Daily Papers

Learned sparse retrieval (LSR) is a family of neural retrieval methods that transform queries and documents into sparse weight vectors aligned with a vocabulary. While LSR approaches like Splade work well for short passages, it is unclear how well they handle longer documents. We investigate existing aggregation approaches for adapting LSR to longer documents and find that proximal scoring is crucial for LSR to handle long documents. To leverage this property, we proposed two adaptations of the Sequential Dependence Model (SDM) to LSR: ExactSDM and SoftSDM. ExactSDM assumes only exact query term dependence, while SoftSDM uses potential functions that model the dependence of query terms and their expansion terms (i.e., terms identified using a transformer's masked language modeling head). Experiments on the MSMARCO Document and TREC Robust04 datasets demonstrate that both ExactSDM and SoftSDM outperform existing LSR aggregation approaches for different document length constraints. Surprisingly, SoftSDM does not provide any performance benefits over ExactSDM. This suggests that soft proximity matching is not necessary for modeling term dependence in LSR. Overall, this study provides insights into handling long documents with LSR, proposing adaptations that improve its performance.

Recent developments in representational learning for information retrieval can be organized in a conceptual framework that establishes two pairs of contrasts: sparse vs. dense representations and unsupervised vs. learned representations. Sparse learned representations can further be decomposed into expansion and term weighting components. This framework allows us to understand the relationship between recently proposed techniques such as DPR, ANCE, DeepCT, DeepImpact, and COIL, and furthermore, gaps revealed by our analysis point to "low hanging fruit" in terms of techniques that have yet to be explored. We present a novel technique dubbed "uniCOIL", a simple extension of COIL that achieves to our knowledge the current state-of-the-art in sparse retrieval on the popular MS MARCO passage ranking dataset. Our implementation using the Anserini IR toolkit is built on the Lucene search library and thus fully compatible with standard inverted indexes.

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

Sparse Attention Vectors (SAVs) have emerged as an excellent training-free alternative to supervised finetuning or low-rank adaptation to improve the performance of Vision Language Models (VLMs). At their heart, SAVs select a few accurate attention heads for a task of interest and use them as classifiers, rather than relying on the model's prediction. In a similar spirit, we find that directly probing the raw activations of the VLM, in the form of scalar values, is sufficient to yield accurate classifiers on diverse visually grounded downstream tasks. Shifting focus from attention vectors to scalar activations dramatically increases the search space for accurate parameters, allowing us to find more discriminative neurons immediately from the first generated token. We call such activations Super Neurons (SNs). In this probing setting, we discover that enough SNs appear in the shallower layers of the large language model to allow for extreme early exiting from the first layer of the model at the first generated token. Compared to the original network, SNs robustly improve the classification performance while achieving a speedup of up to 5.10x.

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

With the dramatically increased number of parameters in language models, sparsity methods have received ever-increasing research focus to compress and accelerate the models. While most research focuses on how to accurately retain appropriate weights while maintaining the performance of the compressed model, there are challenges in the computational overhead and memory footprint of sparse training when compressing large-scale language models. To address this problem, we propose a Parameter-efficient Sparse Training (PST) method to reduce the number of trainable parameters during sparse-aware training in downstream tasks. Specifically, we first combine the data-free and data-driven criteria to efficiently and accurately measure the importance of weights. Then we investigate the intrinsic redundancy of data-driven weight importance and derive two obvious characteristics i.e., low-rankness and structuredness. Based on that, two groups of small matrices are introduced to compute the data-driven importance of weights, instead of using the original large importance score matrix, which therefore makes the sparse training resource-efficient and parameter-efficient. Experiments with diverse networks (i.e., BERT, RoBERTa and GPT-2) on dozens of datasets demonstrate PST performs on par or better than previous sparsity methods, despite only training a small number of parameters. For instance, compared with previous sparsity methods, our PST only requires 1.5% trainable parameters to achieve comparable performance on BERT.

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

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

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

The growing computational demands of large language models (LLMs) make efficient inference and activation strategies increasingly critical. While recent approaches, such as Mixture-of-Experts (MoE), leverage selective activation but require specialized training, training-free sparse activation methods offer broader applicability and superior resource efficiency through their plug-and-play design. However, many existing methods rely solely on hidden state magnitudes to determine activation, resulting in high approximation errors and suboptimal inference accuracy. To address these limitations, we propose WINA (Weight Informed Neuron Activation), a novel, simple, and training-free sparse activation framework that jointly considers hidden state magnitudes and the column-wise ell_2-norms of weight matrices. We show that this leads to a sparsification strategy that obtains optimal approximation error bounds with theoretical guarantees tighter than existing techniques. Empirically, WINA also outperforms state-of-the-art methods (e.g., TEAL) by up to 2.94% in average performance at the same sparsity levels, across a diverse set of LLM architectures and datasets. These results position WINA as a new performance frontier for training-free sparse activation in LLM inference, advancing training-free sparse activation methods and setting a robust baseline for efficient inference. The source code is available at https://github.com/microsoft/wina.

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

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

Open-domain question answering can be formulated as a phrase retrieval problem, in which we can expect huge scalability and speed benefit but often suffer from low accuracy due to the limitation of existing phrase representation models. In this paper, we aim to improve the quality of each phrase embedding by augmenting it with a contextualized sparse representation (Sparc). Unlike previous sparse vectors that are term-frequency-based (e.g., tf-idf) or directly learned (only few thousand dimensions), we leverage rectified self-attention to indirectly learn sparse vectors in n-gram vocabulary space. By augmenting the previous phrase retrieval model (Seo et al., 2019) with Sparc, we show 4%+ improvement in CuratedTREC and SQuAD-Open. Our CuratedTREC score is even better than the best known retrieve & read model with at least 45x faster inference speed.

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

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

This paper introduces Sparsified Late Interaction for Multi-vector (SLIM) retrieval with inverted indexes. Multi-vector retrieval methods have demonstrated their effectiveness on various retrieval datasets, and among them, ColBERT is the most established method based on the late interaction of contextualized token embeddings of pre-trained language models. However, efficient ColBERT implementations require complex engineering and cannot take advantage of off-the-shelf search libraries, impeding their practical use. To address this issue, SLIM first maps each contextualized token vector to a sparse, high-dimensional lexical space before performing late interaction between these sparse token embeddings. We then introduce an efficient two-stage retrieval architecture that includes inverted index retrieval followed by a score refinement module to approximate the sparsified late interaction, which is fully compatible with off-the-shelf lexical search libraries such as Lucene. SLIM achieves competitive accuracy on MS MARCO Passages and BEIR compared to ColBERT while being much smaller and faster on CPUs. To our knowledge, we are the first to explore using sparse token representations for multi-vector retrieval. Source code and data are integrated into the Pyserini IR toolkit.

