two-dimensional space fails to capture high-dimensional structures within the target matrix. Recently, tensor decomposition methods have been explored for fine-tuning LLMs, leveraging their ability to extract structured information. Yet, these approaches primarily rely on random initialization, and the impact of initialization on tensor adaptation remains underexplored. In this paper, we reveal that random initialization significantly diverges from the validation loss achieved by full fine-tuning. To address this, we propose Weight-Decomposed Tensor Adaptation (DoTA), which leverages the Matrix Product Operator (MPO) decomposition of pre-trained weights for effective initialization in fine-tuning LLMs. Additionally, we introduce QDoTA, a quantized version of DoTA designed for 4-bit quantization. Experiments on commonsense and arithmetic reasoning tasks show that DoTA outperforms random initialization methods with fewer parameters. QDoTA further reduces memory consumption and achieves comparable performance to DoTA on commonsense reasoning tasks. We will release our code to support future research.

The machine learning community has witnessed impressive advancements since the first appearance of large language models (LLMs), yet their huge memory consumption has become a major roadblock to large-scale training. Parameter Efficient Fine-Tuning techniques such as Low-Rank Adaptation (LoRA) have been proposed to alleviate this problem, but their performance still fails to match full parameter training in most large-scale fine-tuning settings. Attempting to complement this deficiency, we investigate layerwise properties of LoRA on fine-tuning tasks and observe an uncommon skewness of weight norms across different layers. Utilizing this key observation, a surprisingly simple training strategy is discovered, which outperforms both LoRA and full parameter training in a wide range of settings with memory costs as low as LoRA. We name it Layerwise Importance Sampled AdamW (LISA), a promising alternative for LoRA, which applies the idea of importance sampling to different layers in LLMs and randomly freeze most middle layers during optimization. Experimental results show that with similar or less GPU memory consumption, LISA surpasses LoRA or even full parameter tuning in downstream fine-tuning tasks, where LISA consistently outperforms LoRA by over 11%-37% in terms of MT-Bench scores. On large models, specifically LLaMA-2-70B, LISA achieves on-par or better performance than LoRA on MT-Bench, GSM8K, and PubMedQA, demonstrating its effectiveness across different domains.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Parameter-efficient fine-tuning methods, such as LoRA, reduces the number of trainable parameters. However, they often suffer from scalability issues and differences between their learning pattern and full fine-tuning. To overcome these limitations, we propose Efficient Weight-Decomposed Low-Rank Adaptation (EDoRA): a novel PEFT method that decomposes pre-trained weights into magnitude and directional components. By freezing low-rank matrices, initializing them by singular value decomposition, and introducing a small trainable matrix between them, EDoRA achieves substantial reduction in trainable parameters while maintaining learning capacity. Experimental results on the GLUE benchmark demonstrate that EDoRA achieves competitive or superior performance compared to state-of-the-art methods, such as LoRA and DoRA, with up to 30x fewer trainable parameters. This makes EDoRA a highly efficient solution for adapting LLMs to diverse tasks under memory-constrained settings. Code is available at https://github.com/Hamid-Nasiri/EDoRA .

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

For supervised learning with tabular data, decision tree ensembles produced via boosting techniques generally dominate real-world applications involving iid training/test sets. However for graph data where the iid assumption is violated due to structured relations between samples, it remains unclear how to best incorporate this structure within existing boosting pipelines. To this end, we propose a generalized framework for iterating boosting with graph propagation steps that share node/sample information across edges connecting related samples. Unlike previous efforts to integrate graph-based models with boosting, our approach is anchored in a principled meta loss function such that provable convergence can be guaranteed under relatively mild assumptions. Across a variety of non-iid graph datasets with tabular node features, our method achieves comparable or superior performance than both tabular and graph neural network models, as well as existing hybrid strategies that combine the two. Beyond producing better predictive performance than recently proposed graph models, our proposed techniques are easy to implement, computationally more efficient, and enjoy stronger theoretical guarantees (which make our results more reproducible).

