Daily Papers

Transformer models encounter challenges in scaling hidden dimensions efficiently, as uniformly increasing them inflates computational and memory costs while failing to emphasize the most relevant features for each token. For further understanding, we study hidden dimension sparsity and observe that trained Transformers utilize only a small fraction of token dimensions, revealing an "activation flow" pattern. Notably, there are shared sub-dimensions with sustained activation across multiple consecutive tokens and specialized sub-dimensions uniquely activated for each token. To better model token-relevant sub-dimensions, we propose MoHD (Mixture of Hidden Dimensions), a sparse conditional activation architecture. Particularly, MoHD employs shared sub-dimensions for common token features and a routing mechanism to dynamically activate specialized sub-dimensions. To mitigate potential information loss from sparsity, we design activation scaling and group fusion mechanisms to preserve activation flow. In this way, MoHD expands hidden dimensions with negligible increases in computation or parameters, efficient training and inference while maintaining performance. Evaluations across 10 NLP tasks show that MoHD surpasses Vanilla Transformers in parameter efficiency and task performance. It achieves 1.7% higher performance with 50% fewer activation parameters and 3.7% higher performance with a 3x parameter expansion at constant activation cost. MOHD offers a new perspective for scaling the model, showcasing the potential of hidden dimension sparsity to boost efficiency

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

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.

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.

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.

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

Sparse Autoencoders (SAEs) have proven to be powerful tools for interpreting neural networks by decomposing hidden representations into disentangled, interpretable features via sparsity constraints. However, conventional SAEs are constrained by the fixed sparsity level chosen during training; meeting different sparsity requirements therefore demands separate models and increases the computational footprint during both training and evaluation. We introduce a novel training objective, HierarchicalTopK, which trains a single SAE to optimise reconstructions across multiple sparsity levels simultaneously. Experiments with Gemma-2 2B demonstrate that our approach achieves Pareto-optimal trade-offs between sparsity and explained variance, outperforming traditional SAEs trained at individual sparsity levels. Further analysis shows that HierarchicalTopK preserves high interpretability scores even at higher sparsity. The proposed objective thus closes an important gap between flexibility and interpretability in SAE design.

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.

The research in the field of adversarial attacks and models' vulnerability is one of the fundamental directions in modern machine learning. Recent studies reveal the vulnerability phenomenon, and understanding the mechanisms behind this is essential for improving neural network characteristics and interpretability. In this paper, we propose a novel sparse universal white-box adversarial attack. Our approach is based on truncated power iteration providing sparsity to (p,q)-singular vectors of the hidden layers of Jacobian matrices. Using the ImageNet benchmark validation subset, we analyze the proposed method in various settings, achieving results comparable to dense baselines with more than a 50% fooling rate while damaging only 5% of pixels and utilizing 256 samples for perturbation fitting. We also show that our algorithm admits higher attack magnitude without affecting the human ability to solve the task. Furthermore, we investigate that the constructed perturbations are highly transferable among different models without significantly decreasing the fooling rate. Our findings demonstrate the vulnerability of state-of-the-art models to sparse attacks and highlight the importance of developing robust machine learning systems.

Text embeddings enable numerous NLP applications but face severe privacy risks from embedding inversion attacks, which can expose sensitive attributes or reconstruct raw text. Existing differential privacy defenses assume uniform sensitivity across embedding dimensions, leading to excessive noise and degraded utility. We propose SPARSE, a user-centric framework for concept-specific privacy protection in text embeddings. SPARSE combines (1) differentiable mask learning to identify privacy-sensitive dimensions for user-defined concepts, and (2) the Mahalanobis mechanism that applies elliptical noise calibrated by dimension sensitivity. Unlike traditional spherical noise injection, SPARSE selectively perturbs privacy-sensitive dimensions while preserving non-sensitive semantics. Evaluated across six datasets with three embedding models and attack scenarios, SPARSE consistently reduces privacy leakage while achieving superior downstream performance compared to state-of-the-art DP methods.

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

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

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.

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.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

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.

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

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

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.

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their application becomes more widespread. Here we use the large width Gaussian process limit to analyze the behaviour, at random initialization, of nonlinear activations that induce sparsity in the hidden outputs. A previously unreported form of training instability is proven for arguably two of the most natural candidates for hidden layer sparsification; those being a shifted ReLU (phi(x)=max(0, x-tau) for tauge 0) and soft thresholding (phi(x)=0 for |x|letau and x-sign(x)tau for |x|>tau). We show that this instability is overcome by clipping the nonlinear activation magnitude, at a level prescribed by the shape of the associated Gaussian process variance map. Numerical experiments verify the theory and show that the proposed magnitude clipped sparsifying activations can be trained with training and test fractional sparsity as high as 85\% while retaining close to full accuracy.

