Daily Papers

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

Robustness and compactness are two essential attributes of deep learning models that are deployed in the real world. The goals of robustness and compactness may seem to be at odds, since robustness requires generalization across domains, while the process of compression exploits specificity in one domain. We introduce Adaptive Sharpness-Aware Pruning (AdaSAP), which unifies these goals through the lens of network sharpness. The AdaSAP method produces sparse networks that are robust to input variations which are unseen at training time. We achieve this by strategically incorporating weight perturbations in order to optimize the loss landscape. This allows the model to be both primed for pruning and regularized for improved robustness. AdaSAP improves the robust accuracy of pruned models on image classification by up to +6% on ImageNet C and +4% on ImageNet V2, and on object detection by +4% on a corrupted Pascal VOC dataset, over a wide range of compression ratios, pruning criteria, and network architectures, outperforming recent pruning art by large margins.

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

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.

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

Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily focus on how to search feature interaction in a coarse-grained space, less attention has been given to a finer granularity. In this work, we introduce a hybrid-grained feature interaction selection approach that targets both feature field and feature value for deep sparse networks. To explore such expansive space, we propose a decomposed space which is calculated on the fly. We then develop a selection algorithm called OptFeature, which efficiently selects the feature interaction from both the feature field and the feature value simultaneously. Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

Historically, the pursuit of efficient inference has been one of the driving forces behind research into new deep learning architectures and building blocks. Some recent examples include: the squeeze-and-excitation module, depthwise separable convolutions in Xception, and the inverted bottleneck in MobileNet v2. Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new, the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly, which we open-source for the benefit of the community as part of the XNNPACK library. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1, MobileNet v2 and EfficientNet architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by 1.3-2.4times -- equivalent to approximately one entire generation of MobileNet-family improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures.

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.

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.

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.

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

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

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

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.

Neurons in large language models often exhibit polysemanticity, simultaneously encoding multiple unrelated concepts and obscuring interpretability. Instead of relying on post-hoc methods, we present MoE-X, a Mixture-of-Experts (MoE) language model designed to be intrinsically interpretable. Our approach is motivated by the observation that, in language models, wider networks with sparse activations are more likely to capture interpretable factors. However, directly training such large sparse networks is computationally prohibitive. MoE architectures offer a scalable alternative by activating only a subset of experts for any given input, inherently aligning with interpretability objectives. In MoE-X, we establish this connection by rewriting the MoE layer as an equivalent sparse, large MLP. This approach enables efficient scaling of the hidden size while maintaining sparsity. To further enhance interpretability, we enforce sparse activation within each expert and redesign the routing mechanism to prioritize experts with the highest activation sparsity. These designs ensure that only the most salient features are routed and processed by the experts. We evaluate MoE-X on chess and natural language tasks, showing that it achieves performance comparable to dense models while significantly improving interpretability. MoE-X achieves a perplexity better than GPT-2, with interpretability surpassing even sparse autoencoder (SAE)-based approaches.

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.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

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

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.

Training a unified multilingual model promotes knowledge transfer but inevitably introduces negative interference. Language-specific modeling methods show promise in reducing interference. However, they often rely on heuristics to distribute capacity and struggle to foster cross-lingual transfer via isolated modules. In this paper, we explore intrinsic task modularity within multilingual networks and leverage these observations to circumvent interference under multilingual translation. We show that neurons in the feed-forward layers tend to be activated in a language-specific manner. Meanwhile, these specialized neurons exhibit structural overlaps that reflect language proximity, which progress across layers. Based on these findings, we propose Neuron Specialization, an approach that identifies specialized neurons to modularize feed-forward layers and then continuously updates them through sparse networks. Extensive experiments show that our approach achieves consistent performance gains over strong baselines with additional analyses demonstrating reduced interference and increased knowledge transfer.

