Daily Papers

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.

Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively. However, the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive. To solve this problem, co-attention builds two separate attention distributions for each modality neglecting the interaction between multimodal inputs. In this paper, we propose bilinear attention networks (BAN) that find bilinear attention distributions to utilize given vision-language information seamlessly. BAN considers bilinear interactions among two groups of input channels, while low-rank bilinear pooling extracts the joint representations for each pair of channels. Furthermore, we propose a variant of multimodal residual networks to exploit eight-attention maps of the BAN efficiently. We quantitatively and qualitatively evaluate our model on visual question answering (VQA 2.0) and Flickr30k Entities datasets, showing that BAN significantly outperforms previous methods and achieves new state-of-the-arts on both datasets.

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

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Over the last few years, multi-vector retrieval methods, spearheaded by ColBERT, have become an increasingly popular approach to Neural IR. By storing representations at the token level rather than at the document level, these methods have demonstrated very strong retrieval performance, especially in out-of-domain settings. However, the storage and memory requirements necessary to store the large number of associated vectors remain an important drawback, hindering practical adoption. In this paper, we introduce a simple clustering-based token pooling approach to aggressively reduce the number of vectors that need to be stored. This method can reduce the space & memory footprint of ColBERT indexes by 50% with virtually no retrieval performance degradation. This method also allows for further reductions, reducing the vector count by 66%-to-75% , with degradation remaining below 5% on a vast majority of datasets. Importantly, this approach requires no architectural change nor query-time processing, and can be used as a simple drop-in during indexation with any ColBERT-like model.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).

The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.

Active learning for imbalanced classification tasks is challenging as the minority classes naturally occur rarely. Gathering a large pool of unlabelled data is thus essential to capture minority instances. Standard pool-based active learning is computationally expensive on large pools and often reaches low accuracy by overfitting the initial decision boundary, thus failing to explore the input space and find minority instances. To address these issues we propose AnchorAL. At each iteration, AnchorAL chooses class-specific instances from the labelled set, or anchors, and retrieves the most similar unlabelled instances from the pool. This resulting subpool is then used for active learning. Using a small, fixed-sized subpool AnchorAL allows scaling any active learning strategy to large pools. By dynamically selecting different anchors at each iteration it promotes class balance and prevents overfitting the initial decision boundary, thus promoting the discovery of new clusters of minority instances. Experiments across different classification tasks, active learning strategies, and model architectures AnchorAL is (i) faster, often reducing runtime from hours to minutes, (ii) trains more performant models, (iii) and returns more balanced datasets than competing methods.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

Representation learning is central to many downstream tasks such as search, clustering, classification, and reranking. State-of-the-art sequence encoders typically collapse a variable-length token sequence to a single vector using a pooling operator, most commonly a special [CLS] token or mean pooling over token embeddings. In this paper, we identify systematic weaknesses of these pooling strategies: [CLS] tends to concentrate information toward the initial positions of the sequence and can under-represent distributed evidence, while mean pooling can dilute salient local signals, sometimes leading to worse short-context performance. To address these issues, we introduce Landmark (LMK) pooling, which partitions a sequence into chunks, inserts landmark tokens between chunks, and forms the final representation by mean-pooling the landmark token embeddings. This simple mechanism improves long-context extrapolation without sacrificing local salient features, at the cost of introducing a small number of special tokens. We empirically demonstrate that LMK pooling matches existing methods on short-context retrieval tasks and yields substantial improvements on long-context tasks, making it a practical and scalable alternative to existing pooling methods.

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.

We propose ListT5, a novel reranking approach based on Fusion-in-Decoder (FiD) that handles multiple candidate passages at both train and inference time. We also introduce an efficient inference framework for listwise ranking based on m-ary tournament sort with output caching. We evaluate and compare our model on the BEIR benchmark for zero-shot retrieval task, demonstrating that ListT5 (1) outperforms the state-of-the-art RankT5 baseline with a notable +1.3 gain in the average NDCG@10 score, (2) has an efficiency comparable to pointwise ranking models and surpasses the efficiency of previous listwise ranking models, and (3) overcomes the lost-in-the-middle problem of previous listwise rerankers. Our code, model checkpoints, and the evaluation framework are fully open-sourced at https://github.com/soyoung97/ListT5.

The significant advancements of Large Language Models (LLMs) in generative tasks have led to a growing body of work exploring LLM-based embedding models. While these models, employing different pooling and attention strategies, have achieved state-of-the-art performance on public embedding benchmarks, questions still arise about what constitutes an effective design for LLM-based embedding models. However, these models are often trained on different datasets, using different LLM base models or training settings. Moreover, evaluations on public embedding benchmarks often fail to report statistical significance, making it difficult to determine which designs truly contribute to final performance. This complicates the process for practitioners seeking optimal training recipes for LLM-based embedding models. In this study, we conduct a large-scale experiment by training a series of LLM-based embedding models using the same training data and base model but differing in their pooling and attention strategies. The results show that there is no one-size-fits-all solution: while bidirectional attention and an additional trainable pooling layer outperform in text similarity and information retrieval tasks, they do not significantly surpass simpler designs like EOS-last token pooling and default causal attention in clustering and classification tasks. Furthermore, we propose a new pooling strategy, Multi-Layers Trainable Pooling, which transforms the outputs of all hidden layers, rather than just the last layer, using a cross-attention network. This method proves to be statistically superior in text similarity and retrieval tasks compared to existing pooling methods. Overall, this paper sheds light on effective training strategies for LLM-based embedding models.

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.

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.

In neural Information Retrieval (IR), ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than 9\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes that closely resemble the input volume while, ideally, also being computationally and memory efficient. Meeting both these requirements remains a challenge. To this end, we propose an adaptive and exponentially weighted pooling method: adaPool. Our method learns a regional-specific fusion of two sets of pooling kernels that are based on the exponent of the Dice-Sorensen coefficient and the exponential maximum, respectively. AdaPool improves the preservation of detail on a range of tasks including image and video classification and object detection. A key property of adaPool is its bidirectional nature. In contrast to common pooling methods, the learned weights can also be used to upsample activation maps. We term this method adaUnPool. We evaluate adaUnPool on image and video super-resolution and frame interpolation. For benchmarking, we introduce Inter4K, a novel high-quality, high frame-rate video dataset. Our experiments demonstrate that adaPool systematically achieves better results across tasks and backbones, while introducing a minor additional computational and memory overhead.