Robustness to adversarial attack is typically evaluated with adversarial accuracy. This metric quantifies the number of points for which, given a threat model, successful adversarial perturbations cannot be found. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for each point. In this work we introduce an alternative approach, adversarial sparsity, which quantifies how difficult it is to find a successful perturbation given both an input point and a constraint on the direction of the perturbation. This constraint may be angular (L2 perturbations), or based on the number of pixels (Linf perturbations). We show that sparsity provides valuable insight on neural networks in multiple ways. analyzing the sparsity of existing robust models illustrates important differences between them that accuracy analysis does not, and suggests approaches for improving their robustness. When applying broken defenses effective against weak attacks but not strong ones, sparsity can discriminate between the totally ineffective and the partially effective defenses. Finally, with sparsity we can measure increases in robustness that do not affect accuracy: we show for example that data augmentation can by itself increase adversarial robustness, without using adversarial training.

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

Sparsity in Deep Neural Networks (DNNs) has been widely studied to compress and accelerate the models on resource-constrained environments. It can be generally categorized into unstructured fine-grained sparsity that zeroes out multiple individual weights distributed across the neural network, and structured coarse-grained sparsity which prunes blocks of sub-networks of a neural network. Fine-grained sparsity can achieve a high compression ratio but is not hardware friendly and hence receives limited speed gains. On the other hand, coarse-grained sparsity cannot concurrently achieve both apparent acceleration on modern GPUs and decent performance. In this paper, we are the first to study training from scratch an N:M fine-grained structured sparse network, which can maintain the advantages of both unstructured fine-grained sparsity and structured coarse-grained sparsity simultaneously on specifically designed GPUs. Specifically, a 2:4 sparse network could achieve 2x speed-up without performance drop on Nvidia A100 GPUs. Furthermore, we propose a novel and effective ingredient, sparse-refined straight-through estimator (SR-STE), to alleviate the negative influence of the approximated gradients computed by vanilla STE during optimization. We also define a metric, Sparse Architecture Divergence (SAD), to measure the sparse network's topology change during the training process. Finally, We justify SR-STE's advantages with SAD and demonstrate the effectiveness of SR-STE by performing comprehensive experiments on various tasks. Source codes and models are available at https://github.com/NM-sparsity/NM-sparsity.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

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.

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.

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!

In response to recent data regulation requirements, machine unlearning (MU) has emerged as a critical process to remove the influence of specific examples from a given model. Although exact unlearning can be achieved through complete model retraining using the remaining dataset, the associated computational costs have driven the development of efficient, approximate unlearning techniques. Moving beyond data-centric MU approaches, our study introduces a novel model-based perspective: model sparsification via weight pruning, which is capable of reducing the gap between exact unlearning and approximate unlearning. We show in both theory and practice that model sparsity can boost the multi-criteria unlearning performance of an approximate unlearner, closing the approximation gap, while continuing to be efficient. This leads to a new MU paradigm, termed prune first, then unlearn, which infuses a sparse model prior into the unlearning process. Building on this insight, we also develop a sparsity-aware unlearning method that utilizes sparsity regularization to enhance the training process of approximate unlearning. Extensive experiments show that our proposals consistently benefit MU in various unlearning scenarios. A notable highlight is the 77% unlearning efficacy gain of fine-tuning (one of the simplest unlearning methods) when using sparsity-aware unlearning. Furthermore, we demonstrate the practical impact of our proposed MU methods in addressing other machine learning challenges, such as defending against backdoor attacks and enhancing transfer learning. Codes are available at https://github.com/OPTML-Group/Unlearn-Sparse.

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.

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

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.

Machine learning models for medical image analysis often suffer from poor performance on important subsets of a population that are not identified during training or testing. For example, overall performance of a cancer detection model may be high, but the model still consistently misses a rare but aggressive cancer subtype. We refer to this problem as hidden stratification, and observe that it results from incompletely describing the meaningful variation in a dataset. While hidden stratification can substantially reduce the clinical efficacy of machine learning models, its effects remain difficult to measure. In this work, we assess the utility of several possible techniques for measuring and describing hidden stratification effects, and characterize these effects on multiple medical imaging datasets. We find evidence that hidden stratification can occur in unidentified imaging subsets with low prevalence, low label quality, subtle distinguishing features, or spurious correlates, and that it can result in relative performance differences of over 20% on clinically important subsets. Finally, we explore the clinical implications of our findings, and suggest that evaluation of hidden stratification should be a critical component of any machine learning deployment in medical imaging.