Finetuned LLMs often exhibit poor uncertainty quantification, manifesting as overconfidence, poor calibration, and unreliable prediction results on test data or out-of-distribution samples. One approach commonly used in vision for alleviating this issue is a deep ensemble, which constructs an ensemble by training the same model multiple times using different random initializations. However, there is a huge challenge to ensembling LLMs: the most effective LLMs are very, very large. Keeping a single LLM in memory is already challenging enough: keeping an ensemble of e.g. 5 LLMs in memory is impossible in many settings. To address these issues, we propose an ensemble approach using Low-Rank Adapters (LoRA), a parameter-efficient fine-tuning technique. Critically, these low-rank adapters represent a very small number of parameters, orders of magnitude less than the underlying pre-trained model. Thus, it is possible to construct large ensembles of LoRA adapters with almost the same computational overhead as using the original model. We find that LoRA ensembles, applied on its own or on top of pre-existing regularization techniques, gives consistent improvements in predictive accuracy and uncertainty quantification.

While following different technical routes, both low-rank and orthogonal adaptation techniques can efficiently adapt large-scale pre-training models in specific tasks or domains based on a small piece of trainable parameters. In this study, we bridge the gap between these two techniques, proposing a simple but effective adaptation method based on Householder reflections. Given a pre-trained model, our method fine-tunes its layers by multiplying each frozen weight matrix with an orthogonal matrix constructed by a chain of learnable Householder reflections (HRs). This HR-based orthogonal fine-tuning is equivalent to an adaptive low-rank adaptation. Moreover, we show that the orthogonality of the reflection planes corresponding to the HRs impacts the model capacity and regularity. The analysis motivates us to regularize the orthogonality of the HRs, leading to different implementations of the proposed Householder reflection adaptation (HRA) method. Compared with state-of-the-art methods, HRA achieves superior performance with fewer learnable parameters when adapting large language models and conditional image generators. The code is available at https://github.com/DaShenZi721/HRA

Structural pruning enables model acceleration by removing structurally-grouped parameters from neural networks. However, the parameter-grouping patterns vary widely across different models, making architecture-specific pruners, which rely on manually-designed grouping schemes, non-generalizable to new architectures. In this work, we study a highly-challenging yet barely-explored task, any structural pruning, to tackle general structural pruning of arbitrary architecture like CNNs, RNNs, GNNs and Transformers. The most prominent obstacle towards this goal lies in the structural coupling, which not only forces different layers to be pruned simultaneously, but also expects all removed parameters to be consistently unimportant, thereby avoiding structural issues and significant performance degradation after pruning. To address this problem, we propose a general and {fully automatic} method, Dependency Graph (DepGraph), to explicitly model the dependency between layers and comprehensively group coupled parameters for pruning. In this work, we extensively evaluate our method on several architectures and tasks, including ResNe(X)t, DenseNet, MobileNet and Vision transformer for images, GAT for graph, DGCNN for 3D point cloud, alongside LSTM for language, and demonstrate that, even with a simple norm-based criterion, the proposed method consistently yields gratifying performances.

Low-Rank Adaptation (LoRA) has emerged as a widely adopted technique in text-to-image models, enabling precise rendering of multiple distinct elements, such as characters and styles, in multi-concept image generation. However, current approaches face significant challenges when composing these LoRAs for multi-concept image generation, resulting in diminished generated image quality. In this paper, we initially investigate the role of LoRAs in the denoising process through the lens of the Fourier frequency domain. Based on the hypothesis that applying multiple LoRAs could lead to "semantic conflicts", we find that certain LoRAs amplify high-frequency features such as edges and textures, whereas others mainly focus on low-frequency elements, including the overall structure and smooth color gradients. Building on these insights, we devise a frequency domain based sequencing strategy to determine the optimal order in which LoRAs should be integrated during inference. This strategy offers a methodical and generalizable solution compared to the naive integration commonly found in existing LoRA fusion techniques. To fully leverage our proposed LoRA order sequence determination method in multi-LoRA composition tasks, we introduce a novel, training-free framework, Cached Multi-LoRA (CMLoRA), designed to efficiently integrate multiple LoRAs while maintaining cohesive image generation. With its flexible backbone for multi-LoRA fusion and a non-uniform caching strategy tailored to individual LoRAs, CMLoRA has the potential to reduce semantic conflicts in LoRA composition and improve computational efficiency. Our experimental evaluations demonstrate that CMLoRA outperforms state-of-the-art training-free LoRA fusion methods by a significant margin -- it achieves an average improvement of 2.19% in CLIPScore, and 11.25% in MLLM win rate compared to LoraHub, LoRA Composite, and LoRA Switch.