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.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

Variational inequalities in general and saddle point problems in particular are increasingly relevant in machine learning applications, including adversarial learning, GANs, transport and robust optimization. With increasing data and problem sizes necessary to train high performing models across various applications, we need to rely on parallel and distributed computing. However, in distributed training, communication among the compute nodes is a key bottleneck during training, and this problem is exacerbated for high dimensional and over-parameterized models. Due to these considerations, it is important to equip existing methods with strategies that would allow to reduce the volume of transmitted information during training while obtaining a model of comparable quality. In this paper, we present the first theoretically grounded distributed methods for solving variational inequalities and saddle point problems using compressed communication: MASHA1 and MASHA2. Our theory and methods allow for the use of both unbiased (such as Randk; MASHA1) and contractive (such as Topk; MASHA2) compressors. New algorithms support bidirectional compressions, and also can be modified for stochastic setting with batches and for federated learning with partial participation of clients. We empirically validated our conclusions using two experimental setups: a standard bilinear min-max problem, and large-scale distributed adversarial training of transformers.

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.

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

Despite the recent success in many applications, the high computational requirements of vision transformers limit their use in resource-constrained settings. While many existing methods improve the quadratic complexity of attention, in most vision transformers, self-attention is not the major computation bottleneck, e.g., more than 80% of the computation is spent on fully-connected layers. To improve the computational complexity of all layers, we propose a novel token downsampling method, called Token Pooling, efficiently exploiting redundancies in the images and intermediate token representations. We show that, under mild assumptions, softmax-attention acts as a high-dimensional low-pass (smoothing) filter. Thus, its output contains redundancy that can be pruned to achieve a better trade-off between the computational cost and accuracy. Our new technique accurately approximates a set of tokens by minimizing the reconstruction error caused by downsampling. We solve this optimization problem via cost-efficient clustering. We rigorously analyze and compare to prior downsampling methods. Our experiments show that Token Pooling significantly improves the cost-accuracy trade-off over the state-of-the-art downsampling. Token Pooling is a simple and effective operator that can benefit many architectures. Applied to DeiT, it achieves the same ImageNet top-1 accuracy using 42% fewer computations.

A common architectural choice for deep metric learning is a convolutional neural network followed by global average pooling (GAP). Albeit simple, GAP is a highly effective way to aggregate information. One possible explanation for the effectiveness of GAP is considering each feature vector as representing a different semantic entity and GAP as a convex combination of them. Following this perspective, we generalize GAP and propose a learnable generalized sum pooling method (GSP). GSP improves GAP with two distinct abilities: i) the ability to choose a subset of semantic entities, effectively learning to ignore nuisance information, and ii) learning the weights corresponding to the importance of each entity. Formally, we propose an entropy-smoothed optimal transport problem and show that it is a strict generalization of GAP, i.e., a specific realization of the problem gives back GAP. We show that this optimization problem enjoys analytical gradients enabling us to use it as a direct learnable replacement for GAP. We further propose a zero-shot loss to ease the learning of GSP. We show the effectiveness of our method with extensive evaluations on 4 popular metric learning benchmarks. Code is available at: GSP-DML Framework

We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.

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 optimization has emerged as a promising direction in training large language models (LLMs) to reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work typically projects gradients of linear layers using approaches based on Singular Value Decomposition (SVD). However, applying SVD-based procedures individually to each layer in large models is computationally expensive and incurs additional memory costs due to storing the projection matrices. In this work, we propose a computationally efficient and conceptually simple two-step procedure to approximate SVD-based gradient projections into lower-dimensional spaces. First, we construct a complete orthogonal basis using predefined orthogonal matrices of the Discrete Cosine Transform (DCT). Second, we adaptively select basis columns based on their alignment with the gradient of each layer. Each projection matrix in our method is obtained via a single matrix multiplication followed by a lightweight sorting step to identify the most relevant basis vectors. Due to the predefined nature of the orthogonal bases, they are computed once at the start of training. During training, we store only the indices of the selected columns, avoiding the need to store full projection matrices for each layer. Our numerical experiments on both pre-training and fine-tuning tasks demonstrate the effectiveness of our dual strategy in approximating optimal low-rank projections, matching the performance of costly SVD-based methods while achieving faster runtime and reduced memory usage.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

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.

Learned multivector representations power modern search systems with strong retrieval effectiveness, but their real-world use is limited by the high cost of exhaustive token-level retrieval. Therefore, most systems adopt a gather-and-refine strategy, where a lightweight gather phase selects candidates for full scoring. However, this approach requires expensive searches over large token-level indexes and often misses the documents that would rank highest under full similarity. In this paper, we reproduce several state-of-the-art multivector retrieval methods on two publicly available datasets, providing a clear picture of the current multivector retrieval field and observing the inefficiency of token-level gathering. Building on top of that, we show that replacing the token-level gather phase with a single-vector document retriever -- specifically, a learned sparse retriever (LSR) -- produces a smaller and more semantically coherent candidate set. This recasts the gather-and-refine pipeline into the well-established two-stage retrieval architecture. As retrieval latency decreases, query encoding with two neural encoders becomes the dominant computational bottleneck. To mitigate this, we integrate recent inference-free LSR methods, demonstrating that they preserve the retrieval effectiveness of the dual-encoder pipeline while substantially reducing query encoding time. Finally, we investigate multiple reranking configurations that balance efficiency, memory, and effectiveness, and we introduce two optimization techniques that prune low-quality candidates early. Empirical results show that these techniques improve retrieval efficiency by up to 1.8times with no loss in quality. Overall, our two-stage approach achieves over 24times speedup over the state-of-the-art multivector retrieval systems, while maintaining comparable or superior retrieval quality.

Downsampling layers, including pooling and strided convolutions, are crucial components of the convolutional neural network architecture that determine both the granularity/scale of image feature analysis as well as the receptive field size of a given layer. To fully understand this problem, we analyse the performance of models independently trained with each pooling configurations on CIFAR10, using a ResNet20 network, and show that the position of the downsampling layers can highly influence the performance of a network and predefined downsampling configurations are not optimal. Network Architecture Search (NAS) might be used to optimize downsampling configurations as an hyperparameter. However, we find that common one-shot NAS based on a single SuperNet does not work for this problem. We argue that this is because a SuperNet trained for finding the optimal pooling configuration fully shares its parameters among all pooling configurations. This makes its training hard, because learning some configurations can harm the performance of others. Therefore, we propose a balanced mixture of SuperNets that automatically associates pooling configurations to different weight models and helps to reduce the weight-sharing and inter-influence of pooling configurations on the SuperNet parameters. We evaluate our proposed approach on CIFAR10, CIFAR100, as well as Food101 and show that in all cases, our model outperforms other approaches and improves over the default pooling configurations.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

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.