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.

Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing and rate-distortion theory, we introduce effective data compression methods by developing autoencoders using high dimensional latent spaces that are L^1-regularized to obtain sparse low dimensional representations. We show how these information-rich latent spaces can be used to mitigate blurring and other artifacts to obtain highly effective data compression methods for scientific data. We demonstrate our methods for short angle scattering (SAS) datasets showing they can achieve compression ratios around two orders of magnitude and in some cases better. Our compression methods show promise for use in addressing current bottlenecks in transmission, storage, and analysis in high-performance distributed computing environments. This is central to processing the large volume of SAS data being generated at shared experimental facilities around the world to support scientific investigations. Our approaches provide general ways for obtaining specialized compression methods for targeted scientific datasets.

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how to calculate them. The projectors can be applied to solve linear matrix equations, generate low-rank approximations, or design randomized matrix algorithms. But also, as demonstrated, they can be applied in cryptography to encrypt and decrypt messages. The paper discusses some of the security implications of this application and leaves some questions open for further investigation. The basic concepts are illustrated with source code listings. Finally, this work shares some personal reflections on the meaning and importance of understanding in the time of the artificial intelligence revolution.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

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.

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

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

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.

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.

Neural multivariate regression underpins a wide range of domains such as control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit generalization in classification, we find that analogous collapse in regression consistently degrades performance. To explain this contrast, we analyze models through the lens of intrinsic dimension. Across control tasks and synthetic datasets, we estimate the intrinsic dimension of last-layer features (ID_H) and compare it with that of the regression targets (ID_Y). Collapsed models exhibit ID_H < ID_Y, leading to over-compression and poor generalization, whereas non-collapsed models typically maintain ID_H > ID_Y. For the non-collapsed models, performance with respect to ID_H depends on the data quantity and noise levels. From these observations, we identify two regimes (over-compressed and under-compressed) that determine when expanding or reducing feature dimensionality improves performance. Our results provide new geometric insights into neural regression and suggest practical strategies for enhancing generalization.

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.

While transformer models are widely believed to operate in high-dimensional hidden spaces, we show that attention outputs are confined to a surprisingly low-dimensional subspace, where about 60\% of the directions account for 99\% of the variance--a phenomenon that is induced by the attention output projection matrix and consistently observed across diverse model families and datasets. Critically, we find this low-rank structure as a fundamental cause of the prevalent dead feature problem in sparse dictionary learning, where it creates a mismatch between randomly initialized features and the intrinsic geometry of the activation space. Building on this insight, we propose a subspace-constrained training method for sparse autoencoders (SAEs), initializing feature directions into the active subspace of activations. Our approach reduces dead features from 87\% to below 1\% in Attention Output SAEs with 1M features, and can further extend to other sparse dictionary learning methods. Our findings provide both new insights into the geometry of attention and practical tools for improving sparse dictionary learning in large language models.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

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

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable features are embedded in hidden states. Our experiments reveal high probing accuracy, indicating latent space regularities with functionally important directions. Building on this, we use the directions between hidden states with opposing features to fit control vectors. At inference, we add our control vectors to hidden states and evaluate their impact on predictions. Remarkably, such modifications preserve the feasibility of predictions. We further refine our control vectors using sparse autoencoders (SAEs). This leads to more linear changes in predictions when scaling control vectors. Our approach enables mechanistic interpretation as well as zero-shot generalization to unseen dataset characteristics with negligible computational overhead.

The Lottery Ticket Hypothesis demonstrated that sparse subnetworks can match full-model performance, suggesting parameter redundancy. Meanwhile, in Reinforcement Learning with Verifiable Rewards (RLVR), recent work has shown that updates concentrate on a sparse subset of parameters, which further lends evidence to this underlying redundancy. We study the simplest possible way to exploit this redundancy: training only a randomly selected subset of parameters at extreme sparsities. Empirically, we find that training just 1\% of parameters matches or exceeds full-parameter RLVR finetuning across 3 models and 2 task domains. Moreover, different random masks show minimal overlap (leq 0.005 Jaccard similarity) and yet all succeed, suggesting pretrained models contain many viable sparse subnetworks rather than one privileged set. We term this the Multiple Ticket Hypothesis. We explain this phenomenon through the implicit per-step KL constraint in RLVR, which restricts updates to a low-dimensional subspace, enabling arbitrary sparse masks to succeed.