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

Term-based sparse representations dominate the first-stage text retrieval in industrial applications, due to its advantage in efficiency, interpretability, and exact term matching. In this paper, we study the problem of transferring the deep knowledge of the pre-trained language model (PLM) to Term-based Sparse representations, aiming to improve the representation capacity of bag-of-words(BoW) method for semantic-level matching, while still keeping its advantages. Specifically, we propose a novel framework SparTerm to directly learn sparse text representations in the full vocabulary space. The proposed SparTerm comprises an importance predictor to predict the importance for each term in the vocabulary, and a gating controller to control the term activation. These two modules cooperatively ensure the sparsity and flexibility of the final text representation, which unifies the term-weighting and expansion in the same framework. Evaluated on MSMARCO dataset, SparTerm significantly outperforms traditional sparse methods and achieves state of the art ranking performance among all the PLM-based sparse models.

The energy consumption of large-scale ML models is dominated by data movement - shuffling billions of parameters across memory hierarchies and data centers. Effective sparsification to prune redundant parameters is still challenging: existing methods incur significant accuracy degradation, performance overhead, or both. We introduce (Bl)ock (a)nd (S)parse (T)ransformers (BLaST), a general, robust, and reliable sparsification method applicable to linear layers in all settings. Our method iteratively sparsifies weight matrices into a block sparsity pattern suitable for efficient sparse matrix-matrix (SpMM) multiplication. BLaST achieves up to 95% sparsity in MLP weights with negligible accuracy loss. Our fused, highly optimized Sparse MLP kernel delivers up to 16.7x speedup over dense MLPs across 9 architectures and 8 datasets, resulting in up to 1.6x inference speedup, 1.11x pretraining speedup and up to 3.12x inference memory usage reduction. BLaST enables the next generation of large-scale AI systems by reducing energy use, memory footprint, and latency.

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

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.

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

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

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.

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

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

Recent studies have shown that supervised fine-tuning of LLMs on a small number of high-quality datasets can yield strong reasoning capabilities. However, full fine-tuning (Full FT), while powerful, is computationally expensive and susceptible to overfitting and catastrophic forgetting, particularly when data is limited. Sparse fine-tuning, which previously achieved notable success by updating only a small subset of model parameters, offers a promising trade-off between efficiency and effectiveness. Yet, it has lagged behind in the LLM era due to the difficulty of identifying parameters truly critical for reasoning. In this work, we state that weights with the largest magnitude after low-rank approximation are critical weights for fine-tuning, which we call Principal Weights. Surprisingly, while magnitude-based sparse fine-tuning performs poorly as a baseline on LLM fine-tuning, it becomes highly effective after rank reduction. These insights motivate our method: Low-rank Informed Sparse Fine-Tuning (LIFT). LIFT only updates the top 5% Principal Weights throughout training and consistently achieves better performance on reasoning tasks than Full FT, while maintaining memory efficiency on par with popular parameter-efficient fine-tuning methods. In addition to strong performance on target domains such as arithmetic reasoning, LIFT also retains up to 20% more source-domain knowledge, compared to Full FT and LoRA. Our code is available at: https://github.com/zihanghliu/LIFT.

Large Language Models (LLMs) have become pivotal in advancing the field of artificial intelligence, yet their immense sizes pose significant challenges for both fine-tuning and deployment. Current post-training pruning methods, while reducing the sizes of LLMs, often fail to maintain their original performance. To address these challenges, this paper introduces SPP, a Sparsity-Preserved Parameter-efficient fine-tuning method. Different from existing post-training pruning approaches that struggle with performance retention, SPP proposes to employ lightweight learnable column and row matrices to optimize sparse LLM weights, keeping the structure and sparsity of pruned pre-trained models intact. By element-wise multiplication and residual addition, SPP ensures the consistency of model sparsity pattern and ratio during both training and weight-merging processes. We demonstrate the effectiveness of SPP by applying it to the LLaMA and LLaMA-2 model families with recent post-training pruning methods. Our results show that SPP significantly enhances the performance of models with different sparsity patterns (i.e. unstructured and N:M sparsity), especially for those with high sparsity ratios (e.g. 75%), making it a promising solution for the efficient fine-tuning of sparse LLMs. Code will be made available at https://github.com/Lucky-Lance/SPP.

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

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

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

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

Fine-tuning LLMs is both computationally and memory-intensive. While parameter-efficient fine-tuning methods, such as QLoRA and DoRA, reduce the number of trainable parameters and lower memory usage, they do not decrease computational cost. In some cases, they may even slow down fine-tuning. In this paper, we introduce SparseLoRA, a method that accelerates LLM fine-tuning through contextual sparsity. We propose a lightweight, training-free SVD sparsity estimator that dynamically selects a sparse subset of weights for loss and gradient computation. Also, we systematically analyze and address sensitivity across layers, tokens, and training steps. Our experimental results show that SparseLoRA reduces computational cost by up to 2.2 times and a measured speedup of up to 1.6 times while maintaining accuracy across various downstream tasks, including commonsense and arithmetic reasoning, code generation, and instruction following.

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

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

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

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

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

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.

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

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

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

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

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.

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

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

Learned sparse retrieval (LSR) is a family of first-stage retrieval methods that are trained to generate sparse lexical representations of queries and documents for use with an inverted index. Many LSR methods have been recently introduced, with Splade models achieving state-of-the-art performance on MSMarco. Despite similarities in their model architectures, many LSR methods show substantial differences in effectiveness and efficiency. Differences in the experimental setups and configurations used make it difficult to compare the methods and derive insights. In this work, we analyze existing LSR methods and identify key components to establish an LSR framework that unifies all LSR methods under the same perspective. We then reproduce all prominent methods using a common codebase and re-train them in the same environment, which allows us to quantify how components of the framework affect effectiveness and efficiency. We find that (1) including document term weighting is most important for a method's effectiveness, (2) including query weighting has a small positive impact, and (3) document expansion and query expansion have a cancellation effect. As a result, we show how removing query expansion from a state-of-the-art model can reduce latency significantly while maintaining effectiveness on MSMarco and TripClick benchmarks. Our code is publicly available at https://github.com/thongnt99/learned-sparse-retrieval