The computing cost and memory demand of deep learning pipelines have grown fast in recent years and thus a variety of pruning techniques have been developed to reduce model parameters. The majority of these techniques focus on reducing inference costs by pruning the network after a pass of full training. A smaller number of methods address the reduction of training costs, mostly based on compressing the network via low-rank layer factorizations. Despite their efficiency for linear layers, these methods fail to effectively handle convolutional filters. In this work, we propose a low-parametric training method that factorizes the convolutions into tensor Tucker format and adaptively prunes the Tucker ranks of the convolutional kernel during training. Leveraging fundamental results from geometric integration theory of differential equations on tensor manifolds, we obtain a robust training algorithm that provably approximates the full baseline performance and guarantees loss descent. A variety of experiments against the full model and alternative low-rank baselines are implemented, showing that the proposed method drastically reduces the training costs, while achieving high performance, comparable to or better than the full baseline, and consistently outperforms competing low-rank approaches.

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

The paper ``Tropical Geometry of Deep Neural Networks'' by L. Zhang et al. introduces an equivalence between integer-valued neural networks (IVNN) with ReLU_{t} and tropical rational functions, which come with a map to polytopes. Here, IVNN refers to a network with integer weights but real biases, and ReLU_{t} is defined as ReLU_{t}(x)=max(x,t) for tinRcup{-infty}. For every poset with n points, there exists a corresponding order polytope, i.e., a convex polytope in the unit cube [0,1]^n whose coordinates obey the inequalities of the poset. We study neural networks whose associated polytope is an order polytope. We then explain how posets with four points induce neural networks that can be interpreted as 2times 2 convolutional filters. These poset filters can be added to any neural network, not only IVNN. Similarly to maxout, poset pooling filters update the weights of the neural network during backpropagation with more precision than average pooling, max pooling, or mixed pooling, without the need to train extra parameters. We report experiments that support our statements. We also define the structure of algebra over the operad of posets on poset neural networks and tropical polynomials. This formalism allows us to study the composition of poset neural network arquitectures and the effect on their corresponding Newton polytopes, via the introduction of the generalization of two operations on polytopes: the Minkowski sum and the convex envelope.

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it is competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs. Our code is published at https://github.com/ipsitmantri/GLOT.

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of Obigl(NKD^3bigr) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to Obigl(NKD^2bigr) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.

Neural ranking models (NRMs) have become one of the most important techniques in information retrieval (IR). Due to the limitation of relevance labels, the training of NRMs heavily relies on negative sampling over unlabeled data. In general machine learning scenarios, it has shown that training with hard negatives (i.e., samples that are close to positives) could lead to better performance. Surprisingly, we find opposite results from our empirical studies in IR. When sampling top-ranked results (excluding the labeled positives) as negatives from a stronger retriever, the performance of the learned NRM becomes even worse. Based on our investigation, the superficial reason is that there are more false negatives (i.e., unlabeled positives) in the top-ranked results with a stronger retriever, which may hurt the training process; The root is the existence of pooling bias in the dataset constructing process, where annotators only judge and label very few samples selected by some basic retrievers. Therefore, in principle, we can formulate the false negative issue in training NRMs as learning from labeled datasets with pooling bias. To solve this problem, we propose a novel Coupled Estimation Technique (CET) that learns both a relevance model and a selection model simultaneously to correct the pooling bias for training NRMs. Empirical results on three retrieval benchmarks show that NRMs trained with our technique can achieve significant gains on ranking effectiveness against other baseline strategies.

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.

We focus on addressing the dense backward propagation issue for training efficiency of N:M fine-grained sparsity that preserves at most N out of M consecutive weights and achieves practical speedups supported by the N:M sparse tensor core. Therefore, we present a novel method of Bi-directional Masks (Bi-Mask) with its two central innovations in: 1) Separate sparse masks in the two directions of forward and backward propagation to obtain training acceleration. It disentangles the forward and backward weight sparsity and overcomes the very dense gradient computation. 2) An efficient weight row permutation method to maintain performance. It picks up the permutation candidate with the most eligible N:M weight blocks in the backward to minimize the gradient gap between traditional uni-directional masks and our bi-directional masks. Compared with existing uni-directional scenario that applies a transposable mask and enables backward acceleration, our Bi-Mask is experimentally demonstrated to be more superior in performance. Also, our Bi-Mask performs on par with or even better than methods that fail to achieve backward acceleration. Project of this paper is available at https://github.com/zyxxmu/Bi-Mask.

Recently, Qiao, Duan, and Cheng~(2019) proposed a distributed nearest-neighbor classification method, in which a massive dataset is split into smaller groups, each processed with a k-nearest-neighbor classifier, and the final class label is predicted by a majority vote among these groupwise class labels. This paper shows that the distributed algorithm with k=1 over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions, for both regression and classification problems. Roughly speaking, distributed 1-nearest-neighbor rules with M groups has a performance comparable to standard Theta(M)-nearest-neighbor rules. In the analysis, alternative rules with a refined aggregation method are proposed and shown to attain exact minimax optimal rates.

We study the polynomial-time approximability of the optimal online stochastic bipartite matching algorithm, initiated by Papadimitriou et al. (EC'21). Here, nodes on one side of the graph are given upfront, while at each time t, an online node and its edge weights are drawn from a time-dependent distribution. The optimal algorithm is PSPACE-hard to approximate within some universal constant. We refer to this optimal algorithm, which requires time to think (compute), as a philosopher, and refer to polynomial-time online approximations of the above as philosopher inequalities. The best known philosopher inequality for online matching yields a 0.652-approximation. In contrast, the best possible prophet inequality, or approximation of the optimum offline solution, is 0.5. Our main results are a 0.678-approximate algorithm and a 0.685-approximation for a vertex-weighted special case. Notably, both bounds exceed the 0.666-approximation of the offline optimum obtained by Tang, Wu, and Wu (STOC'22) for the vertex-weighted problem. Building on our algorithms and the recent black-box reduction of Banihashem et al. (SODA'24), we provide polytime (pricing-based) truthful mechanisms which 0.678-approximate the social welfare of the optimal online allocation for bipartite matching markets. Our online allocation algorithm relies on the classic pivotal sampling algorithm (Srinivasan FOCS'01, Gandhi et al. J.ACM'06), along with careful discarding to obtain negative correlations between offline nodes. Consequently, the analysis boils down to examining the distribution of a weighted sum X of negatively correlated Bernoulli variables, specifically lower bounding its mass below a threshold, E[min(1,X)], of possible independent interest. Interestingly, our bound relies on an imaginary invocation of pivotal sampling.