We identify and overcome two key obstacles in extending the success of BERT-style pre-training, or the masked image modeling, to convolutional networks (convnets): (i) convolution operation cannot handle irregular, random-masked input images; (ii) the single-scale nature of BERT pre-training is inconsistent with convnet's hierarchical structure. For (i), we treat unmasked pixels as sparse voxels of 3D point clouds and use sparse convolution to encode. This is the first use of sparse convolution for 2D masked modeling. For (ii), we develop a hierarchical decoder to reconstruct images from multi-scale encoded features. Our method called Sparse masKed modeling (SparK) is general: it can be used directly on any convolutional model without backbone modifications. We validate it on both classical (ResNet) and modern (ConvNeXt) models: on three downstream tasks, it surpasses both state-of-the-art contrastive learning and transformer-based masked modeling by similarly large margins (around +1.0%). Improvements on object detection and instance segmentation are more substantial (up to +3.5%), verifying the strong transferability of features learned. We also find its favorable scaling behavior by observing more gains on larger models. All this evidence reveals a promising future of generative pre-training on convnets. Codes and models are released at https://github.com/keyu-tian/SparK.

Non-uniformed 3D sparse data, e.g., point clouds or voxels in different spatial positions, make contribution to the task of 3D object detection in different ways. Existing basic components in sparse convolutional networks (Sparse CNNs) process all sparse data, regardless of regular or submanifold sparse convolution. In this paper, we introduce two new modules to enhance the capability of Sparse CNNs, both are based on making feature sparsity learnable with position-wise importance prediction. They are focal sparse convolution (Focals Conv) and its multi-modal variant of focal sparse convolution with fusion, or Focals Conv-F for short. The new modules can readily substitute their plain counterparts in existing Sparse CNNs and be jointly trained in an end-to-end fashion. For the first time, we show that spatially learnable sparsity in sparse convolution is essential for sophisticated 3D object detection. Extensive experiments on the KITTI, nuScenes and Waymo benchmarks validate the effectiveness of our approach. Without bells and whistles, our results outperform all existing single-model entries on the nuScenes test benchmark at the paper submission time. Code and models are at https://github.com/dvlab-research/FocalsConv.

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.

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.

LOBSTER (LOss-Based SensiTivity rEgulaRization) is a method for training neural networks having a sparse topology. Let the sensitivity of a network parameter be the variation of the loss function with respect to the variation of the parameter. Parameters with low sensitivity, i.e. having little impact on the loss when perturbed, are shrunk and then pruned to sparsify the network. Our method allows to train a network from scratch, i.e. without preliminary learning or rewinding. Experiments on multiple architectures and datasets show competitive compression ratios with minimal computational overhead.

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.

Finding human-understandable circuits in language models is a central goal of the field of mechanistic interpretability. We train models to have more understandable circuits by constraining most of their weights to be zeros, so that each neuron only has a few connections. To recover fine-grained circuits underlying each of several hand-crafted tasks, we prune the models to isolate the part responsible for the task. These circuits often contain neurons and residual channels that correspond to natural concepts, with a small number of straightforwardly interpretable connections between them. We study how these models scale and find that making weights sparser trades off capability for interpretability, and scaling model size improves the capability-interpretability frontier. However, scaling sparse models beyond tens of millions of nonzero parameters while preserving interpretability remains a challenge. In addition to training weight-sparse models de novo, we show preliminary results suggesting our method can also be adapted to explain existing dense models. Our work produces circuits that achieve an unprecedented level of human understandability and validates them with considerable rigor.