Sparsity-aware training is an effective approach for transforming large language models (LLMs) into hardware-friendly sparse patterns, thereby reducing latency and memory consumption during inference. In this paper, we propose Continuous Adaptive Sparse Trainer (CAST), a fully continuous and differentiable sparsity-aware training framework for semi-structured (or "N:M") sparse models. Unlike previous approaches that optimize sparsity patterns and weights separately, CAST enables seamless joint optimization during training, while progressively transforming the model into the desired sparsity format. Specifically, CAST introduces three key components: 1) AdamS, a sparsity-aware optimizer that leverages adaptive L1 decay to promote uniform sparsification across all parameters; 2) Weight Scaling, a module designed to mitigate the magnitude reduction caused by decay while preserving desired sparsity patterns; 3) Knowledge Distillation, which employs the dense model as a self-teacher to enhance training efficiency. We evaluate CAST under 2:4 sparsity patterns across multiple model families, ranging from 125M to 13B parameters. Our results demonstrate significant improvements over previous state-of-the-art methods in both perplexity and zero-shot accuracy with minimal training resources. Notably, on LLaMA2-7B, our 2:4 sparse model achieves a negligible perplexity increase of 0.09 and a 0.36% gain in zero-shot accuracy compared to the dense model using only 2% of the original pretraining tokens. Additionally, we establish an accurate and robust empirical scaling law to predict sparse model performance given adequate training resources. Finally, we demonstrate the practical applicability of our sparse models by evaluating them under quantization and fine-tuning scenarios.

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

Generative Large Multimodal Models (LMMs) like LLaVA and Qwen-VL excel at a wide variety of vision-language (VL) tasks such as image captioning or visual question answering. Despite strong performance, LMMs are not directly suited for foundational discriminative vision-language tasks (i.e., tasks requiring discrete label predictions) such as image classification and multiple-choice VQA. One key challenge in utilizing LMMs for discriminative tasks is the extraction of useful features from generative models. To overcome this issue, we propose an approach for finding features in the model's latent space to more effectively leverage LMMs for discriminative tasks. Toward this end, we present Sparse Attention Vectors (SAVs) -- a finetuning-free method that leverages sparse attention head activations (fewer than 1\% of the heads) in LMMs as strong features for VL tasks. With only few-shot examples, SAVs demonstrate state-of-the-art performance compared to a variety of few-shot and finetuned baselines on a collection of discriminative tasks. Our experiments also imply that SAVs can scale in performance with additional examples and generalize to similar tasks, establishing SAVs as both effective and robust multimodal feature representations.

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

Many machine learning algorithms require the input to be represented as a fixed-length feature vector. When it comes to texts, one of the most common fixed-length features is bag-of-words. Despite their popularity, bag-of-words features have two major weaknesses: they lose the ordering of the words and they also ignore semantics of the words. For example, "powerful," "strong" and "Paris" are equally distant. In this paper, we propose Paragraph Vector, an unsupervised algorithm that learns fixed-length feature representations from variable-length pieces of texts, such as sentences, paragraphs, and documents. Our algorithm represents each document by a dense vector which is trained to predict words in the document. Its construction gives our algorithm the potential to overcome the weaknesses of bag-of-words models. Empirical results show that Paragraph Vectors outperform bag-of-words models as well as other techniques for text representations. Finally, we achieve new state-of-the-art results on several text classification and sentiment analysis tasks.

Current pre-trained language model approaches to information retrieval can be broadly divided into two categories: sparse retrievers (to which belong also non-neural approaches such as bag-of-words methods, e.g., BM25) and dense retrievers. Each of these categories appears to capture different characteristics of relevance. Previous work has investigated how relevance signals from sparse retrievers could be combined with those from dense retrievers via interpolation. Such interpolation would generally lead to higher retrieval effectiveness. In this paper we consider the problem of combining the relevance signals from sparse and dense retrievers in the context of Pseudo Relevance Feedback (PRF). This context poses two key challenges: (1) When should interpolation occur: before, after, or both before and after the PRF process? (2) Which sparse representation should be considered: a zero-shot bag-of-words model (BM25), or a learnt sparse representation? To answer these questions we perform a thorough empirical evaluation considering an effective and scalable neural PRF approach (Vector-PRF), three effective dense retrievers (ANCE, TCTv2, DistillBERT), and one state-of-the-art learnt sparse retriever (uniCOIL). The empirical findings from our experiments suggest that, regardless of sparse representation and dense retriever, interpolation both before and after PRF achieves the highest effectiveness across most datasets and metrics.

Large language models (LLMs) augmented with retrieval exhibit robust performance and extensive versatility by incorporating external contexts. However, the input length grows linearly in the number of retrieved documents, causing a dramatic increase in latency. In this paper, we propose a novel paradigm named Sparse RAG, which seeks to cut computation costs through sparsity. Specifically, Sparse RAG encodes retrieved documents in parallel, which eliminates latency introduced by long-range attention of retrieved documents. Then, LLMs selectively decode the output by only attending to highly relevant caches auto-regressively, which are chosen via prompting LLMs with special control tokens. It is notable that Sparse RAG combines the assessment of each individual document and the generation of the response into a single process. The designed sparse mechanism in a RAG system can facilitate the reduction of the number of documents loaded during decoding for accelerating the inference of the RAG system. Additionally, filtering out undesirable contexts enhances the model's focus on relevant context, inherently improving its generation quality. Evaluation results of two datasets show that Sparse RAG can strike an optimal balance between generation quality and computational efficiency, demonstrating its generalizability across both short- and long-form generation tasks.

Product search is a crucial component of modern e-commerce platforms, with billions of user queries every day. In product search systems, first-stage retrieval should achieve high recall while ensuring efficient online deployment. Sparse retrieval is particularly attractive in this context due to its interpretability and storage efficiency. However, sparse retrieval methods suffer from severe vocabulary mismatch issues, leading to suboptimal performance in product search scenarios. With their potential for semantic analysis, large language models (LLMs) offer a promising avenue for mitigating vocabulary mismatch issues and thereby improving retrieval quality. Directly applying LLMs to sparse retrieval in product search exposes two key challenges:(1)Queries and product titles are typically short and highly susceptible to LLM-induced hallucinations, such as generating irrelevant expansion terms or underweighting critical literal terms like brand names and model numbers;(2)The large vocabulary space of LLMs leads to difficulty in initializing training effectively, making it challenging to learn meaningful sparse representations in such ultra-high-dimensional spaces.To address these challenges, we propose PROSPER, a framework for PROduct search leveraging LLMs as SParsE Retrievers. PROSPER incorporates: (1)A literal residual network that alleviates hallucination in lexical expansion by reinforcing underweighted literal terms through a residual compensation mechanism; and (2)A lexical focusing window that facilitates effective training initialization via a coarse-to-fine sparsification strategy.Extensive offline and online experiments show that PROSPER significantly outperforms sparse baselines and achieves recall performance comparable to advanced dense retrievers, while also achieving revenue increments online.