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, we first design a counter-example to illustrate the invalidation of such LLS condition. Then by formulating BLPs from the view point of optimistic bi-level and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for generic bi-level optimization. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules. Additionally, as an interesting byproduct, we also improve these conventional first-order bi-level schemes (under the LLS simplification). Particularly, we establish their convergences with weaker assumptions. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

Graph neural networks (GNNs) are one of the most popular approaches to using deep learning on graph-structured data, and they have shown state-of-the-art performances on a variety of tasks. However, according to a recent study, a careful choice of pooling functions, which are used for the aggregation and readout operations in GNNs, is crucial for enabling GNNs to extrapolate. Without proper choices of pooling functions, which varies across tasks, GNNs completely fail to generalize to out-of-distribution data, while the number of possible choices grows exponentially with the number of layers. In this paper, we present GNP, a L^p norm-like pooling function that is trainable end-to-end for any given task. Notably, GNP generalizes most of the widely-used pooling functions. We verify experimentally that simply using GNP for every aggregation and readout operation enables GNNs to extrapolate well on many node-level, graph-level, and set-related tasks; and GNP sometimes performs even better than the best-performing choices among existing pooling functions.

Deep learning models have achieved state-of-the-art performances on many relation extraction datasets. A common element in these deep learning models involves the pooling mechanisms where a sequence of hidden vectors is aggregated to generate a single representation vector, serving as the features to perform prediction for RE. Unfortunately, the models in the literature tend to employ different strategies to perform pooling for RE, leading to the challenge to determine the best pooling mechanism for this problem, especially in the biomedical domain. In order to answer this question, in this work, we conduct a comprehensive study to evaluate the effectiveness of different pooling mechanisms for the deep learning models in biomedical RE. The experimental results suggest that dependency-based pooling is the best pooling strategy for RE in the biomedical domain, yielding the state-of-the-art performance on two benchmark datasets for this problem.

Hierarchical graph pooling(HGP) are designed to consider the fact that conventional graph neural networks(GNN) are inherently flat and are also not multiscale. However, most HGP methods suffer not only from lack of considering global topology of the graph and focusing on the feature learning aspect, but also they do not align local and global features since graphs should inherently be analyzed in a multiscale way. LGRPool is proposed in the present paper as a HGP in the framework of expectation maximization in machine learning that aligns local and global aspects of message passing with each other using a regularizer to force the global topological information to be inline with the local message passing at different scales through the representations at different layers of HGP. Experimental results on some graph classification benchmarks show that it slightly outperforms some baselines.

Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs are nearly power-law distributed: their values are mostly clustered into a small number of codewords. This phenomenon encourages us to compact typical BNNs and obtain further close performance through learning non-repetitive kernels within a binary kernel subspace. Specifically, we regard the binarization process as kernel grouping in terms of a binary codebook, and our task lies in learning to select a smaller subset of codewords from the full codebook. We then leverage the Gumbel-Sinkhorn technique to approximate the codeword selection process, and develop the Permutation Straight-Through Estimator (PSTE) that is able to not only optimize the selection process end-to-end but also maintain the non-repetitive occupancy of selected codewords. Experiments verify that our method reduces both the model size and bit-wise computational costs, and achieves accuracy improvements compared with state-of-the-art BNNs under comparable budgets.

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.

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.

Streaming submodular maximization is a natural model for the task of selecting a representative subset from a large-scale dataset. If datapoints have sensitive attributes such as gender or race, it becomes important to enforce fairness to avoid bias and discrimination. This has spurred significant interest in developing fair machine learning algorithms. Recently, such algorithms have been developed for monotone submodular maximization under a cardinality constraint. In this paper, we study the natural generalization of this problem to a matroid constraint. We give streaming algorithms as well as impossibility results that provide trade-offs between efficiency, quality and fairness. We validate our findings empirically on a range of well-known real-world applications: exemplar-based clustering, movie recommendation, and maximum coverage in social networks.

Efficiently ranking relevant items from large candidate pools is a cornerstone of modern information retrieval systems -- such as web search, recommendation, and retrieval-augmented generation. Listwise rerankers, which improve relevance by jointly considering multiple candidates, are often limited in practice: either by model input size constraints, or by degraded quality when processing large sets. We propose a model-agnostic method for fast reranking large sets that exceed a model input limits. The method first partitions candidate items into overlapping blocks, each of which is ranked independently in parallel. Implicit pairwise comparisons are then derived from these local rankings. Finally, these comparisons are aggregated to construct a global ranking using algorithms such as Winrate or PageRank. Experiments on TREC DL-2019 show that our method achieves an nDCG@10 of 70.88 compared to the 57.68 for full-context listwise approach using gpt-4.1-mini as long-context model, while reducing latency from 21 to 8 seconds. The implementation of the algorithm and the experiments is available in the repository: https://github.com/V3RGANz/jointrank

Block-sparse attention is promising for accelerating long-context LLM pre-filling, yet identifying relevant blocks efficiently remains a bottleneck. Existing methods typically employ coarse-grained attention as a proxy for block importance estimation, but often resort to expensive token-level searching or scoring, resulting in significant selection overhead. In this work, we trace the inaccuracy of standard coarse-grained attention via mean pooling to a theoretical root cause: the interaction between mean pooling and Rotary Positional Embeddings (RoPE). We prove that mean pooling acts as a low-pass filter that induces destructive interference in high-frequency dimensions, effectively creating a "blind spot" for local positional information (e.g., slash patterns). To address this, we introduce Prism, a training-free spectral-aware approach that decomposes block selection into high-frequency and low-frequency branches. By applying energy-based temperature calibration, Prism restores the attenuated positional signals directly from pooled representations, enabling block importance estimation using purely block-level operations, thereby improving efficiency. Extensive evaluations confirm that Prism maintains accuracy parity with full attention while delivering up to 5.1times speedup.

Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based listwise methods, while aiming to optimise entire lists, require complex tuning and yield only marginal improvements over robust pairwise models. To overcome these limitations, we introduce Travelling Salesman Problem Rank (TSPRank), a hybrid pairwise-listwise ranking method. TSPRank reframes the ranking problem as a Travelling Salesman Problem (TSP), a well-known combinatorial optimisation challenge that has been extensively studied for its numerous solution algorithms and applications. This approach enables the modelling of pairwise relationships and leverages combinatorial optimisation to determine the listwise ranking. This approach can be directly integrated as an additional component into embeddings generated by existing backbone models to enhance ranking performance. Our extensive experiments across three backbone models on diverse tasks, including stock ranking, information retrieval, and historical events ordering, demonstrate that TSPRank significantly outperforms both pure pairwise and listwise methods. Our qualitative analysis reveals that TSPRank's main advantage over existing methods is its ability to harness global information better while ranking. TSPRank's robustness and superior performance across different domains highlight its potential as a versatile and effective LETOR solution.