Making statements about the performance of trained models on tasks involving new data is one of the primary goals of machine learning, i.e., to understand the generalization power of a model. Various capacity measures try to capture this ability, but usually fall short in explaining important characteristics of models that we observe in practice. In this study, we propose the local effective dimension as a capacity measure which seems to correlate well with generalization error on standard data sets. Importantly, we prove that the local effective dimension bounds the generalization error and discuss the aptness of this capacity measure for machine learning models.

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.

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

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

Sparse Autoencoders (SAEs) have emerged as a promising approach to decompose the activations of Large Language Models (LLMs) into human-interpretable latents. In this paper, we pose two questions. First, to what extent do SAEs extract monosemantic and interpretable latents? Second, to what extent does varying the sparsity or the size of the SAE affect monosemanticity / interpretability? By investigating these questions in the context of a simple first-letter identification task where we have complete access to ground truth labels for all tokens in the vocabulary, we are able to provide more detail than prior investigations. Critically, we identify a problematic form of feature-splitting we call feature absorption where seemingly monosemantic latents fail to fire in cases where they clearly should. Our investigation suggests that varying SAE size or sparsity is insufficient to solve this issue, and that there are deeper conceptual issues in need of resolution.

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

With the rapid growth of artificial intelligence (AI) in healthcare, there has been a significant increase in the generation and storage of sensitive medical data. This abundance of data, in turn, has propelled the advancement of medical AI technologies. However, concerns about unauthorized data exploitation, such as training commercial AI models, often deter researchers from making their invaluable datasets publicly available. In response to the need to protect this hard-to-collect data while still encouraging medical institutions to share it, one promising solution is to introduce imperceptible noise into the data. This method aims to safeguard the data against unauthorized training by inducing degradation in model generalization. Although existing methods have shown commendable data protection capabilities in general domains, they tend to fall short when applied to biomedical data, mainly due to their failure to account for the sparse nature of medical images. To address this problem, we propose the Sparsity-Aware Local Masking (SALM) method, a novel approach that selectively perturbs significant pixel regions rather than the entire image as previous strategies have done. This simple-yet-effective approach significantly reduces the perturbation search space by concentrating on local regions, thereby improving both the efficiency and effectiveness of data protection for biomedical datasets characterized by sparse features. Besides, we have demonstrated that SALM maintains the essential characteristics of the data, ensuring its clinical utility remains uncompromised. Our extensive experiments across various datasets and model architectures demonstrate that SALM effectively prevents unauthorized training of deep-learning models and outperforms previous state-of-the-art data protection methods.

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

Sparse autoencoders (SAEs) have emerged as powerful techniques for interpretability of large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the ell_0 sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method, a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

Reinforcement learning (RL) yields substantial improvements in large language models (LLMs) downstream task performance and alignment with human values. Surprisingly, such large gains result from updating only a small subnetwork comprising just 5 percent to 30 percent of the parameters, with the rest effectively unchanged. We refer to this phenomenon as parameter update sparsity induced by RL. It is observed across all 7 widely used RL algorithms (e.g., PPO, GRPO, DPO) and all 10 LLMs from different families in our experiments. This sparsity is intrinsic and occurs without any explicit sparsity promoting regularizations or architectural constraints. Finetuning the subnetwork alone recovers the test accuracy, and, remarkably, produces a model nearly identical to the one obtained via full finetuning. The subnetworks from different random seeds, training data, and even RL algorithms show substantially greater overlap than expected by chance. Our analysis suggests that this sparsity is not due to updating only a subset of layers, instead, nearly all parameter matrices receive similarly sparse updates. Moreover, the updates to almost all parameter matrices are nearly full-rank, suggesting RL updates a small subset of parameters that nevertheless span almost the full subspaces that the parameter matrices can represent. We conjecture that the this update sparsity can be primarily attributed to training on data that is near the policy distribution, techniques that encourage the policy to remain close to the pretrained model, such as the KL regularization and gradient clipping, have limited impact.

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

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.