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

Large language models (LLMs) have revolutionized Natural Language Processing (NLP), but their size creates computational bottlenecks. We introduce a novel approach to create accurate, sparse foundational versions of performant LLMs that achieve full accuracy recovery for fine-tuning tasks at up to 70% sparsity. We achieve this for the LLaMA-2 7B model by combining the SparseGPT one-shot pruning method and sparse pretraining of those models on a subset of the SlimPajama dataset mixed with a Python subset of The Stack dataset. We exhibit training acceleration due to sparsity on Cerebras CS-3 chips that closely matches theoretical scaling. In addition, we establish inference acceleration of up to 3x on CPUs by utilizing Neural Magic's DeepSparse engine and 1.7x on GPUs through Neural Magic's nm-vllm engine. The above gains are realized via sparsity alone, thus enabling further gains through additional use of quantization. Specifically, we show a total speedup on CPUs for sparse-quantized LLaMA models of up to 8.6x. We demonstrate these results across diverse, challenging tasks, including chat, instruction following, code generation, arithmetic reasoning, and summarization to prove their generality. This work paves the way for rapidly creating smaller and faster LLMs without sacrificing accuracy.

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

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

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

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

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

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.

The exponential growth of scientific literature has made it increasingly difficult for researchers to keep up with the literature. In an attempt to alleviate this problem, we propose CASPER, a sparse retrieval model for scientific search that utilizes tokens and keyphrases as representation units (i.e. dimensions in the sparse embedding space), enabling it to represent queries and documents with research concepts and match them at both granular and conceptual levels. To overcome the lack of suitable training data, we propose mining training data by leveraging scholarly references (i.e. signals that capture how research concepts of papers are expressed in different settings), including titles, citation contexts, author-assigned keyphrases, and co-citations. CASPER outperforms strong dense and sparse retrieval baselines on eight scientific retrieval benchmarks. Moreover, we demonstrate that through simple post-processing, CASPER can be effectively used for the keyphrase generation tasks, achieving competitive performance with the established CopyRNN while producing more diverse keyphrases and being nearly four times faster.

We present ROCKET, a training-free model compression method that achieves state-of-the-art performance in comparison with factorization, structured-sparsification and dynamic compression baselines. Operating under a global compression budget, ROCKET comprises two key innovations: First, it formulates layer-wise compression allocation as a multi-choice knapsack problem, selecting the optimal compression level for each layer to minimize total reconstruction error while adhering to a target model size. Second, it introduces a single-step sparse matrix factorization inspired by dictionary learning: using only a small calibration set, it sparsifies weight coefficients based on activation-weights sensitivity and then updates the dictionary in closed form via least squares bypassing iterative optimization, sparse coding, or backpropagation entirely. ROCKET consistently outperforms existing compression approaches across different model architectures at 20-50\% compression rates. Notably, it retains over 90\% of the original model's performance at 30\% compression without any fine-tuning. Moreover, when applying a light fine-tuning phase, recovery is substantially enhanced: for instance, compressing Qwen3-14B to an 8B-parameter model and healing it with just 30 million tokens yields performance nearly on par with the original Qwen3-8B. The code for ROCKET is at github.com/mts-ai/ROCKET/tree/main.

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

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

Sparse autoencoders (SAEs) provide a powerful mechanism for decomposing the dense representations produced by Large Language Models (LLMs) into interpretable latent features. We posit that SAEs constitute a natural foundation for Learned Sparse Retrieval (LSR), whose objective is to encode queries and documents into high-dimensional sparse representations optimized for efficient retrieval. In contrast to existing LSR approaches that project input sequences into the vocabulary space, SAE-based representations offer the potential to produce more semantically structured, expressive, and language-agnostic features. Building on this insight, we introduce SPLARE, a method to train SAE-based LSR models. Our experiments, relying on recently released open-source SAEs, demonstrate that this technique consistently outperforms vocabulary-based LSR in multilingual and out-of-domain settings. SPLARE-7B, a multilingual retrieval model capable of producing generalizable sparse latent embeddings for a wide range of languages and domains, achieves top results on MMTEB's multilingual and English retrieval tasks. We also developed a 2B-parameter variant with a significantly lighter footprint.

Recent sparse detectors with multiple, e.g. six, decoder layers achieve promising performance but much inference time due to complex heads. Previous works have explored using dense priors as initialization and built one-decoder-layer detectors. Although they gain remarkable acceleration, their performance still lags behind their six-decoder-layer counterparts by a large margin. In this work, we aim to bridge this performance gap while retaining fast speed. We find that the architecture discrepancy between dense and sparse detectors leads to feature conflict, hampering the performance of one-decoder-layer detectors. Thus we propose Adaptive Sparse Anchor Generator (ASAG) which predicts dynamic anchors on patches rather than grids in a sparse way so that it alleviates the feature conflict problem. For each image, ASAG dynamically selects which feature maps and which locations to predict, forming a fully adaptive way to generate image-specific anchors. Further, a simple and effective Query Weighting method eases the training instability from adaptiveness. Extensive experiments show that our method outperforms dense-initialized ones and achieves a better speed-accuracy trade-off. The code is available at https://github.com/iSEE-Laboratory/ASAG.

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

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

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

Generative retrieval has emerged as a powerful paradigm for LLM-based recommendation. However, industrial recommender systems often benefit from restricting the output space to a constrained subset of items based on business logic (e.g. enforcing content freshness or product category), which standard autoregressive decoding cannot natively support. Moreover, existing constrained decoding methods that make use of prefix trees (Tries) incur severe latency penalties on hardware accelerators (TPUs/GPUs). In this work, we introduce STATIC (Sparse Transition Matrix-Accelerated Trie Index for Constrained Decoding), an efficient and scalable constrained decoding technique designed specifically for high-throughput LLM-based generative retrieval on TPUs/GPUs. By flattening the prefix tree into a static Compressed Sparse Row (CSR) matrix, we transform irregular tree traversals into fully vectorized sparse matrix operations, unlocking massive efficiency gains on hardware accelerators. We deploy STATIC on a large-scale industrial video recommendation platform serving billions of users. STATIC produces significant product metric impact with minimal latency overhead (0.033 ms per step and 0.25% of inference time), achieving a 948x speedup over a CPU trie implementation and a 47-1033x speedup over a hardware-accelerated binary-search baseline. Furthermore, the runtime overhead of STATIC remains extremely low across a wide range of practical configurations. To the best of our knowledge, STATIC enables the first production-scale deployment of strictly constrained generative retrieval. In addition, evaluation on academic benchmarks demonstrates that STATIC can considerably improve cold-start performance for generative retrieval. Our code is available at https://github.com/youtube/static-constraint-decoding.