High-fidelity 3D object synthesis remains significantly more challenging than 2D image generation due to the unstructured nature of mesh data and the cubic complexity of dense volumetric grids. Existing two-stage pipelines-compressing meshes with a VAE (using either 2D or 3D supervision), followed by latent diffusion sampling-often suffer from severe detail loss caused by inefficient representations and modality mismatches introduced in VAE. We introduce Sparc3D, a unified framework that combines a sparse deformable marching cubes representation Sparcubes with a novel encoder Sparconv-VAE. Sparcubes converts raw meshes into high-resolution (1024^3) surfaces with arbitrary topology by scattering signed distance and deformation fields onto a sparse cube, allowing differentiable optimization. Sparconv-VAE is the first modality-consistent variational autoencoder built entirely upon sparse convolutional networks, enabling efficient and near-lossless 3D reconstruction suitable for high-resolution generative modeling through latent diffusion. Sparc3D achieves state-of-the-art reconstruction fidelity on challenging inputs, including open surfaces, disconnected components, and intricate geometry. It preserves fine-grained shape details, reduces training and inference cost, and integrates naturally with latent diffusion models for scalable, high-resolution 3D generation.

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

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better uncertainty quantification. For the success of BNN, search an appropriate architecture of the neural networks is an important task, and various algorithms to find good sparse neural networks have been proposed. In this paper, we propose a new node-sparse BNN model which has good theoretical properties and is computationally feasible. We prove that the posterior concentration rate to the true model is near minimax optimal and adaptive to the smoothness of the true model. In particular the adaptiveness is the first of its kind for node-sparse BNNs. In addition, we develop a novel MCMC algorithm which makes the Bayesian inference of the node-sparse BNN model feasible in practice.

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.

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

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.

Distributed Acoustic Sensing (DAS) is an emerging technology for earthquake monitoring and subsurface imaging. The recorded seismic signals by DAS have several distinct characteristics, such as unknown coupling effects, strong anthropogenic noise, and ultra-dense spatial sampling. These aspects differ from conventional seismic data recorded by seismic networks, making it challenging to utilize DAS at present for seismic monitoring. New data analysis algorithms are needed to extract useful information from DAS data. Previous studies on conventional seismic data demonstrated that deep learning models could achieve performance close to human analysts in picking seismic phases. However, phase picking on DAS data is still a difficult problem due to the lack of manual labels. Further, the differences in mathematical structure between these two data formats, i.e., ultra-dense DAS arrays and sparse seismic networks, make model fine-tuning or transfer learning difficult to implement on DAS data. In this work, we design a new approach using semi-supervised learning to solve the phase-picking task on DAS arrays. We use a pre-trained PhaseNet model as a teacher network to generate noisy labels of P and S arrivals on DAS data and apply the Gaussian mixture model phase association (GaMMA) method to refine these noisy labels to build training datasets. We develop a new deep learning model, PhaseNet-DAS, to process the 2D spatial-temporal data of DAS arrays and train the model on DAS data. The new deep learning model achieves high picking accuracy and good earthquake detection performance. We then apply the model to process continuous data and build earthquake catalogs directly from DAS recording. Our approach using semi-supervised learning provides a way to build effective deep learning models for DAS, which have the potential to improve earthquake monitoring using large-scale fiber networks.

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

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

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

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

Transfer learning is a classic paradigm by which models pretrained on large "upstream" datasets are adapted to yield good results on "downstream" specialized datasets. Generally, more accurate models on the "upstream" dataset tend to provide better transfer accuracy "downstream". In this work, we perform an in-depth investigation of this phenomenon in the context of convolutional neural networks (CNNs) trained on the ImageNet dataset, which have been pruned - that is, compressed by sparsifying their connections. We consider transfer using unstructured pruned models obtained by applying several state-of-the-art pruning methods, including magnitude-based, second-order, re-growth, lottery-ticket, and regularization approaches, in the context of twelve standard transfer tasks. In a nutshell, our study shows that sparse models can match or even outperform the transfer performance of dense models, even at high sparsities, and, while doing so, can lead to significant inference and even training speedups. At the same time, we observe and analyze significant differences in the behaviour of different pruning methods.