Activation sparsity can enable practical inference speedups in large language models (LLMs) by reducing the compute and memory-movement required for matrix multiplications during the forward pass. However, existing methods face limitations that inhibit widespread adoption. Some approaches are tailored towards older models with ReLU-based sparsity, while others require extensive continued pre-training on up to hundreds of billions of tokens. This paper describes TEAL, a simple training-free method that applies magnitude-based activation sparsity to hidden states throughout the entire model. TEAL achieves 40-50% model-wide sparsity with minimal performance degradation across Llama-2, Llama-3, and Mistral families, with sizes varying from 7B to 70B. We improve existing sparse kernels and demonstrate wall-clock decoding speed-ups of up to 1.53times and 1.8times at 40% and 50% model-wide sparsity. TEAL is compatible with weight quantization, enabling further efficiency gains.

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

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

We study the problem of single-image 3D object reconstruction. Recent works have diverged into two directions: regression-based modeling and generative modeling. Regression methods efficiently infer visible surfaces, but struggle with occluded regions. Generative methods handle uncertain regions better by modeling distributions, but are computationally expensive and the generation is often misaligned with visible surfaces. In this paper, we present SPAR3D, a novel two-stage approach aiming to take the best of both directions. The first stage of SPAR3D generates sparse 3D point clouds using a lightweight point diffusion model, which has a fast sampling speed. The second stage uses both the sampled point cloud and the input image to create highly detailed meshes. Our two-stage design enables probabilistic modeling of the ill-posed single-image 3D task while maintaining high computational efficiency and great output fidelity. Using point clouds as an intermediate representation further allows for interactive user edits. Evaluated on diverse datasets, SPAR3D demonstrates superior performance over previous state-of-the-art methods, at an inference speed of 0.7 seconds. Project page with code and model: https://spar3d.github.io

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

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

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

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

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.

Supervised contour detection methods usually require many labeled training images to obtain satisfactory performance. However, a large set of annotated data might be unavailable or extremely labor intensive. In this paper, we investigate the usage of semi-supervised learning (SSL) to obtain competitive detection accuracy with very limited training data (three labeled images). Specifically, we propose a semi-supervised structured ensemble learning approach for contour detection built on structured random forests (SRF). To allow SRF to be applicable to unlabeled data, we present an effective sparse representation approach to capture inherent structure in image patches by finding a compact and discriminative low-dimensional subspace representation in an unsupervised manner, enabling the incorporation of abundant unlabeled patches with their estimated structured labels to help SRF perform better node splitting. We re-examine the role of sparsity and propose a novel and fast sparse coding algorithm to boost the overall learning efficiency. To the best of our knowledge, this is the first attempt to apply SSL for contour detection. Extensive experiments on the BSDS500 segmentation dataset and the NYU Depth dataset demonstrate the superiority of the proposed method.

Objective: To allow efficient learning using the Recurrent Inference Machine (RIM) for image reconstruction whereas not being strictly dependent on the training data distribution so that unseen modalities and pathologies are still accurately recovered. Methods: Theoretically, the RIM learns to solve the inverse problem of accelerated-MRI reconstruction whereas being robust to variable imaging conditions. The efficiency and generalization capabilities with different training datasets were studied, as well as recurrent network units with decreasing complexity: the Gated Recurrent Unit (GRU), the Minimal Gated Unit (MGU), and the Independently Recurrent Neural Network (IndRNN), to reduce inference times. Validation was performed against Compressed Sensing (CS) and further assessed based on data unseen during training. A pathology study was conducted by reconstructing simulated white matter lesions and prospectively undersampled data of a Multiple Sclerosis patient. Results: Training on a single modality of 3T T_1-weighted brain data appeared sufficient to also reconstruct 7T T_{2}^*-weighted brain and 3T T_2-weighted knee data. The IndRNN is an efficient recurrent unit, reducing inference time by 68\% compared to CS, whereas maintaining performance. The RIM was able to reconstruct lesions unseen during training more accurately than CS when trained on T_2-weighted knee data. Training on T_1-weighted brain data and on combined data slightly enhanced the signal compared to CS. Conclusion: The RIM is efficient when decreasing its complexity, which reduces the inference time, whereas still being able to reconstruct data and pathology that was unseen during training.

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.

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.

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

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

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.