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

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

Learned sparse representations form an attractive class of contextual embeddings for text retrieval. That is so because they are effective models of relevance and are interpretable by design. Despite their apparent compatibility with inverted indexes, however, retrieval over sparse embeddings remains challenging. That is due to the distributional differences between learned embeddings and term frequency-based lexical models of relevance such as BM25. Recognizing this challenge, a great deal of research has gone into, among other things, designing retrieval algorithms tailored to the properties of learned sparse representations, including approximate retrieval systems. In fact, this task featured prominently in the latest BigANN Challenge at NeurIPS 2023, where approximate algorithms were evaluated on a large benchmark dataset by throughput and recall. In this work, we propose a novel organization of the inverted index that enables fast yet effective approximate retrieval over learned sparse embeddings. Our approach organizes inverted lists into geometrically-cohesive blocks, each equipped with a summary vector. During query processing, we quickly determine if a block must be evaluated using the summaries. As we show experimentally, single-threaded query processing using our method, Seismic, reaches sub-millisecond per-query latency on various sparse embeddings of the MS MARCO dataset while maintaining high recall. Our results indicate that Seismic is one to two orders of magnitude faster than state-of-the-art inverted index-based solutions and further outperforms the winning (graph-based) submissions to the BigANN Challenge by a significant margin.

As their size increases, Large Languages Models (LLMs) are natural candidates for network pruning methods: approaches that drop a subset of network weights while striving to preserve performance. Existing methods, however, require either retraining, which is rarely affordable for billion-scale LLMs, or solving a weight reconstruction problem reliant on second-order information, which may also be computationally expensive. In this paper, we introduce a novel, straightforward yet effective pruning method, termed Wanda (Pruning by Weights and activations), designed to induce sparsity in pretrained LLMs. Motivated by the recent observation of emergent large magnitude features in LLMs, our approach prunes weights with the smallest magnitudes multiplied by the corresponding input activations, on a per-output basis. Notably, Wanda requires no retraining or weight update, and the pruned LLM can be used as is. We conduct a thorough evaluation of our method Wanda on LLaMA and LLaMA-2 across various language benchmarks. Wanda significantly outperforms the established baseline of magnitude pruning and performs competitively against recent method involving intensive weight update. Code is available at https://github.com/locuslab/wanda.

Post-training compression of large language models (LLMs) largely relies on low-rank weight approximation, which represents each column of a weight matrix in a shared low-dimensional subspace. While this is a computationally efficient strategy, the imposed structural constraint is rigid and can lead to a noticeable model accuracy drop. In this work, we propose CoSpaDi (Compression via Sparse Dictionary Learning), a novel training-free compression framework that replaces low-rank decomposition with a more flexible structured sparse factorization in which each weight matrix is represented with a dense dictionary and a column-sparse coefficient matrix. This formulation enables a union-of-subspaces representation: different columns of the original weight matrix are approximated in distinct subspaces spanned by adaptively selected dictionary atoms, offering greater expressiveness than a single invariant basis. Crucially, CoSpaDi leverages a small calibration dataset to optimize the factorization such that the output activations of compressed projection layers closely match those of the original ones, thereby minimizing functional reconstruction error rather than mere weight approximation. This data-aware strategy preserves better model fidelity without any fine-tuning under reasonable compression ratios. Moreover, the resulting structured sparsity allows efficient sparse-dense matrix multiplication and is compatible with post-training quantization for further memory and latency gains. We evaluate CoSpaDi across multiple Llama and Qwen models under per-layer and per-group settings at 20-50\% compression ratios, demonstrating consistent superiority over state-of-the-art data-aware low-rank methods both in accuracy and perplexity. Our results establish structured sparse dictionary learning as a powerful alternative to conventional low-rank approaches for efficient LLM deployment.

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

Large Language Models (LLMs) with a billion or more parameters are prime targets for network pruning, which aims to reduce a portion of the network weights without compromising performance. Prior approaches such as Weights Magnitude, SparseGPT, and Wanda, either concentrated solely on weights or integrated weights with activations for sparsity. However, they overlooked the informative gradients derived from pretrained large language models. In this paper, we present a novel sparsity-centric pruning method for pretrained LLMs, termed Gradient-based Language Model Pruner (GBLM-Pruner). GBLM-Pruner leverages the first-order term of the Taylor expansion, operating in a training-free manner by harnessing properly normalized gradients from a few calibration samples to determine the importance pruning score, and substantially outperforms competitive counterparts like SparseGPT and Wanda in multiple benchmarks. Intriguing, after incorporating gradients, the unstructured pruning method tends to reveal some structural patterns post-pruning, which mirrors the geometric interdependence inherent in the LLMs' parameter structure. Additionally, GBLM-Pruner functions without any subsequent retraining or weight updates to maintain its simplicity as other counterparts. Extensive evaluations on LLaMA-1 and LLaMA-2 across various language benchmarks and perplexity show that GBLM-Pruner surpasses magnitude pruning, Wanda (weights+activations) and SparseGPT (weights+activations+weight update) by significant margins. Our code and models are available at https://github.com/RocktimJyotiDas/GBLM-Pruner.

Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We empirically compare standard Principal Component Analysis (PCA) with its sparse variant (SPCA) as front-end feature extractors for downstream classifiers, and we complement these experiments with a theoretical analysis. On the theory side, we derive exact robustness certificates for linear heads applied to SPCA features: for both ell_infty and ell_2 threat models (binary and multiclass), the certified radius grows as the dual norms of W^top u shrink, where W is the projection and u the head weights. We further show that for general (non-linear) heads, sparsity reduces operator-norm bounds through a Lipschitz composition argument, predicting lower input sensitivity. Empirically, with a small non-linear network after the projection, SPCA consistently degrades more gracefully than PCA under strong white-box and black-box attacks while maintaining competitive clean accuracy. Taken together, the theory identifies the mechanism (sparser projections reduce adversarial leverage) and the experiments verify that this benefit persists beyond the linear setting. Our code is available at https://github.com/killian31/SPCARobustness.

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

We introduce, Q-Sparse, a simple yet effective approach to training sparsely-activated large language models (LLMs). Q-Sparse enables full sparsity of activations in LLMs which can bring significant efficiency gains in inference. This is achieved by applying top-K sparsification to the activations and the straight-through-estimator to the training. The key results from this work are, (1) Q-Sparse can achieve results comparable to those of baseline LLMs while being much more efficient at inference time; (2) We present an inference-optimal scaling law for sparsely-activated LLMs; (3) Q-Sparse is effective in different settings, including training-from-scratch, continue-training of off-the-shelf LLMs, and finetuning; (4) Q-Sparse works for both full-precision and 1-bit LLMs (e.g., BitNet b1.58). Particularly, the synergy of BitNet b1.58 and Q-Sparse (can be equipped with MoE) provides the cornerstone and a clear path to revolutionize the efficiency, including cost and energy consumption, of future LLMs.