Parameter-efficient fine-tuning (PEFT) is widely studied for its effectiveness and efficiency in the era of large language models. Low-rank adaptation (LoRA) has demonstrated commendable performance as a popular and representative method. However, it is implemented with a fixed intrinsic rank that might not be the ideal setting for the downstream tasks. Recognizing the need for more flexible downstream task adaptation, we extend the methodology of LoRA to an innovative approach we call allocating low-rank adaptation (ALoRA) that enables dynamic adjustments to the intrinsic rank during the adaptation process. First, we propose a novel method, AB-LoRA, that can effectively estimate the importance score of each LoRA rank. Second, guided by AB-LoRA, we gradually prune abundant and negatively impacting LoRA ranks and allocate the pruned LoRA budgets to important Transformer modules needing higher ranks. We have conducted experiments on various tasks, and the experimental results demonstrate that our ALoRA method can outperform the recent baselines with comparable tunable parameters.

The in-memory algorithms for approximate nearest neighbor search (ANNS) have achieved great success for fast high-recall search, but are extremely expensive when handling very large scale database. Thus, there is an increasing request for the hybrid ANNS solutions with small memory and inexpensive solid-state drive (SSD). In this paper, we present a simple but efficient memory-disk hybrid indexing and search system, named SPANN, that follows the inverted index methodology. It stores the centroid points of the posting lists in the memory and the large posting lists in the disk. We guarantee both disk-access efficiency (low latency) and high recall by effectively reducing the disk-access number and retrieving high-quality posting lists. In the index-building stage, we adopt a hierarchical balanced clustering algorithm to balance the length of posting lists and augment the posting list by adding the points in the closure of the corresponding clusters. In the search stage, we use a query-aware scheme to dynamically prune the access of unnecessary posting lists. Experiment results demonstrate that SPANN is 2times faster than the state-of-the-art ANNS solution DiskANN to reach the same recall quality 90% with same memory cost in three billion-scale datasets. It can reach 90% recall@1 and recall@10 in just around one millisecond with only 32GB memory cost. Code is available at: {\footnotesizeblue{https://github.com/microsoft/SPTAG}}.

As the research of Multimodal Large Language Models (MLLMs) becomes popular, an advancing MLLM model is typically required to handle various textual and visual tasks (e.g., VQA, Detection, OCR, and ChartQA) simultaneously for real-world applications. However, due to the significant differences in representation and distribution among data from various tasks, simply mixing data of all tasks together leads to the well-known``multi-task conflict" issue, resulting in performance degradation across various tasks. To address this issue, we propose Awaker2.5-VL, a Mixture of Experts~(MoE) architecture suitable for MLLM, which acquires the multi-task capabilities through multiple sparsely activated experts. To speed up the training and inference of Awaker2.5-VL, each expert in our model is devised as a low-rank adaptation (LoRA) structure. Extensive experiments on multiple latest benchmarks demonstrate the effectiveness of Awaker2.5-VL. The code and model weight are released in our Project Page: https://github.com/MetabrainAGI/Awaker.

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success of convolutional networks in the image domain. In this work, we systematically explore structured matrices as replacements for dense matrices. We show that different structures often require drastically different initialization scales and learning rates, which are crucial to performance, especially as models scale. Using insights from the Maximal Update Parameterization, we determine the optimal scaling for initialization and learning rates of these unconventional layers. Finally, we measure the scaling laws of different structures to compare how quickly their performance improves with compute. We propose a novel matrix family containing Monarch matrices, the Block Tensor-Train (BTT), which we show performs better than dense matrices for the same compute on multiple tasks. On CIFAR-10/100 with augmentation, BTT achieves exponentially lower training loss than dense when training MLPs and ViTs. BTT matches dense ViT-S/32 performance on ImageNet-1k with 3.8 times less compute and is more efficient than dense for training small GPT-2 language models.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