Sparse autoencoders (SAEs) are useful for detecting and steering interpretable features in neural networks, with particular potential for understanding complex multimodal representations. Given their ability to uncover interpretable features, SAEs are particularly valuable for analyzing large-scale vision-language models (e.g., CLIP and SigLIP), which are fundamental building blocks in modern systems yet remain challenging to interpret and control. However, current SAE methods are limited by optimizing both reconstruction quality and sparsity simultaneously, as they rely on either activation suppression or rigid sparsity constraints. To this end, we introduce Matryoshka SAE (MSAE), a new architecture that learns hierarchical representations at multiple granularities simultaneously, enabling a direct optimization of both metrics without compromise. MSAE establishes a new state-of-the-art Pareto frontier between reconstruction quality and sparsity for CLIP, achieving 0.99 cosine similarity and less than 0.1 fraction of variance unexplained while maintaining ~80% sparsity. Finally, we demonstrate the utility of MSAE as a tool for interpreting and controlling CLIP by extracting over 120 semantic concepts from its representation to perform concept-based similarity search and bias analysis in downstream tasks like CelebA.

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

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATEs are non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose to perform partial identification of CATEs or, equivalently, aim at estimating of lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our framework is of direct relevance in practice where the validity of CATE estimation is of importance.

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.

Vision-Language Models (VLMs) excel across diverse tasks but suffer from high inference costs in time and memory. Token sparsity mitigates inefficiencies in token usage, while neuron sparsity reduces high-dimensional computations, both offering promising solutions to enhance efficiency. Recently, these two sparsity paradigms have evolved largely in parallel, fostering the prevailing assumption that they function independently. However, a fundamental yet underexplored question remains: Do they truly operate in isolation, or is there a deeper underlying interplay that has yet to be uncovered? In this paper, we conduct the first comprehensive investigation into this question. By introducing and analyzing the matching mechanism between Core Neurons and Core Tokens, we found that key neurons and tokens for inference mutually influence and reinforce each other. Building on this insight, we propose CoreMatching, a co-adaptive sparse inference framework, which leverages the synergy between token and neuron sparsity to enhance inference efficiency. Through theoretical analysis and efficiency evaluations, we demonstrate that the proposed method surpasses state-of-the-art baselines on ten image understanding tasks and three hardware devices. Notably, on the NVIDIA Titan Xp, it achieved 5x FLOPs reduction and a 10x overall speedup. Code is released at https://github.com/wangqinsi1/2025-ICML-CoreMatching/tree/main.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose Mutual Feature Regularization (MFR), a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate MFR by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that MFR can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale MFR to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that MFR can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

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.

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many real-life datasets, however, are of increasingly high dimensionality, where a large number of features may be irrelevant for both supervised and unsupervised learning tasks. The inclusion of such features would not only introduce unwanted noise but also increase computational complexity. Furthermore, due to high non-linearity and dependency among a large number of features, DNN models tend to be unavoidably opaque and perceived as black-box methods because of their not well-understood internal functioning. Their algorithmic complexity is often simply beyond the capacities of humans to understand the interplay among myriads of hyperparameters. A well-interpretable model can identify statistically significant features and explain the way they affect the model's outcome. In this paper, we propose an efficient method to improve the interpretability of black-box models for classification tasks in the case of high-dimensional datasets. First, we train a black-box model on a high-dimensional dataset to learn the embeddings on which the classification is performed. To decompose the inner working principles of the black-box model and to identify top-k important features, we employ different probing and perturbing techniques. We then approximate the behavior of the black-box model by means of an interpretable surrogate model on the top-k feature space. Finally, we derive decision rules and local explanations from the surrogate model to explain individual decisions. Our approach outperforms state-of-the-art methods like TabNet and XGboost when tested on different datasets with varying dimensionality between 50 and 20,000 w.r.t metrics and explainability.

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

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

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

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

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

Sparse Autoencoders (SAEs) have emerged as a promising tool for interpreting neural networks by decomposing their activations into sparse sets of human-interpretable features. Recent work has introduced multiple SAE variants and successfully scaled them to frontier models. Despite much excitement, a growing number of negative results in downstream tasks casts doubt on whether SAEs recover meaningful features. To directly investigate this, we perform two complementary evaluations. On a synthetic setup with known ground-truth features, we demonstrate that SAEs recover only 9% of true features despite achieving 71% explained variance, showing that they fail at their core task even when reconstruction is strong. To evaluate SAEs on real activations, we introduce three baselines that constrain SAE feature directions or their activation patterns to random values. Through extensive experiments across multiple SAE architectures, we show that our baselines match fully-trained SAEs in interpretability (0.87 vs 0.90), sparse probing (0.69 vs 0.72), and causal editing (0.73 vs 0.72). Together, these results suggest that SAEs in their current state do not reliably decompose models' internal mechanisms.

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 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.