Low-Rank Adaptation (LoRA) has become a widely adopted technique for fine-tuning large-scale pre-trained models with minimal parameter updates. However, existing methods rely on fixed ranks or focus solely on either rank pruning or expansion, failing to adapt ranks dynamically to match the importance of different layers during training. In this work, we propose ElaLoRA, an adaptive low-rank adaptation framework that dynamically prunes and expands ranks based on gradient-derived importance scores. To the best of our knowledge, ElaLoRA is the first method that enables both rank pruning and expansion during fine-tuning. Experiments across multiple benchmarks demonstrate that ElaLoRA consistently outperforms existing PEFT methods across different parameter budgets. Furthermore, our studies validate that layers receiving higher rank allocations contribute more significantly to model performance, providing theoretical justification for our adaptive strategy. By introducing a principled and adaptive rank allocation mechanism, ElaLoRA offers a scalable and efficient fine-tuning solution, particularly suited for resource-constrained environments.

Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally expensive job. To mitigate this, many techniques have been developed that prime efficiency, a prominent one being Low-Rank Adaptation (LoRA). However, LoRA and its variants employ re-parametrized additive updates. In this paper, we propose Low-Rank Multiplicative Adaptation (LoRMA), which shifts the paradigm of additive updates to a richer space of matrix multiplicative transformations. We tackle challenges such as computational complexity and rank bottleneck of matrix multiplication by effectively re-ordering operations and introducing rank inflation strategies. We conduct extensive experiments to demonstrate the effectiveness of our approach in terms of various evaluation metrics.

This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into {GPU} memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm.

Convolutional Neural Networks (CNNs) use pooling to decrease the size of activation maps. This process is crucial to increase the receptive fields and to reduce computational requirements of subsequent convolutions. An important feature of the pooling operation is the minimization of information loss, with respect to the initial activation maps, without a significant impact on the computation and memory overhead. To meet these requirements, we propose SoftPool: a fast and efficient method for exponentially weighted activation downsampling. Through experiments across a range of architectures and pooling methods, we demonstrate that SoftPool can retain more information in the reduced activation maps. This refined downsampling leads to improvements in a CNN's classification accuracy. Experiments with pooling layer substitutions on ImageNet1K show an increase in accuracy over both original architectures and other pooling methods. We also test SoftPool on video datasets for action recognition. Again, through the direct replacement of pooling layers, we observe consistent performance improvements while computational loads and memory requirements remain limited.

We investigate the design of pooling methods used to summarize the outputs of transformer embedding models, primarily motivated by reinforcement learning and vision applications. This work considers problems where a subset of the input vectors contains requisite information for a downstream task (signal) while the rest are distractors (noise). By framing pooling as vector quantization with the goal of minimizing signal loss, we demonstrate that the standard methods used to aggregate transformer outputs, AvgPool, MaxPool, and ClsToken, are vulnerable to performance collapse as the signal-to-noise ratio (SNR) of inputs fluctuates. We then show that an attention-based adaptive pooling method can approximate the signal-optimal vector quantizer within derived error bounds for any SNR. Our theoretical results are first validated by supervised experiments on a synthetic dataset designed to isolate the SNR problem, then generalized to standard relational reasoning, multi-agent reinforcement learning, and vision benchmarks with noisy observations, where transformers with adaptive pooling display superior robustness across tasks.

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

Spatial pooling has been proven highly effective in capturing long-range contextual information for pixel-wise prediction tasks, such as scene parsing. In this paper, beyond conventional spatial pooling that usually has a regular shape of NxN, we rethink the formulation of spatial pooling by introducing a new pooling strategy, called strip pooling, which considers a long but narrow kernel, i.e., 1xN or Nx1. Based on strip pooling, we further investigate spatial pooling architecture design by 1) introducing a new strip pooling module that enables backbone networks to efficiently model long-range dependencies, 2) presenting a novel building block with diverse spatial pooling as a core, and 3) systematically comparing the performance of the proposed strip pooling and conventional spatial pooling techniques. Both novel pooling-based designs are lightweight and can serve as an efficient plug-and-play module in existing scene parsing networks. Extensive experiments on popular benchmarks (e.g., ADE20K and Cityscapes) demonstrate that our simple approach establishes new state-of-the-art results. Code is made available at https://github.com/Andrew-Qibin/SPNet.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

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.

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

In this paper, we address the challenges associated with merging low-rank adaptations of large neural networks. With the rise of parameter-efficient adaptation techniques, such as Low-Rank Adaptation (LoRA), model fine-tuning has become more accessible. While fine-tuning models with LoRA is highly efficient, existing merging methods often sacrifice this efficiency by merging fully-sized weight matrices. We propose the Core Space merging framework, which enables the merging of LoRA-adapted models within a common alignment basis, thereby preserving the efficiency of low-rank adaptation while substantially improving accuracy across tasks. We further provide a formal proof that projection into Core Space ensures no loss of information and provide a complexity analysis showing the efficiency gains. Extensive empirical results demonstrate that Core Space significantly improves existing merging techniques and achieves state-of-the-art results on both vision and language tasks while utilizing a fraction of the computational resources. Codebase is available at https://github.com/apanariello4/core-space-merging.

Hyper-Connections (HC) generalizes residual connections by introducing dynamic residual matrices that mix information across multiple residual streams, accelerating convergence in deep neural networks. However, unconstrained residual matrices can compromise training stability. To address this, DeepSeek's Manifold-Constrained Hyper-Connections (mHC) approximately projects these matrices onto the Birkhoff polytope via iterative Sinkhorn--Knopp (SK) normalization. We identify two limitations of this approach: (i) finite SK iterations do not guarantee exact doubly stochasticity, leaving an approximation gap that can accumulate through network depth and undermine stability; (ii) efficient SK implementation requires highly specialized CUDA kernels, raising engineering barriers and reducing portability. Motivated by the Birkhoff--von Neumann theorem, we propose mHC-lite, a simple reparameterization that explicitly constructs doubly stochastic matrices as convex combinations of permutation matrices. This approach guarantees exact doubly stochasticity by construction and can be implemented using only native matrix operations. Extensive experiments demonstrate that mHC-lite matches or exceeds mHC in performance while achieving higher training throughput with a naive implementation and eliminating the residual instabilities observed in both HC and mHC. The code is publicly available at https://github.com/FFTYYY/mhc-lite.