In this paper, we introduce a subspace-inspired Low-Rank Adaptation (LoRA) method, which is computationally efficient, easy to implement, and readily applicable to large language, multimodal, and diffusion models. Initially, we equivalently decompose the weights of LoRA into two subspaces, and find that simply mixing them can enhance performance. To study such a phenomenon, we revisit it through a fine-grained subspace lens, showing that such modification is equivalent to employing a fixed mixer to fuse the subspaces. To be more flexible, we jointly learn the mixer with the original LoRA weights, and term the method Mixture-of-Subspaces LoRA (MoSLoRA). MoSLoRA consistently outperforms LoRA on tasks in different modalities, including commonsense reasoning, visual instruction tuning, and subject-driven text-to-image generation, demonstrating its effectiveness and robustness. Codes are available at https://github.com/wutaiqiang/MoSLoRA{github}.

In recent years, Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) have significantly enhanced the adaptability of large-scale pre-trained models. Weight-Decomposed Low-Rank Adaptation (DoRA) improves upon LoRA by separating the magnitude and direction components of the weight matrix, leading to superior performance. However, DoRA's improvements are limited to the vertical dimension, resulting in an asymmetrical pattern between horizontal and vertical dimensions. This paper introduces BoRA, an innovative extension of LoRA and DoRA, characterized by symmetrical properties across horizontal and vertical dimensions. Our approach optimizes the weight matrix symmetrically by adjusting both column-wise and row-wise magnitudes. Extensive experiments demonstrate that BoRA surpasses state-of-the-art PEFT methods, including LoRA and DoRA, achieving superior results across various benchmarks.

Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the concept of unrolling an iterative algorithm and training it like a neural network. It has had great success on sparse recovery. In this paper, we show that adding momentum to intermediate variables in the LISTA network achieves a better convergence rate and, in particular, the network with instance-optimal parameters is superlinearly convergent. Moreover, our new theoretical results lead to a practical approach of automatically and adaptively calculating the parameters of a LISTA network layer based on its previous layers. Perhaps most surprisingly, such an adaptive-parameter procedure reduces the training of LISTA to tuning only three hyperparameters from data: a new record set in the context of the recent advances on trimming down LISTA complexity. We call this new ultra-light weight network HyperLISTA. Compared to state-of-the-art LISTA models, HyperLISTA achieves almost the same performance on seen data distributions and performs better when tested on unseen distributions (specifically, those with different sparsity levels and nonzero magnitudes). Code is available: https://github.com/VITA-Group/HyperLISTA.

The rapid scaling of large language models necessitates more lightweight finetuning methods to reduce the explosive GPU memory overhead when numerous customized models are served simultaneously. Targeting more parameter-efficient low-rank adaptation (LoRA), parameter sharing presents a promising solution. Empirically, our research into high-level sharing principles highlights the indispensable role of differentiation in reversing the detrimental effects of pure sharing. Guided by this finding, we propose Mixture of Shards (MoS), incorporating both inter-layer and intra-layer sharing schemes, and integrating four nearly cost-free differentiation strategies, namely subset selection, pair dissociation, vector sharding, and shard privatization. Briefly, it selects a designated number of shards from global pools with a Mixture-of-Experts (MoE)-like routing mechanism before sequentially concatenating them to low-rank matrices. Hence, it retains all the advantages of LoRA while offering enhanced parameter efficiency, and effectively circumvents the drawbacks of peer parameter-sharing methods. Our empirical experiments demonstrate approximately 8x parameter savings in a standard LoRA setting. The ablation study confirms the significance of each component. Our insights into parameter sharing and MoS method may illuminate future developments of more parameter-efficient finetuning methods.