The rapid advancement in Large Language Models (LLMs) has markedly enhanced the capabilities of language understanding and generation. However, the substantial model size poses hardware challenges, affecting both memory size for serving and inference latency for token generation. To address those challenges, we propose Dependency-aware Semi-structured Sparsity (DaSS), a novel method for the recent prevalent SwiGLU-based LLMs pruning. Our approach incorporates structural dependency into the weight magnitude-based unstructured pruning. We introduce an MLP-specific pruning metric that evaluates the importance of each weight by jointly considering its magnitude and its corresponding MLP intermediate activation norms. DaSS facilitates a balance between the adaptability offered by unstructured pruning and the structural consistency inherent in dependency-based structured pruning. Empirical evaluations on Mistral and LLaMA2 model families demonstrate that DaSS not only outperforms both SparseGPT and Wanda in achieving hardware-friendly N:M sparsity patterns but also maintains the computational efficiency of Wanda.

In vision-language models (VLMs), visual tokens usually consume a significant amount of computational overhead, despite their sparser information density compared to text tokens. To address this, most existing methods learn a network to prune redundant visual tokens and require additional training data. Differently, we propose an efficient training-free token optimization mechanism dubbed SparseVLM without extra parameters or fine-tuning costs. Concretely, given that visual tokens complement text tokens in VLMs for linguistic reasoning, we select visual-relevant text tokens to rate the significance of vision tokens within the self-attention matrix extracted from the VLMs. Then we progressively prune irrelevant tokens. To maximize sparsity while retaining essential information, we introduce a rank-based strategy to adaptively determine the sparsification ratio for each layer, alongside a token recycling method that compresses pruned tokens into more compact representations. Experimental results show that our SparseVLM improves the efficiency of various VLMs across a range of image and video understanding tasks. In particular, LLaVA equipped with SparseVLM reduces 61% to 67% FLOPs with a compression ratio of 78% while maintaining 93% of the accuracy. Our code is available at https://github.com/Gumpest/SparseVLMs.

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.

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

The pre-training and fine-tuning paradigm has contributed to a number of breakthroughs in Natural Language Processing (NLP). Instead of directly training on a downstream task, language models are first pre-trained on large datasets with cross-domain knowledge (e.g., Pile, MassiveText, etc.) and then fine-tuned on task-specific data (e.g., natural language generation, text summarization, etc.). Scaling the model and dataset size has helped improve the performance of LLMs, but unfortunately, this also lead to highly prohibitive computational costs. Pre-training LLMs often require orders of magnitude more FLOPs than fine-tuning and the model capacity often remains the same between the two phases. To achieve training efficiency w.r.t training FLOPs, we propose to decouple the model capacity between the two phases and introduce Sparse Pre-training and Dense Fine-tuning (SPDF). In this work, we show the benefits of using unstructured weight sparsity to train only a subset of weights during pre-training (Sparse Pre-training) and then recover the representational capacity by allowing the zeroed weights to learn (Dense Fine-tuning). We demonstrate that we can induce up to 75% sparsity into a 1.3B parameter GPT-3 XL model resulting in a 2.5x reduction in pre-training FLOPs, without a significant loss in accuracy on the downstream tasks relative to the dense baseline. By rigorously evaluating multiple downstream tasks, we also establish a relationship between sparsity, task complexity and dataset size. Our work presents a promising direction to train large GPT models at a fraction of the training FLOPs using weight sparsity, while retaining the benefits of pre-trained textual representations for downstream tasks.

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

Learned Sparse Retrievers (LSR) have evolved into an effective retrieval strategy that can bridge the gap between traditional keyword-based sparse retrievers and embedding-based dense retrievers. At its core, learned sparse retrievers try to learn the most important semantic keyword expansions from a query and/or document which can facilitate better retrieval with overlapping keyword expansions. LSR like SPLADE has typically been using encoder only models with MLM (masked language modeling) style objective in conjunction with known ways of retrieval performance improvement such as hard negative mining, distillation, etc. In this work, we propose to use decoder-only model for learning semantic keyword expansion. We posit, decoder only models that have seen much higher magnitudes of data are better equipped to learn keyword expansions needed for improved retrieval. We use Mistral as the backbone to develop our Learned Sparse Retriever similar to SPLADE and train it on a subset of sentence-transformer data which is often used for training text embedding models. Our experiments support the hypothesis that a sparse retrieval model based on decoder only large language model (LLM) surpasses the performance of existing LSR systems, including SPLADE and all its variants. The LLM based model (Echo-Mistral-SPLADE) now stands as a state-of-the-art learned sparse retrieval model on the BEIR text retrieval benchmark.

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

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

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

Recent works have shown a surprising result: a small fraction of Large Language Model (LLM) parameter outliers are disproportionately important to the quality of the model. LLMs contain billions of parameters, so these small fractions, such as 0.01%, translate to hundreds of thousands of parameters. In this work, we present an even more surprising finding: Pruning as few as a single parameter can destroy an LLM's ability to generate text -- increasing perplexity by 3 orders of magnitude and reducing zero-shot accuracy to guessing. We propose a data-free method for identifying such parameters, termed super weights, using a single forward pass through the model. We additionally find that these super weights induce correspondingly rare and large activation outliers, termed super activations. When preserved with high precision, super activations can improve simple round-to-nearest quantization to become competitive with state-of-the-art methods. For weight quantization, we similarly find that by preserving the super weight and clipping other weight outliers, round-to-nearest quantization can scale to much larger block sizes than previously considered. To facilitate further research into super weights, we provide an index of super weight coordinates for common, openly available LLMs.

Sparse autoencoders (SAEs) are widely used in mechanistic interpretability research for large language models; however, the state-of-the-art method of using k-sparse autoencoders lacks a theoretical grounding for selecting the hyperparameter k that represents the number of nonzero activations, often denoted by ell_0. In this paper, we reveal a theoretical link that the ell_2-norm of the sparse feature vector can be approximated with the ell_2-norm of the dense vector with a closed-form error, which allows sparse autoencoders to be trained without the need to manually determine ell_0. Specifically, we validate two applications of our theoretical findings. First, we introduce a new methodology that can assess the feature activations of pre-trained SAEs by computing the theoretically expected value from the input embedding, which has been overlooked by existing SAE evaluation methods and loss functions. Second, we introduce a novel activation function, top-AFA, which builds upon our formulation of approximate feature activation (AFA). This function enables top-k style activation without requiring a constant hyperparameter k to be tuned, dynamically determining the number of activated features for each input. By training SAEs on three intermediate layers to reconstruct GPT2 hidden embeddings for over 80 million tokens from the OpenWebText dataset, we demonstrate the empirical merits of this approach and compare it with current state-of-the-art k-sparse autoencoders. Our code is available at: https://github.com/SewoongLee/top-afa-sae.