Retrieval augmentation enables large language models to take advantage of external knowledge, for example on tasks like question answering and data imputation. However, the performance of such retrieval-augmented models is limited by the data quality of their underlying retrieval corpus. In this paper, we propose an algorithm based on multilinear extension for evaluating the data importance of retrieved data points. There are exponentially many terms in the multilinear extension, and one key contribution of this paper is a polynomial time algorithm that computes exactly, given a retrieval-augmented model with an additive utility function and a validation set, the data importance of data points in the retrieval corpus using the multilinear extension of the model's utility function. We further proposed an even more efficient ({\epsilon}, {\delta})-approximation algorithm. Our experimental results illustrate that we can enhance the performance of large language models by only pruning or reweighting the retrieval corpus, without requiring further training. For some tasks, this even allows a small model (e.g., GPT-JT), augmented with a search engine API, to outperform GPT-3.5 (without retrieval augmentation). Moreover, we show that weights based on multilinear extension can be computed efficiently in practice (e.g., in less than ten minutes for a corpus with 100 million elements).

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they serve as algebraic primitives that can be analysed without reference to input and can describe structures ranging from linear concepts to complicated manifolds. This work uses bilinear autoencoders to efficiently decompose representations into quadratic polynomials. We discuss improvements that induce importance ordering, clustering, and activation sparsity. This is an initial step toward nonlinear yet analysable latents through their algebraic properties.

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 significantly advanced parameter-efficient fine-tuning of large pretrained models. LoRA augments the pre-trained weights of a model by adding the product of two smaller matrices that together form a low-rank matrix update. Recent research has shown that scale disparities between these two matrices often cause unstable training dynamics, leading to suboptimal performance. In this paper, we propose SingLoRA, which reformulates low-rank adaptation by learning the weights update as a decomposition of a single low-rank matrix multiplied by its transpose. This simple design inherently removes inter-matrix scale conflicts, ensuring stable optimization, and roughly halves the parameter count. We analyze SingLoRA within the infinite-width neural network framework, showing that it guarantees stable feature learning by construction. Extensive experiments on multiple tasks validate these benefits. In common sense reasoning, fine-tuning LLama 7B on MNLI with SingLoRA achieves 91.3% accuracy - surpassing LoRA (89.1%) and LoRA+ (90.2%) - while using only 60% of their parameter budget. In image generation, fine-tuning Stable Diffusion with SingLoRA significantly improves image fidelity on DreamBooth, achieving a DINO similarity score of 0.151, compared to scores of 0.148 and 0.143 for DoRA and LoRA, respectively.

Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -- and building on other recent work for finding simple network structures -- we propose a new architecture that consists solely of convolutional layers and yields competitive or state of the art performance on several object recognition datasets (CIFAR-10, CIFAR-100, ImageNet). To analyze the network we introduce a new variant of the "deconvolution approach" for visualizing features learned by CNNs, which can be applied to a broader range of network structures than existing approaches.

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

While large language models (LLMs) have achieved remarkable performance across a wide range of tasks, their massive scale incurs prohibitive computational and memory costs for pre-training from scratch. Recent studies have investigated the use of low-rank parameterization as a means of reducing model size and training cost. In this context, sparsity is often employed as a complementary technique to recover important information lost in low-rank compression by capturing salient features in the residual space. However, existing approaches typically combine low-rank and sparse components in a simplistic or ad hoc manner, often resulting in undesirable performance degradation compared to full-rank training. In this paper, we propose LOw-rank and Sparse pre-Training (LOST) for LLMs, a novel method that ingeniously integrates low-rank and sparse structures to enable effective training of LLMs from scratch under strict efficiency constraints. LOST applies singular value decomposition to weight matrices, preserving the dominant low-rank components, while allocating the remaining singular values to construct channel-wise sparse components to complement the expressiveness of low-rank training. We evaluate LOST on LLM pretraining ranging from 60M to 7B parameters. Our experiments show that LOST achieves competitive or superior performance compared to full-rank models, while significantly reducing both memory and compute overhead. Moreover, Code is available at https://github.com/JiaxiLi1/LOST-Low-rank-and-Sparse-Training-for-Large-Language-Models{LOST Repo}

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or fully-connected) layer by slicing its channels into multiple groups and decomposing each group via low-rank decomposition. At the core of our algorithm is the derivation of layer-wise error bounds from the Eckart Young Mirsky theorem. We then leverage these bounds to frame the compression problem as an optimization problem where we wish to minimize the maximum compression error across layers and propose an efficient algorithm towards a solution. Our experiments indicate that our method outperforms existing low-rank compression approaches across a wide range of networks and data sets. We believe that our results open up new avenues for future research into the global performance-size trade-offs of modern neural networks. Our code is available at https://github.com/lucaslie/torchprune.

Parameter-efficient fine-tuning methods have gained considerable popularity for adapting large-scale models to downstream tasks, particularly LoRA and its variants. Existing methods perform low-rank adaptation over the full parameter space. However, fine-tuning within a subspace can achieve comparable effectiveness. Inspired by the observation that pre-trained models possess non-trivial null spaces, we propose Null-space based Low-Rank Adaptation (Null-LoRA). Null-LoRA effectively reduces redundancy and enhances effective rank by freezing portions of the low-rank matrices. To further improve parameter efficiency, Null-LoRA constrains the entire incremental update within the null space, maximizing the utilization of incremental updates to adapt to new task paradigms. Null-LoRA surpasses the state of the art with fewer parameters in extensive experiments across image-text retrieval and visual question answering tasks.

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions, each evaluating a weighted mutual information between the features and the latent labels, subject to supervision constraints from the labeled samples. Our formulation mitigates the class-balance bias encoded in standard information maximization approaches, thereby handling effectively both short-tailed and long-tailed data sets. We report extensive experiments and comparisons demonstrating that our PIM model consistently sets new state-of-the-art performances in GCD across six different datasets, more so when dealing with challenging fine-grained problems.

Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by fitting a fast hash function from training data. In this work, we propose improvements to this previous work, targeted to the deep learning inference setting, where one has access to both training data and fixed (already learned) model weight matrices. We further propose a fine-tuning procedure for accelerating entire neural networks while minimizing loss in accuracy. Finally, we analyze the proposed method on a simple image classification task. While we show improvements to prior work, overall classification accuracy remains substantially diminished compared to exact matrix multiplication. Our work, despite this negative result, points the way towards future efforts to accelerate inner products with fast nonlinear hashing methods.

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

Existing neural information retrieval (IR) models have often been studied in homogeneous and narrow settings, which has considerably limited insights into their out-of-distribution (OOD) generalization capabilities. To address this, and to facilitate researchers to broadly evaluate the effectiveness of their models, we introduce Benchmarking-IR (BEIR), a robust and heterogeneous evaluation benchmark for information retrieval. We leverage a careful selection of 18 publicly available datasets from diverse text retrieval tasks and domains and evaluate 10 state-of-the-art retrieval systems including lexical, sparse, dense, late-interaction and re-ranking architectures on the BEIR benchmark. Our results show BM25 is a robust baseline and re-ranking and late-interaction-based models on average achieve the best zero-shot performances, however, at high computational costs. In contrast, dense and sparse-retrieval models are computationally more efficient but often underperform other approaches, highlighting the considerable room for improvement in their generalization capabilities. We hope this framework allows us to better evaluate and understand existing retrieval systems, and contributes to accelerating progress towards better robust and generalizable systems in the future. BEIR is publicly available at https://github.com/UKPLab/beir.