In this work, we re-formulate the model compression problem into the customized compensation problem: Given a compressed model, we aim to introduce residual low-rank paths to compensate for compression errors under customized requirements from users (e.g., tasks, compression ratios), resulting in greater flexibility in adjusting overall capacity without being constrained by specific compression formats. However, naively applying SVD to derive residual paths causes suboptimal utilization of the low-rank representation capacity. Instead, we propose Training-free Eigenspace Low-Rank Approximation (EoRA), a method that directly minimizes compression-induced errors without requiring gradient-based training, achieving fast optimization in minutes using a small amount of calibration data. EoRA projects compression errors into the eigenspace of input activations, leveraging eigenvalues to effectively prioritize the reconstruction of high-importance error components. Moreover, EoRA can be seamlessly integrated with fine-tuning and quantization to further improve effectiveness and efficiency. EoRA consistently outperforms previous methods in compensating errors for compressed LLaMA2/3 models on various tasks, such as language generation, commonsense reasoning, and math reasoning tasks (e.g., 31.31%/12.88% and 9.69% improvements on ARC-Easy/ARC-Challenge and MathQA when compensating LLaMA3-8B that is quantized to 4-bit and pruned to 2:4 sparsity). EoRA offers a scalable, training-free solution to compensate for compression errors, making it a powerful tool to deploy LLMs in various capacity and efficiency requirements.

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous O(n^{5/6}polylog(n)) fair approximation for cost to a near polylogarithmic O(n^delta polylog(n)) fair approximation for any constant deltain(0,1). This result establishes a cost-fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

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

Low-rank adaptation~(LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices A and B to represent the weight change, i.e., Delta W=BA. Despite LoRA's progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats Delta W as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover Delta W. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. Our code is released at https://github.com/Chaos96/fourierft.

LoRA (Low-Rank Adaptation) has emerged as a preferred method for efficiently adapting Large Language Models (LLMs) with remarkable simplicity and efficacy. This note extends the original LoRA paper by offering new perspectives that were not initially discussed and presents a series of insights for deploying LoRA at scale. Without introducing new experiments, we aim to improve the understanding and application of LoRA.

The scalability of deep learning models is fundamentally limited by computing resources, memory, and communication. Although methods like low-rank adaptation (LoRA) have reduced the cost of model finetuning, its application in model pre-training remains largely unexplored. This paper explores extending LoRA to model pre-training, identifying the inherent constraints and limitations of standard LoRA in this context. We introduce LoRA-the-Explorer (LTE), a novel bi-level optimization algorithm designed to enable parallel training of multiple low-rank heads across computing nodes, thereby reducing the need for frequent synchronization. Our approach includes extensive experimentation on vision transformers using various vision datasets, demonstrating that LTE is competitive with standard pre-training.

Low Rank Adaptation (LoRA) has emerged as one of the most widely adopted methods for Parameter Efficient Fine-Tuning (PEFT) of Large Language Models (LLMs). LoRA reduces the number of trainable parameters and memory usage while achieving comparable performance to full fine-tuning. We aim to assess the viability of training and serving LLMs fine-tuned with LoRA in real-world applications. First, we measure the quality of LLMs fine-tuned with quantized low rank adapters across 10 base models and 31 tasks for a total of 310 models. We find that 4-bit LoRA fine-tuned models outperform base models by 34 points and GPT-4 by 10 points on average. Second, we investigate the most effective base models for fine-tuning and assess the correlative and predictive capacities of task complexity heuristics in forecasting the outcomes of fine-tuning. Finally, we evaluate the latency and concurrency capabilities of LoRAX, an open-source Multi-LoRA inference server that facilitates the deployment of multiple LoRA fine-tuned models on a single GPU using shared base model weights and dynamic adapter loading. LoRAX powers LoRA Land, a web application that hosts 25 LoRA fine-tuned Mistral-7B LLMs on a single NVIDIA A100 GPU with 80GB memory. LoRA Land highlights the quality and cost-effectiveness of employing multiple specialized LLMs over a single, general-purpose LLM.

Various common deep learning architectures, such as LSTMs, GRUs, Resnets and Highway Networks, employ state passthrough connections that support training with high feed-forward depth or recurrence over many time steps. These "Passthrough Networks" architectures also enable the decoupling of the network state size from the number of parameters of the network, a possibility has been studied by Sak2014 with their low-rank parametrization of the LSTM. In this work we extend this line of research, proposing effective, low-rank and low-rank plus diagonal matrix parametrizations for Passthrough Networks which exploit this decoupling property, reducing the data complexity and memory requirements of the network while preserving its memory capacity. This is particularly beneficial in low-resource settings as it supports expressive models with a compact parametrization less susceptible to overfitting. We present competitive experimental results on several tasks, including language modeling and a near state of the art result on sequential randomly-permuted MNIST classification, a hard task on natural data.