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

State-of-the-art Learned Sparse Retrieval (LSR) models, such as Splade, typically employ a Language Modeling (LM) head to project latent hidden states into a lexically-anchored logit matrix. This intermediate matrix is subsequently transformed into a sparse lexical representation through element-wise operations (ReLU, Log1P) and max-pooling over the sequence dimension. Despite its effectiveness, the LM head creates a massive memory bottleneck due to the sheer size of the vocabulary (V), which can range from 30,000 to over 250,000 tokens in recent models. Materializing this matrix creates a significant memory bottleneck, limiting model scaling. The resulting I/O overhead between operators further throttles throughput and runtime performance. In this paper, we propose Sparton, a fast memory-efficient Triton kernel tailored for the LM head in LSR models. Sparton utilizes a fused approach that integrates the tiled matrix multiplication, ReLU, Log1P, and max-reduction into a single GPU kernel. By performing an early online reduction directly on raw logit tiles, Sparton avoids materializing the full logit matrix in memory. Our experiments demonstrate that the Sparton kernel, in isolation, achieves up to a 4.8x speedup and an order-of-magnitude reduction in peak memory usage compared to PyTorch baselines. Integrated into Splade (|V| ~ 30k), Sparton enables a 33% larger batch size and 14% faster training with no effectiveness loss. On a multilingual backbone (|V| ~ 250k), these gains jump to a 26x larger batch size and 2.5x faster training.

Large language models (LLMs) present significant deployment challenges due to their immense computational and memory requirements. While semi-structured pruning, particularly 2:4 sparsity, offers a path to practical hardware acceleration, existing methods often incur substantial performance degradation. To bridge this gap, we introduce ARMOR: (Adaptive Representation with Matrix-factORization), a novel one-shot post-training pruning algorithm. Instead of directly pruning weights, ARMOR factorizes each weight matrix into a 2:4 sparse core wrapped by two low-overhead, block diagonal matrices. These wrappers act as efficient pre and post-transformation error correctors, offering greater flexibility to preserve model quality compared to conventional 2:4 pruning techniques. The sparse core and block diagonal wrappers are chosen through a block coordinate descent algorithm that minimizes a layer-wise proxy loss. We theoretically prove this optimization is guaranteed to converge to a solution with a proxy loss less than or equal to state-of-the-art pruning algorithms. Experiments on Llama (Touvron et al., 2023; Dubey et al., 2024) and Qwen (Yang et al., 2025) model families demonstrate that ARMOR consistently and significantly outperforms state-of-the-art 2:4 pruning methods across a wide range of downstream tasks and perplexity evaluations. ARMOR achieves this superior performance while retaining the inference speedups and substantial memory usage reductions of 2:4 pruning, establishing a more effective trade-off between model compression and task accuracy

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

Semi-structured N:M sparsity and low-bit quantization (e.g., 1.58-bit BitNet) are two promising approaches for improving the efficiency of large language models (LLMs), yet they have largely been studied in isolation. In this work, we investigate their interaction and show that 1.58-bit BitNet is naturally more compatible with N:M sparsity than full-precision models. To study this effect, we propose Sparse-BitNet, a unified framework that jointly applies 1.58-bit quantization and dynamic N:M sparsification while ensuring stable training for the first time. Across multiple model scales and training regimes (sparse pretraining and dense-to-sparse schedules), 1.58-bit BitNet consistently exhibits smaller performance degradation than full-precision baselines at the same sparsity levels and can tolerate higher structured sparsity before accuracy collapse. Moreover, using our custom sparse tensor core, Sparse-BitNet achieves substantial speedups in both training and inference, reaching up to 1.30X. These results highlight that combining extremely low-bit quantization with semi-structured N:M sparsity is a promising direction for efficient LLMs. Code available at https://github.com/AAzdi/Sparse-BitNet

The transformative impact of large language models (LLMs) like LLaMA and GPT on natural language processing is countered by their prohibitive computational demands. Pruning has emerged as a pivotal compression strategy, introducing sparsity to enhance both memory and computational efficiency. Yet, traditional global pruning is impractical for LLMs due to scalability issues, while local pruning, despite its efficiency, leads to suboptimal solutions. Addressing these challenges, we propose SparseLLM, a novel framework that redefines the global pruning process into manageable, coordinated subproblems, allowing for resource-efficient optimization with global optimality. SparseLLM's approach, which conceptualizes LLMs as a chain of modular functions and leverages auxiliary variables for problem decomposition, not only facilitates a pragmatic application on LLMs but also demonstrates significant performance improvements, particularly in high-sparsity regimes where it surpasses current state-of-the-art methods.

The increasing size of large language models (LLMs) challenges their usage on resource-constrained platforms. For example, memory on modern GPUs is insufficient to hold LLMs that are hundreds of Gigabytes in size. Offloading is a popular method to escape this constraint by storing weights of an LLM model to host CPU memory and SSD, then loading each weight to GPU before every use. In our case study of offloaded inference, we found that due to the low bandwidth between storage devices and GPU, the latency of transferring large model weights from its offloaded location to GPU memory becomes the critical bottleneck with actual compute taking nearly 0% of runtime. To effectively reduce the weight transfer latency, we propose a novel sparse format that compresses the unstructured sparse pattern of pruned LLM weights to non-zero values with high compression ratio and low decompression overhead. Endor achieves this by expressing the positions of non-zero elements with a bitmap. Compared to offloaded inference using the popular Huggingface Accelerate, applying Endor accelerates OPT-66B by 1.70x and Llama2-70B by 1.78x. When direct weight transfer from SSD to GPU is leveraged, Endor achieves 2.25x speedup on OPT-66B and 2.37x speedup on Llama2-70B.

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

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

The emergence of long-context text applications utilizing large language models (LLMs) has presented significant scalability challenges, particularly in memory footprint. The linear growth of the Key-Value (KV) cache responsible for storing attention keys and values to minimize redundant computations can lead to substantial increases in memory consumption, potentially causing models to fail to serve with limited memory resources. To address this issue, we propose a novel approach called Cache Sparse Representation (CSR), which converts the KV cache by transforming the dense Key-Value cache tensor into sparse indexes and weights, offering a more memory-efficient representation during LLM inference. Furthermore, we introduce NeuralDict, a novel neural network-based method for automatically generating the dictionary used in our sparse representation. Our extensive experiments demonstrate that CSR achieves performance comparable to state-of-the-art KV cache quantization algorithms while maintaining robust functionality in memory-constrained environments.