There is an increasingly apparent need for validating the classifications made by deep learning systems in safety-critical applications like autonomous vehicle systems. A number of recent papers have proposed methods for detecting anomalous image data that appear different from known inlier data samples, including reconstruction-based autoencoders. Autoencoders optimize the compression of input data to a latent space of a dimensionality smaller than the original input and attempt to accurately reconstruct the input using that compressed representation. Since the latent vector is optimized to capture the salient features from the inlier class only, it is commonly assumed that images of objects from outside of the training class cannot effectively be compressed and reconstructed. Some thus consider reconstruction error as a kind of novelty measure. Here we suggest that reconstruction-based approaches fail to capture particular anomalies that lie far from known inlier samples in latent space but near the latent dimension manifold defined by the parameters of the model. We propose incorporating the Mahalanobis distance in latent space to better capture these out-of-distribution samples and our results show that this method often improves performance over the baseline approach.

Deploying large language models (LLMs) for long-context inference remains challenging due to their substantial memory and computational demands. While techniques such as Key-Value (KV) cache compression are designed to reduce memory usage, they often neglect the structured sparsity inherent in the relationship between hidden states and their corresponding KV cache. In this work, we explore the role of uncertainty as a potential indicator of sparsity within LLMs. We propose UNComp, an uncertainty-aware framework that leverages truncated matrix entropy to identify areas of low information content, thereby revealing sparsity patterns that can be used for adaptive compression. Unlike traditional methods that apply uniform compression, UNComp dynamically adjusts its approach to compression, guided by uncertainty measures that reflect the importance of various model components. Our analysis shows that sparsity patterns, when derived from uncertainty estimates, can be exploited to reveal special long-range dependencies, such as retrieval heads and retrieval layers. This perspective not only enhances our understanding of how compression can be optimized but also provides new insights into the inherent sparsity of LLMs during long-context inference. By focusing on uncertainty to analyze the sparsity pattern in detail, UNComp reduces the KV cache size to 4.74% of the original, achieves a 6% prefill speedup, and improves throughput by 6.4x - not only delivering strong lossless compression performance, but also validating the effectiveness of the underlying theoretical tool. We release the code at https://github.com/menik1126/UNComp.

In the field of monocular 3D detection, it is common practice to utilize scene geometric clues to enhance the detector's performance. However, many existing works adopt these clues explicitly such as estimating a depth map and back-projecting it into 3D space. This explicit methodology induces sparsity in 3D representations due to the increased dimensionality from 2D to 3D, and leads to substantial information loss, especially for distant and occluded objects. To alleviate this issue, we propose MonoNeRD, a novel detection framework that can infer dense 3D geometry and occupancy. Specifically, we model scenes with Signed Distance Functions (SDF), facilitating the production of dense 3D representations. We treat these representations as Neural Radiance Fields (NeRF) and then employ volume rendering to recover RGB images and depth maps. To the best of our knowledge, this work is the first to introduce volume rendering for M3D, and demonstrates the potential of implicit reconstruction for image-based 3D perception. Extensive experiments conducted on the KITTI-3D benchmark and Waymo Open Dataset demonstrate the effectiveness of MonoNeRD. Codes are available at https://github.com/cskkxjk/MonoNeRD.

Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of deep neural networks. In this article, we present a relatively new mathematical framework that provides the beginning of a deeper understanding of deep learning. This framework precisely characterizes the functional properties of neural networks that are trained to fit to data. The key mathematical tools which support this framework include transform-domain sparse regularization, the Radon transform of computed tomography, and approximation theory, which are all techniques deeply rooted in signal processing. This framework explains the effect of weight decay regularization in neural network training, the use of skip connections and low-rank weight matrices in network architectures, the role of sparsity in neural networks, and explains why neural networks can perform well in high-dimensional problems.

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

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

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or its representation internal to the network. While margins have been shown to be correlated with the generalization ability of a model when measured at its hidden representations (hidden margins), no such link between large margins and generalization has been established for input margins. We show that while input margins are not generally predictive of generalization, they can be if the search space is appropriately constrained. We develop such a measure based on input margins, which we refer to as `constrained margins'. The predictive power of this new measure is demonstrated on the 'Predicting Generalization in Deep Learning' (PGDL) dataset and contrasted with hidden representation margins. We find that constrained margins achieve highly competitive scores and outperform other margin measurements in general. This provides a novel insight on the relationship between generalization and classification margins, and highlights the importance of considering the data manifold for investigations of generalization in DNNs.