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

This paper investigates the impact of loss function selection in deep unfolding techniques for sparse signal recovery algorithms. Deep unfolding transforms iterative optimization algorithms into trainable lightweight neural networks by unfolding their iterations as network layers, with various loss functions employed for parameter learning depending on application contexts. We focus on deep unfolded versions of the fundamental iterative shrinkage thresholding algorithm (ISTA) and the iterative hard thresholding algorithm (IHT), comparing supervised learning using mean squared error with unsupervised learning using the objective function of the original optimization problem. Our simulation results reveal that the effect of the choice of loss function significantly depends on the convexity of the optimization problem. For convex ell_1-regularized problems, supervised-ISTA achieves better final recovery accuracy but fails to minimize the original objective function, whereas we empirically observe that unsupervised-ISTA converges to a nearly identical solution as conventional ISTA but with accelerated convergence. Conversely, for nonconvex ell_0-regularized problems, both supervised-IHT and unsupervised-IHT converge to better local minima than the original IHT, showing similar performance regardless of the loss function employed. These findings provide valuable insights into the design of effective deep unfolded networks for sparse signal recovery applications.

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

We introduce DLSIA (Deep Learning for Scientific Image Analysis), a Python-based machine learning library that empowers scientists and researchers across diverse scientific domains with a range of customizable convolutional neural network (CNN) architectures for a wide variety of tasks in image analysis to be used in downstream data processing, or for experiment-in-the-loop computing scenarios. DLSIA features easy-to-use architectures such as autoencoders, tunable U-Nets, and parameter-lean mixed-scale dense networks (MSDNets). Additionally, we introduce sparse mixed-scale networks (SMSNets), generated using random graphs and sparse connections. As experimental data continues to grow in scale and complexity, DLSIA provides accessible CNN construction and abstracts CNN complexities, allowing scientists to tailor their machine learning approaches, accelerate discoveries, foster interdisciplinary collaboration, and advance research in scientific image analysis.

While frontier large language models (LLMs) continue to push capability boundaries, their deployment remains confined to GPU-powered cloud infrastructure. We challenge this paradigm with SmallThinker, a family of LLMs natively designed - not adapted - for the unique constraints of local devices: weak computational power, limited memory, and slow storage. Unlike traditional approaches that mainly compress existing models built for clouds, we architect SmallThinker from the ground up to thrive within these limitations. Our innovation lies in a deployment-aware architecture that transforms constraints into design principles. First, We introduce a two-level sparse structure combining fine-grained Mixture-of-Experts (MoE) with sparse feed-forward networks, drastically reducing computational demands without sacrificing model capacity. Second, to conquer the I/O bottleneck of slow storage, we design a pre-attention router that enables our co-designed inference engine to prefetch expert parameters from storage while computing attention, effectively hiding storage latency that would otherwise cripple on-device inference. Third, for memory efficiency, we utilize NoPE-RoPE hybrid sparse attention mechanism to slash KV cache requirements. We release SmallThinker-4B-A0.6B and SmallThinker-21B-A3B, which achieve state-of-the-art performance scores and even outperform larger LLMs. Remarkably, our co-designed system mostly eliminates the need for expensive GPU hardware: with Q4_0 quantization, both models exceed 20 tokens/s on ordinary consumer CPUs, while consuming only 1GB and 8GB of memory respectively. SmallThinker is publicly available at hf.co/PowerInfer/SmallThinker-4BA0.6B-Instruct and hf.co/PowerInfer/SmallThinker-21BA3B-Instruct.