Large language models (LLMs) have grown in their usage to provide support for question answering across numerous disciplines. The models on their own have already shown promise for answering basic questions, however fail quickly where expert domain knowledge is required or the question is nuanced. Scientific research often involves searching for relevant literature, distilling pertinent information from that literature and analysing how the findings support or contradict one another. The information is often encapsulated in the full text body of research articles, rather than just in the abstracts. Statements within these articles frequently require the wider article context to be fully understood. We have built an LLM-based system that performs such search and distillation of information encapsulated in scientific literature, and we evaluate our keyword based search and information distillation system against a set of biology related questions from previously released literature benchmarks. We demonstrate sparse retrieval methods exhibit results close to state of the art without the need for dense retrieval, with its associated infrastructure and complexity overhead. We also show how to increase the coverage of relevant documents for literature review generation.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

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

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.

The rapid development of large language models has revolutionized natural language processing, but their fine-tuning remains computationally expensive, hindering broad deployment. Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, have emerged as solutions. Recent work like DoRA attempts to further decompose weight adaptation into direction and magnitude components. However, existing formulations often define direction heuristically at the column level, lacking a principled geometric foundation. In this paper, we propose MAP, a novel framework that reformulates weight matrices as high-dimensional vectors and decouples their adaptation into direction and magnitude in a rigorous manner. MAP normalizes the pre-trained weights, learns a directional update, and introduces two scalar coefficients to independently scale the magnitude of the base and update vectors. This design enables more interpretable and flexible adaptation, and can be seamlessly integrated into existing PEFT methods. Extensive experiments show that MAP significantly improves performance when coupling with existing methods, offering a simple yet powerful enhancement to existing PEFT methods. Given the universality and simplicity of MAP, we hope it can serve as a default setting for designing future PEFT methods.

Large Language Models (LLMs), while demonstrating remarkable capabilities across various applications, present significant challenges during inference due to their substantial model size, especially when deployed on edge devices. Activation sparsity offers a promising solution to reduce computation and memory movement, enabling more efficient inference, particularly for small-batch on-device applications. However, current approaches face limitations with non-ReLU activation function, which are foundational to most advanced LLMs, or require heavy continual training. Additionally, the difficulty in predicting active channels and limited achievable sparsity ratios constrain the effectiveness of activation sparsity-based methods. In this paper, we introduce R-Sparse, a training-free activation sparsity approach capable of achieving high sparsity levels in advanced LLMs. We conducted two preliminary investigations into how different components contribute to the output within a single linear layer and found two key observations: (i) the non-sparse components of the input function can be regarded as a few bias terms, and (ii) The full computation can be effectively approximated by an appropriate combination of input channels and weight singular values. Building on this, we replace the linear layers in LLMs with a rank-aware sparse inference method that leverages the sparsity of input channels and singular value components, eliminating the need for active channel prediction like the output sparsity based approaches. Experiments on Llama-2/3 and Mistral models across ten diverse tasks demonstrate that R-Sparse achieves comparable performance at 50% model-level sparsity, resulting in a significant 43% end-to-end efficient improvements with customized kernels.

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

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

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}

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.

While dense retrieval models have become the standard for state-of-the-art information retrieval, their deployment is often constrained by high memory requirements and reliance on GPU accelerators for vector similarity search. Learned sparse retrieval offers a compelling alternative by enabling efficient search via inverted indices, yet it has historically received less attention than dense approaches. In this report, we introduce LACONIC, a family of learned sparse retrievers based on the Llama-3 architecture (1B, 3B, and 8B). We propose a streamlined two-phase training curriculum consisting of (1) weakly supervised pre-finetuning to adapt causal LLMs for bidirectional contextualization and (2) high-signal finetuning using curated hard negatives. Our results demonstrate that LACONIC effectively bridges the performance gap with dense models: the 8B variant achieves a state-of-the-art 60.2 nDCG on the MTEB Retrieval benchmark, ranking 15th on the leaderboard as of January 1, 2026, while utilizing 71\% less index memory than an equivalent dense model. By delivering high retrieval effectiveness on commodity CPU hardware with a fraction of the compute budget required by competing models, LACONIC provides a scalable and efficient solution for real-world search applications.

In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional, incurring substantial costs in storage, memory, and inference latency. To address these, Contrastive Sparse Representation (CSR) is recently proposed as a promising direction, mapping dense embeddings into high-dimensional but k-sparse vectors, in contrast to compact dense embeddings such as Matryoshka Representation Learning (MRL). Despite its promise, CSR suffers severe degradation in the ultra-sparse regime, where over 80% of neurons remain inactive, leaving much of its efficiency potential unrealized. In this paper, we introduce CSRv2, a principled training approach designed to make ultra-sparse embeddings viable. CSRv2 stabilizes sparsity learning through progressive k-annealing, enhances representational quality via supervised contrastive objectives, and ensures end-to-end adaptability with full backbone finetuning. CSRv2 reduces dead neurons from 80% to 20% and delivers a 14% accuracy gain at k=2, bringing ultra-sparse embeddings on par with CSR at k=8 and MRL at 32 dimensions, all with only two active features. While maintaining comparable performance, CSRv2 delivers a 7x speedup over MRL, and yields up to 300x improvements in compute and memory efficiency relative to dense embeddings in text representation. Extensive experiments across text and vision demonstrate that CSRv2 makes ultra-sparse embeddings practical without compromising performance, where CSRv2 achieves 7%/4% improvement over CSR when k=4 and further increases this gap to 14%/6% when k=2 in text/vision representation. By making extreme sparsity viable, CSRv2 broadens the design space for real-time and edge-deployable AI systems where both embedding quality and efficiency are critical.

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.

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

Sparse attention offers a promising strategy to extend long-context capabilities in Transformer LLMs, yet its viability, its efficiency-accuracy trade-offs, and systematic scaling studies remain unexplored. To address this gap, we perform a careful comparison of training-free sparse attention methods at varying model scales, sequence lengths, and sparsity levels on a diverse collection of long-sequence tasks-including novel ones that rely on natural language while remaining controllable and easy to evaluate. Based on our experiments, we report a series of key findings: 1) an isoFLOPS analysis reveals that for very long sequences, larger and highly sparse models are preferable to smaller and dense ones. 2) The level of sparsity attainable while statistically guaranteeing accuracy preservation is higher during decoding than prefilling, and correlates with model size in the former. 3) There is no clear strategy that performs best across tasks and phases, with different units of sparsification or budget adaptivity needed for different scenarios. Even moderate sparsity levels often result in significant performance degradation on at least one task, highlighting that sparse attention is not a universal solution. 4) We introduce and validate novel scaling laws specifically tailored for sparse attention, providing evidence that our findings are likely to hold true beyond our range of experiments. Through these insights, we demonstrate that sparse attention is a key tool to enhance the capabilities of Transformer LLMs for processing longer sequences, but requires careful evaluation of trade-offs for performance-sensitive applications.