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

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.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

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

Joint Embedding Predictive Architectures (JEPA) have emerged as a powerful framework for learning general-purpose representations. However, these models often lack interpretability and suffer from inefficiencies due to dense embedding representations. We propose SparseJEPA, an extension that integrates sparse representation learning into the JEPA framework to enhance the quality of learned representations. SparseJEPA employs a penalty method that encourages latent space variables to be shared among data features with strong semantic relationships, while maintaining predictive performance. We demonstrate the effectiveness of SparseJEPA by training on the CIFAR-100 dataset and pre-training a lightweight Vision Transformer. The improved embeddings are utilized in linear-probe transfer learning for both image classification and low-level tasks, showcasing the architecture's versatility across different transfer tasks. Furthermore, we provide a theoretical proof that demonstrates that the grouping mechanism enhances representation quality. This was done by displaying that grouping reduces Multiinformation among latent-variables, including proofing the Data Processing Inequality for Multiinformation. Our results indicate that incorporating sparsity not only refines the latent space but also facilitates the learning of more meaningful and interpretable representations. In further work, hope to further extend this method by finding new ways to leverage the grouping mechanism through object-centric representation learning.

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.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

This paper introduces Least Volume-a simple yet effective regularization inspired by geometric intuition-that can reduce the necessary number of latent dimensions needed by an autoencoder without requiring any prior knowledge of the intrinsic dimensionality of the dataset. We show that the Lipschitz continuity of the decoder is the key to making it work, provide a proof that PCA is just a linear special case of it, and reveal that it has a similar PCA-like importance ordering effect when applied to nonlinear models. We demonstrate the intuition behind the regularization on some pedagogical toy problems, and its effectiveness on several benchmark problems, including MNIST, CIFAR-10 and CelebA.

KV-Cache compression methods generally sample a KV-Cache of effectual tokens or quantize it into lower bits. However, these methods cannot exploit the redundancy of the hidden dimension of KV tensors. This paper investigates a unique hidden dimension approach called Palu, a novel KV-Cache compression framework that utilizes low-rank projection. Palu decomposes the linear layers into low-rank matrices, caches the smaller intermediate states, and reconstructs the full keys and values on the fly. To improve accuracy, compression rate, and efficiency, Palu further encompasses (1) a medium-grained low-rank decomposition scheme, (2) an efficient rank search algorithm, (3) a low-rank-aware quantization algorithm, and (4) matrix fusion with optimized GPU kernels. Our extensive experiments with popular LLMs show that Palu can compress KV-Cache by more than 91.25% while maintaining a significantly better accuracy (up to 1.19 lower perplexity) than state-of-the-art KV-Cache quantization methods at a similar or even higher memory usage. When compressing KV-Cache for 50%, Palu delivers up to 1.61x end-to-end speedup for the attention module. Our code is publicly available at https://github.com/shadowpa0327/Palu.

We study the problem of privately estimating the parameters of d-dimensional Gaussian Mixture Models (GMMs) with k components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to privatize existing non-private algorithms in a blackbox manner, while incurring only a small overhead in the sample complexity and running time. As the main application of our framework, we develop an (varepsilon, delta)-differentially private algorithm to learn GMMs using the non-private algorithm of Moitra and Valiant [MV10] as a blackbox. Consequently, this gives the first sample complexity upper bound and first polynomial time algorithm for privately learning GMMs without any boundedness assumptions on the parameters. As part of our analysis, we prove a tight (up to a constant factor) lower bound on the total variation distance of high-dimensional Gaussians which can be of independent interest.

Scaling recommendation models into large recommendation models has become one of the most widely discussed topics. Recent efforts focus on components beyond the scaling embedding dimension, as it is believed that scaling embedding may lead to performance degradation. Although there have been some initial observations on embedding, the root cause of their non-scalability remains unclear. Moreover, whether performance degradation occurs across different types of models and datasets is still an unexplored area. Regarding the effect of embedding dimensions on performance, we conduct large-scale experiments across 10 datasets with varying sparsity levels and scales, using 4 representative classical architectures. We surprisingly observe two novel phenomenon: double-peak and logarithmic. For the former, as the embedding dimension increases, performance first improves, then declines, rises again, and eventually drops. For the latter, it exhibits a perfect logarithmic curve. Our contributions are threefold. First, we discover two novel phenomena when scaling collaborative filtering models. Second, we gain an understanding of the underlying causes of the double-peak phenomenon. Lastly, we theoretically analyze the noise robustness of collaborative filtering models, with results matching empirical observations.

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

We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the L^q-norm for qin[1,infty] (q=infty corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.

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

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

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.

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.