Popular parameter-efficient fine-tuning (PEFT) methods, such as LoRA and its variants, freeze pre-trained model weights \(W\) and inject learnable matrices \(\Delta W\). These \(\Delta W\) matrices are structured for efficient parameterization, often using techniques like low-rank approximations or scaling vectors. However, these methods typically show a performance gap compared to full fine-tuning. Although recent PEFT methods have narrowed this gap, they do so at the cost of additional learnable parameters. We propose SVFT, a simple approach that fundamentally differs from existing methods: the structure imposed on \(\Delta W\) depends on the specific weight matrix \(W\). Specifically, SVFT updates \(W\) as a sparse combination of outer products of its singular vectors, training only the coefficients (scales) of these sparse combinations. This approach allows fine-grained control over expressivity through the number of coefficients. Extensive experiments on language and vision benchmarks show that SVFT recovers up to 96% of full fine-tuning performance while training only 0.006 to 0.25% of parameters, outperforming existing methods that only recover up to 85% performance using 0.03 to 0.8% of the trainable parameter budget.

Post-training quantization of Large Language Models (LLMs) is challenging. In this work, we introduce Low-rank Quantization Error Reduction (LQER), which combines quantization and low-rank approximation to recover the model capability. LQER leverages an activation-induced scale matrix to drive the singular value distribution of quantization error towards a desirable distribution, which enables nearly-lossless W4A8 quantization on various LLMs and downstream tasks without the need for knowledge distillation, grid search, or gradient-base iterative optimization. Unlike existing methods, the computation pattern of LQER eliminates the need for specialized Scatter and Gather processes to collect high-precision weights from irregular memory locations. Our W4A8 LLMs achieve near-lossless performance on six popular downstream tasks, while using 1.36times fewer hardware resources than the leading state-of-the-art method. We will open-source our framework once the paper is accepted.

Training large-scale neural networks in vision, and multimodal domains demands substantial memory resources, primarily due to the storage of optimizer states. While LoRA, a popular parameter-efficient method, reduces memory usage, it often suffers from suboptimal performance due to the constraints of low-rank updates. Low-rank gradient projection methods (e.g., GaLore, Flora) reduce optimizer memory by projecting gradients and moment estimates into low-rank spaces via singular value decomposition or random projection. However, they fail to account for inter-projection correlation, causing performance degradation, and their projection strategies often incur high computational costs. In this paper, we present COAP (Correlation-Aware Gradient Projection), a memory-efficient method that minimizes computational overhead while maintaining training performance. Evaluated across various vision, language, and multimodal tasks, COAP outperforms existing methods in both training speed and model performance. For LLaMA-1B, it reduces optimizer memory by 61% with only 2% additional time cost, achieving the same PPL as AdamW. With 8-bit quantization, COAP cuts optimizer memory by 81% and achieves 4x speedup over GaLore for LLaVA-v1.5-7B fine-tuning, while delivering higher accuracy.

As the heart of a search engine, the ranking system plays a crucial role in satisfying users' information demands. More recently, neural rankers fine-tuned from pre-trained language models (PLMs) establish state-of-the-art ranking effectiveness. However, it is nontrivial to directly apply these PLM-based rankers to the large-scale web search system due to the following challenging issues:(1) the prohibitively expensive computations of massive neural PLMs, especially for long texts in the web-document, prohibit their deployments in an online ranking system that demands extremely low latency;(2) the discrepancy between existing ranking-agnostic pre-training objectives and the ad-hoc retrieval scenarios that demand comprehensive relevance modeling is another main barrier for improving the online ranking system;(3) a real-world search engine typically involves a committee of ranking components, and thus the compatibility of the individually fine-tuned ranking model is critical for a cooperative ranking system. In this work, we contribute a series of successfully applied techniques in tackling these exposed issues when deploying the state-of-the-art Chinese pre-trained language model, i.e., ERNIE, in the online search engine system. We first articulate a novel practice to cost-efficiently summarize the web document and contextualize the resultant summary content with the query using a cheap yet powerful Pyramid-ERNIE architecture. Then we endow an innovative paradigm to finely exploit the large-scale noisy and biased post-click behavioral data for relevance-oriented pre-training. We also propose a human-anchored fine-tuning strategy tailored for the online ranking system, aiming to stabilize the ranking signals across various online components. Extensive offline and online experimental results show that the proposed techniques significantly boost the search engine's performance.