Pretrained large language models (LLMs) exhibit exceptional general language processing capabilities but come with significant demands on memory and computational resources. As a powerful compression technology, binarization can extremely reduce model weights to a mere 1 bit, lowering the expensive computation and memory requirements. However, existing quantization techniques fall short of maintaining LLM performance under ultra-low bit-widths. In response to this challenge, we present BiLLM, a groundbreaking 1-bit post-training quantization scheme tailored for pretrained LLMs. Based on the weight distribution of LLMs, BiLLM first identifies and structurally selects salient weights, and minimizes the compression loss through an effective binary residual approximation strategy. Moreover, considering the bell-shaped distribution of the non-salient weights, we propose an optimal splitting search to group and binarize them accurately. BiLLM achieving for the first time high-accuracy inference (e.g. 8.41 perplexity on LLaMA2-70B) with only 1.08-bit weights across various LLMs families and evaluation metrics, outperforms SOTA quantization methods of LLM by significant margins. Moreover, BiLLM enables the binarization process of the LLM with 7 billion weights within 0.5 hours on a single GPU, demonstrating satisfactory time efficiency.

While Low-Rank Adaptation (LoRA) has proven beneficial for efficiently fine-tuning large models, LoRA fine-tuned text-to-image diffusion models lack diversity in the generated images, as the model tends to copy data from the observed training samples. This effect becomes more pronounced at higher values of adapter strength and for adapters with higher ranks which are fine-tuned on smaller datasets. To address these challenges, we present FouRA, a novel low-rank method that learns projections in the Fourier domain along with learning a flexible input-dependent adapter rank selection strategy. Through extensive experiments and analysis, we show that FouRA successfully solves the problems related to data copying and distribution collapse while significantly improving the generated image quality. We demonstrate that FouRA enhances the generalization of fine-tuned models thanks to its adaptive rank selection. We further show that the learned projections in the frequency domain are decorrelated and prove effective when merging multiple adapters. While FouRA is motivated for vision tasks, we also demonstrate its merits for language tasks on the GLUE benchmark.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Hyper-Connections (HC) generalize residual connections into multiple streams, employing residual matrices for cross-stream feature mixing to enrich model expressivity. However, unconstrained mixing disrupts the identity mapping property intrinsic to the residual connection, causing unstable training. To address this, Manifold-Constrained Hyper-Connections (mHC) and its variant restrict these matrices to the Birkhoff polytope (doubly stochastic matrices) via Sinkhorn iterations or permutation-based parameterizations. We reveal three limitations of this polytope constraint: (1) identity degeneration, where learned matrices collapse around the identity and diminish cross-stream interactions, (2) an expressivity bottleneck, as the non-negativity constraint prevents subtractive feature disentanglement, and (3) parameterization inefficiencies, manifesting as unstable Sinkhorn iterations or the factorial-scaling overhead of permutation-based parameterizations. To overcome these flaws, we propose Spectral-Sphere-Constrained Hyper-Connections (sHC). By geometrically shifting the feasible set from a rigid polytope to a spectral norm sphere, sHC allows negative entries, unlocking subtractive interactions for selective feature diversification. This shift eliminates unstable Sinkhorn projections and factorial parameterization, enabling expressive, non-degenerate residual matrices while preserving training stability.

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.

Large language models (LLMs) have rapidly scaled in size, bringing severe memory and computational challenges that hinder their deployment. Singular Value Decomposition (SVD)-based compression has emerged as an appealing post-training compression technique for LLMs, yet most existing methods apply a uniform compression ratio across all layers, implicitly assuming homogeneous information included in various layers. This overlooks the substantial intra-layer heterogeneity observed in LLMs, where middle layers tend to encode richer information while early and late layers are more redundant. In this work, we revisit the existing SVD-based compression method and propose D-Rank, a framework with layer-wise balanced Dynamic Rank allocation for LLMs compression. We first introduce effective rank as a principled metric to measure the information density of weight matrices, and then allocate ranks via a Lagrange multiplier-based optimization scheme to adaptively assign more capacity to groups with higher information density under a fixed compression ratio. Moreover, we rebalance the allocated ranks across attention layers to account for their varying importance and extend D-Rank to latest LLMs with grouped-query attention. Extensive experiments on various LLMs with different scales across multiple compression ratios demonstrate that D-Rank consistently outperforms SVD-LLM, ASVD, and Basis Sharing, achieving more than 15 lower perplexity with LLaMA-3-8B model on C4 datasets at 20% compression ratio and up to 5% higher zero-shot reasoning accuracy with LLaMA-7B model at 40% compression ratio while achieving even higher throughput.

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

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

Multi-vector models, such as ColBERT, are a significant advancement in neural information retrieval (IR), delivering state-of-the-art performance by representing queries and documents by multiple contextualized token-level embeddings. However, this increased representation size introduces considerable storage and computational overheads which have hindered widespread adoption in practice. A common approach to mitigate this overhead is to cluster the model's frozen vectors, but this strategy's effectiveness is fundamentally limited by the intrinsic clusterability of these embeddings. In this work, we introduce CRISP (Clustered Representations with Intrinsic Structure Pruning), a novel multi-vector training method which learns inherently clusterable representations directly within the end-to-end training process. By integrating clustering into the training phase rather than imposing it post-hoc, CRISP significantly outperforms post-hoc clustering at all representation sizes, as well as other token pruning methods. On the BEIR retrieval benchmarks, CRISP achieves a significant rate of ~3x reduction in the number of vectors while outperforming the original unpruned model. This indicates that learned clustering effectively denoises the model by filtering irrelevant information, thereby generating more robust multi-vector representations. With more aggressive clustering, CRISP achieves an 11x reduction in the number of vectors with only a 3.6% quality loss.

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.

We study both stream-based and pool-based active learning with neural network approximations. A recent line of works proposed bandit-based approaches that transformed active learning into a bandit problem, achieving both theoretical and empirical success. However, the performance and computational costs of these methods may be susceptible to the number of classes, denoted as K, due to this transformation. Therefore, this paper seeks to answer the question: "How can we mitigate the adverse impacts of K while retaining the advantages of principled exploration and provable performance guarantees in active learning?" To tackle this challenge, we propose two algorithms based on the newly designed exploitation and exploration neural networks for stream-based and pool-based active learning. Subsequently, we provide theoretical performance guarantees for both algorithms in a non-parametric setting, demonstrating a slower error-growth rate concerning K for the proposed approaches. We use extensive experiments to evaluate the proposed algorithms, which consistently outperform state-of-the-art baselines.