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

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by quantizing their continuous features into what we call codebook features. Codebook features are produced by finetuning neural networks with vector quantization bottlenecks at each layer, producing a network whose hidden features are the sum of a small number of discrete vector codes chosen from a larger codebook. Surprisingly, we find that neural networks can operate under this extreme bottleneck with only modest degradation in performance. This sparse, discrete bottleneck also provides an intuitive way of controlling neural network behavior: first, find codes that activate when the desired behavior is present, then activate those same codes during generation to elicit that behavior. We validate our approach by training codebook Transformers on several different datasets. First, we explore a finite state machine dataset with far more hidden states than neurons. In this setting, our approach overcomes the superposition problem by assigning states to distinct codes, and we find that we can make the neural network behave as if it is in a different state by activating the code for that state. Second, we train Transformer language models with up to 410M parameters on two natural language datasets. We identify codes in these models representing diverse, disentangled concepts (ranging from negative emotions to months of the year) and find that we can guide the model to generate different topics by activating the appropriate codes during inference. Overall, codebook features appear to be a promising unit of analysis and control for neural networks and interpretability. Our codebase and models are open-sourced at https://github.com/taufeeque9/codebook-features.

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.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.

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

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

Explaining the predictions of deep neural nets has been a topic of great interest in the computer vision literature. While several gradient-based interpretation schemes have been proposed to reveal the influential variables in a neural net's prediction, standard gradient-based interpretation frameworks have been commonly observed to lack robustness to input perturbations and flexibility for incorporating prior knowledge of sparsity and group-sparsity structures. In this work, we propose MoreauGrad as an interpretation scheme based on the classifier neural net's Moreau envelope. We demonstrate that MoreauGrad results in a smooth and robust interpretation of a multi-layer neural network and can be efficiently computed through first-order optimization methods. Furthermore, we show that MoreauGrad can be naturally combined with L_1-norm regularization techniques to output a sparse or group-sparse explanation which are prior conditions applicable to a wide range of deep learning applications. We empirically evaluate the proposed MoreauGrad scheme on standard computer vision datasets, showing the qualitative and quantitative success of the MoreauGrad approach in comparison to standard gradient-based interpretation methods.

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.

Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at eliminating some parameters with tolerable performance degradation. In this paper, we propose a novel momentum-SGD-based optimization method to reduce the network complexity by on-the-fly pruning. Concretely, given a global compression ratio, we categorize all the parameters into two parts at each training iteration which are updated using different rules. In this way, we gradually zero out the redundant parameters, as we update them using only the ordinary weight decay but no gradients derived from the objective function. As a departure from prior methods that require heavy human works to tune the layer-wise sparsity ratios, prune by solving complicated non-differentiable problems or finetune the model after pruning, our method is characterized by 1) global compression that automatically finds the appropriate per-layer sparsity ratios; 2) end-to-end training; 3) no need for a time-consuming re-training process after pruning; and 4) superior capability to find better winning tickets which have won the initialization lottery.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state-of-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary experience is that the sparse architectures produced by pruning are difficult to train from the start, which would similarly improve training performance. We find that a standard pruning technique naturally uncovers subnetworks whose initializations made them capable of training effectively. Based on these results, we articulate the "lottery ticket hypothesis:" dense, randomly-initialized, feed-forward networks contain subnetworks ("winning tickets") that - when trained in isolation - reach test accuracy comparable to the original network in a similar number of iterations. The winning tickets we find have won the initialization lottery: their connections have initial weights that make training particularly effective. We present an algorithm to identify winning tickets and a series of experiments that support the lottery ticket hypothesis and the importance of these fortuitous initializations. We consistently find winning tickets that are less than 10-20% of the size of several fully-connected and convolutional feed-forward architectures for MNIST and CIFAR10. Above this size, the winning tickets that we find learn faster than the original network and reach higher test accuracy.

We present an approach to tackle the speaker recognition problem using Triplet Neural Networks. Currently, the i-vector representation with probabilistic linear discriminant analysis (PLDA) is the most commonly used technique to solve this problem, due to high classification accuracy with a relatively short computation time. In this paper, we explore a neural network approach, namely Triplet Neural Networks (TNNs), to built a latent space for different classifiers to solve the Multi-Target Speaker Detection and Identification Challenge Evaluation 2018 (MCE 2018) dataset. This training set contains i-vectors from 3,631 speakers, with only 3 samples for each speaker, thus making speaker recognition a challenging task. When using the train and development set for training both the TNN and baseline model (i.e., similarity evaluation directly on the i-vector representation), our proposed model outperforms the baseline by 23%. When reducing the training data to only using the train set, our method results in 309 confusions for the Multi-target speaker identification task, which is 46% better than the baseline model. These results show that the representational power of TNNs is especially evident when training on small datasets with few instances available per class.