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

Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.git

Training deep neural networks in low rank, i.e. with factorised layers, is of particular interest to the community: it offers efficiency over unfactorised training in terms of both memory consumption and training time. Prior work has focused on low rank approximations of pre-trained networks and training in low rank space with additional objectives, offering various ad hoc explanations for chosen practice. We analyse techniques that work well in practice, and through extensive ablations on models such as GPT2 we provide evidence falsifying common beliefs in the field, hinting in the process at exciting research opportunities that still need answering.

Large pre-trained models (LPMs), such as LLaMA and GLM, have shown exceptional performance across various tasks through fine-tuning. Although low-rank adaption (LoRA) has emerged to cheaply fine-tune these LPMs on downstream tasks, their deployment is still hindered by the vast model scale and computational costs. Neural network pruning offers a way to compress LPMs. However, the current pruning methods designed for LPMs are not compatible with LoRA. This is due to their utilization of unstructured pruning on LPMs, impeding the merging of LoRA weights, or their dependence on the gradients of pre-trained weights to guide pruning, which can impose significant memory overhead. To this end, we propose LoRAPrune, a new framework that delivers an accurate, compact model for efficient inference in a highly memory-effective manner. Specifically, we first design a LoRA-guided pruning criterion, which uses the weights and gradients of LoRA, rather than the gradients of pre-trained weights for importance estimation. We then propose a structured iterative pruning procedure, to remove redundant channels and heads. Extensive experimental results demonstrate the superior performance of our LoRAPrune over existing approaches on the LLaMA series models. For instance, at a 50\% compression rate, LoRAPrune outperforms LLM-Pruner by a perplexity reduction of 8.0 on WikiText2 and 16.05 on PTB datasets, while concurrently reducing memory usage by 52.6\%. The code will be released after review

Recent innovations in Transformer-based ranking models have advanced the state-of-the-art in information retrieval. However, these Transformers are computationally expensive, and their opaque hidden states make it hard to understand the ranking process. In this work, we modularize the Transformer ranker into separate modules for text representation and interaction. We show how this design enables substantially faster ranking using offline pre-computed representations and light-weight online interactions. The modular design is also easier to interpret and sheds light on the ranking process in Transformer rankers.

Graph Structure Learning (GSL) focuses on capturing intrinsic dependencies and interactions among nodes in graph-structured data by generating novel graph structures. Graph Neural Networks (GNNs) have emerged as promising GSL solutions, utilizing recursive message passing to encode node-wise inter-dependencies. However, many existing GSL methods heavily depend on explicit graph structural information as supervision signals, leaving them susceptible to challenges such as data noise and sparsity. In this work, we propose GraphEdit, an approach that leverages large language models (LLMs) to learn complex node relationships in graph-structured data. By enhancing the reasoning capabilities of LLMs through instruction-tuning over graph structures, we aim to overcome the limitations associated with explicit graph structural information and enhance the reliability of graph structure learning. Our approach not only effectively denoises noisy connections but also identifies node-wise dependencies from a global perspective, providing a comprehensive understanding of the graph structure. We conduct extensive experiments on multiple benchmark datasets to demonstrate the effectiveness and robustness of GraphEdit across various settings. We have made our model implementation available at: https://github.com/HKUDS/GraphEdit.

Hierarchical structures are popular in recent vision transformers, however, they require sophisticated designs and massive datasets to work well. In this paper, we explore the idea of nesting basic local transformers on non-overlapping image blocks and aggregating them in a hierarchical way. We find that the block aggregation function plays a critical role in enabling cross-block non-local information communication. This observation leads us to design a simplified architecture that requires minor code changes upon the original vision transformer. The benefits of the proposed judiciously-selected design are threefold: (1) NesT converges faster and requires much less training data to achieve good generalization on both ImageNet and small datasets like CIFAR; (2) when extending our key ideas to image generation, NesT leads to a strong decoder that is 8times faster than previous transformer-based generators; and (3) we show that decoupling the feature learning and abstraction processes via this nested hierarchy in our design enables constructing a novel method (named GradCAT) for visually interpreting the learned model. Source code is available https://github.com/google-research/nested-transformer.