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models such as Tucker, tensor train (TT) and tensor ring (TR). However, identifying the best tensor network structure from data for a given task is challenging. In this work, we leverage the TN formalism to develop a generic and efficient adaptive algorithm to jointly learn the structure and the parameters of a TN from data. Our method is based on a simple greedy approach starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function. Experiments on tensor decomposition, tensor completion and model compression tasks demonstrate the effectiveness of the proposed algorithm. In particular, our method outperforms the state-of-the-art evolutionary topology search [Li and Sun, 2020] for tensor decomposition of images (while being orders of magnitude faster) and finds efficient tensor network structures to compress neural networks outperforming popular TT based approaches [Novikov et al., 2015].

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

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~li2022permutation showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that Omega(2^N) evaluations are typically required in TNLS for reaching the objective reduction in the neighborhood, while ideally O(N^2R) evaluations are sufficient in TnALE, where N denotes the tensor order and R reflects the ``low-rankness'' of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

Few Shot Class Incremental Learning (FSCIL) with few examples per class for each incremental session is the realistic setting of continual learning since obtaining large number of annotated samples is not feasible and cost effective. We present the framework MASIL as a step towards learning the maximal separable classifier. It addresses the common problem i.e forgetting of old classes and over-fitting to novel classes by learning the classifier weights to be maximally separable between classes forming a simplex Equiangular Tight Frame. We propose the idea of concept factorization explaining the collapsed features for base session classes in terms of concept basis and use these to induce classifier simplex for few shot classes. We further adds fine tuning to reduce any error occurred during factorization and train the classifier jointly on base and novel classes without retaining any base class samples in memory. Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that MASIL outperforms all the benchmarks.

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.

The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional approaches to distributed inference often struggle with achieving true sparsity in high-dimensional datasets and involve high computational costs. We propose a novel, two-stage, distributed best subset selection algorithm to address these issues. Our approach starts by efficiently estimating the active set while adhering to the ell_0 norm-constrained surrogate likelihood function, effectively reducing dimensionality and isolating key variables. A refined estimation within the active set follows, ensuring sparse estimates and matching the minimax ell_2 error bound. We introduce a new splicing technique for adaptive parameter selection to tackle subproblems under ell_0 constraints and a Generalized Information Criterion (GIC). Our theoretical and numerical studies show that the proposed algorithm correctly finds the true sparsity pattern, has the oracle property, and greatly lowers communication costs. This is a big step forward in distributed sparse estimation.

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.

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the ell_1 distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot product function. In this paper, we propose a new representation learning framework for dense retrieval. Instead of learning a vector for each query and document, our framework learns a multivariate distribution and uses negative multivariate KL divergence to compute the similarity between distributions. For simplicity and efficiency reasons, we assume that the distributions are multivariate normals and then train large language models to produce mean and variance vectors for these distributions. We provide a theoretical foundation for the proposed framework and show that it can be seamlessly integrated into the existing approximate nearest neighbor algorithms to perform retrieval efficiently. We conduct an extensive suite of experiments on a wide range of datasets, and demonstrate significant improvements compared to competitive dense retrieval models.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.

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.

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

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based bounds when the condition numbers of weight matrices are small. Especially, it is completely independent of the width of the network if the weight matrices are orthogonal. Our bound does not contradict to the existing bounds but is a complement to the existing bounds. As supported by several existing empirical results, low-rankness is not the only reason for generalization. Furthermore, our bound can be combined with the existing bounds to obtain a tighter bound. Our result sheds new light on understanding generalization of neural networks with full-rank weight matrices, and it provides a connection between operator-theoretic analysis and generalization of neural networks.

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.

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.

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

A supervised ranking model, despite its advantage of being effective, usually involves complex processing - typically multiple stages of task-specific pre-training and fine-tuning. This has motivated researchers to explore simpler pipelines leveraging large language models (LLMs) that are capable of working in a zero-shot manner. However, since zero-shot inference does not make use of a training set of pairs of queries and their relevant documents, its performance is mostly worse than that of supervised models, which are trained on such example pairs. Motivated by the existing findings that training examples generally improve zero-shot performance, in our work, we explore if this also applies to ranking models. More specifically, given a query and a pair of documents, the preference prediction task is improved by augmenting examples of preferences for similar queries from a training set. Our proposed pairwise few-shot ranker demonstrates consistent improvements over the zero-shot baseline on both in-domain (TREC DL) and out-domain (BEIR subset) retrieval benchmarks. Our method also achieves a close performance to that of a supervised model without requiring any complex training pipeline.

Mixture of experts (MoE) has a well-principled finite mixture model construction for prediction, allowing the gating network (mixture weights) to learn from the predictors (explanatory variables) together with the experts' network (mixture component densities). We investigate the estimation properties of MoEs in a high-dimensional setting, where the number of predictors is much larger than the sample size, for which the literature lacks computational and especially theoretical results. We consider the class of finite MoE models with softmax gating functions and Gaussian regression experts, and focus on the theoretical properties of their l_1-regularized estimation via the Lasso. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures an l_1-oracle inequality is satisfied by the Lasso estimator according to the Kullback--Leibler loss. We further state an l_1-ball oracle inequality for the l_1-penalized maximum likelihood estimator from the model selection.

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.

Memory-efficient optimization is critical for training increasingly large language models (LLMs). A popular strategy involves gradient low-rank projection, storing only the projected optimizer states, with GaLore being a representative example. However, a significant drawback of many such methods is their lack of convergence guarantees, as various low-rank projection approaches introduce inherent biases relative to the original optimization algorithms, which contribute to performance gaps compared to full-parameter training. Aiming to tackle this problem, this paper investigates the layerwise sampling technique for debiasing low-rank projection mechanisms. In particular, an instantiation of the paradigm gives rise to a novel and unbiased low-rank optimization method built upon GaLore's mechanism and the Muon algorithm, named GaLore Unbiased with Muon (GUM). We theoretically prove our method matches the convergence guarantees of the base Muon algorithm while preserving the memory efficiency of low-rank techniques. Empirical experiments on LLM fine-tuning and pretraining also demonstrate non-trivial improvements over GaLore and even better performance than full-parameter training. Further investigation shows that the improvement of this technique comes from a more uniform distribution of knowledge inside layers, leading to more efficient utilization of the model parameter space and better memorization.

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.