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.

We propose Tied-LoRA, a simple paradigm utilizes weight tying and selective training to further increase parameter efficiency of the Low-rank adaptation (LoRA) method. Our investigations include all feasible combinations parameter training/freezing in conjunction with weight tying to identify the optimal balance between performance and the number of trainable parameters. Through experiments covering a variety of tasks and two base language models, we provide analysis revealing trade-offs between efficiency and performance. Our experiments uncovered a particular Tied-LoRA configuration that stands out by demonstrating comparable performance across several tasks while employing only 13~\% percent of parameters utilized by the standard LoRA method.

Federated fine-tuning (FedFT) has been proposed to fine-tune the pre-trained language models in a distributed manner. However, there are two critical challenges for efficient FedFT in practical applications, i.e., resource constraints and system heterogeneity. Existing works rely on parameter-efficient fine-tuning methods, e.g., low-rank adaptation (LoRA), but with major limitations. Herein, based on the inherent characteristics of FedFT, we observe that LoRA layers with higher ranks added close to the output help to save resource consumption while achieving comparable fine-tuning performance. Then we propose a novel LoRA-based FedFT framework, termed LEGEND, which faces the difficulty of determining the number of LoRA layers (called, LoRA depth) and the rank of each LoRA layer (called, rank distribution). We analyze the coupled relationship between LoRA depth and rank distribution, and design an efficient LoRA configuration algorithm for heterogeneous devices, thereby promoting fine-tuning efficiency. Extensive experiments are conducted on a physical platform with 80 commercial devices. The results show that LEGEND can achieve a speedup of 1.5-2.8times and save communication costs by about 42.3% when achieving the target accuracy, compared to the advanced solutions.

Music is characterized by complex hierarchical structures. Developing a comprehensive model to capture these structures has been a significant challenge in the field of Music Information Retrieval (MIR). Prior research has mainly focused on addressing individual tasks for specific hierarchical levels, rather than providing a unified approach. In this paper, we introduce a versatile, all-in-one model that jointly performs beat and downbeat tracking as well as functional structure segmentation and labeling. The model leverages source-separated spectrograms as inputs and employs dilated neighborhood attentions to capture temporal long-term dependencies, along with non-dilated attentions for local instrumental dependencies. Consequently, the proposed model achieves state-of-the-art performance in all four tasks on the Harmonix Set while maintaining a relatively lower number of parameters compared to recent state-of-the-art models. Furthermore, our ablation study demonstrates that the concurrent learning of beats, downbeats, and segments can lead to enhanced performance, with each task mutually benefiting from the others.

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.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges, particularly on consumer-grade hardware. This paper introduces an innovative approach for the parametric and practical compression of LLMs based on reduced order modelling, which entails low-rank decomposition within the feature space and re-parameterization in the weight space. Notably, this compression technique operates in a layer-wise manner, obviating the need for a GPU device and enabling the compression of billion-scale models within stringent constraints of both memory and time. Our method represents a significant advancement in model compression by leveraging matrix decomposition, demonstrating superior efficacy compared to the prevailing state-of-the-art structured pruning method.

Training multiple tasks jointly in one deep network yields reduced latency during inference and better performance over the single-task counterpart by sharing certain layers of a network. However, over-sharing a network could erroneously enforce over-generalization, causing negative knowledge transfer across tasks. Prior works rely on human intuition or pre-computed task relatedness scores for ad hoc branching structures. They provide sub-optimal end results and often require huge efforts for the trial-and-error process. In this work, we present an automated multi-task learning algorithm that learns where to share or branch within a network, designing an effective network topology that is directly optimized for multiple objectives across tasks. Specifically, we propose a novel tree-structured design space that casts a tree branching operation as a gumbel-softmax sampling procedure. This enables differentiable network splitting that is end-to-end trainable. We validate the proposed method on controlled synthetic data, CelebA, and Taskonomy.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.