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

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.

Having precise perception of the environment is crucial for ensuring the secure and reliable functioning of autonomous driving systems. Radar object detection networks are one fundamental part of such systems. CNN-based object detectors showed good performance in this context, but they require large compute resources. This paper investigates sparse convolutional object detection networks, which combine powerful grid-based detection with low compute resources. We investigate radar specific challenges and propose sparse kernel point pillars (SKPP) and dual voxel point convolutions (DVPC) as remedies for the grid rendering and sparse backbone architectures. We evaluate our SKPP-DPVCN architecture on nuScenes, which outperforms the baseline by 5.89% and the previous state of the art by 4.19% in Car AP4.0. Moreover, SKPP-DPVCN reduces the average scale error (ASE) by 21.41% over the baseline.

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

Deep learning has revolutionized medical imaging, but its effectiveness is severely limited by insufficient labeled training data. This paper introduces a novel GAN-based semi-supervised learning framework specifically designed for low labeled-data regimes, evaluated across settings with 5 to 50 labeled samples per class. Our approach integrates three specialized neural networks -- a generator for class-conditioned image translation, a discriminator for authenticity assessment and classification, and a dedicated classifier -- within a three-phase training framework. The method alternates between supervised training on limited labeled data and unsupervised learning that leverages abundant unlabeled images through image-to-image translation rather than generation from noise. We employ ensemble-based pseudo-labeling that combines confidence-weighted predictions from the discriminator and classifier with temporal consistency through exponential moving averaging, enabling reliable label estimation for unlabeled data. Comprehensive evaluation across eleven MedMNIST datasets demonstrates that our approach achieves statistically significant improvements over six state-of-the-art GAN-based semi-supervised methods, with particularly strong performance in the extreme 5-shot setting where the scarcity of labeled data is most challenging. The framework maintains its superiority across all evaluated settings (5, 10, 20, and 50 shots per class). Our approach offers a practical solution for medical imaging applications where annotation costs are prohibitive, enabling robust classification performance even with minimal labeled data. Code is available at https://github.com/GuidoManni/SPARSE.

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

Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet we lack principled methods to measure superposition. We present an information-theoretic framework measuring a neural representation's effective degrees of freedom. We apply Shannon entropy to sparse autoencoder activations to compute the number of effective features as the minimum neurons needed for interference-free encoding. Equivalently, this measures how many "virtual neurons" the network simulates through superposition. When networks encode more effective features than actual neurons, they must accept interference as the price of compression. Our metric strongly correlates with ground truth in toy models, detects minimal superposition in algorithmic tasks, and reveals systematic reduction under dropout. Layer-wise patterns mirror intrinsic dimensionality studies on Pythia-70M. The metric also captures developmental dynamics, detecting sharp feature consolidation during grokking. Surprisingly, adversarial training can increase effective features while improving robustness, contradicting the hypothesis that superposition causes vulnerability. Instead, the effect depends on task complexity and network capacity: simple tasks with ample capacity allow feature expansion (abundance regime), while complex tasks or limited capacity force reduction (scarcity regime). By defining superposition as lossy compression, this work enables principled measurement of how neural networks organize information under computational constraints, connecting superposition to adversarial robustness.

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

We frame the problem of unifying representations in neural models as one of sparse model recovery and introduce a framework that extends sparse autoencoders (SAEs) to lifted spaces and infinite-dimensional function spaces, enabling mechanistic interpretability of large neural operators (NO). While the Platonic Representation Hypothesis suggests that neural networks converge to similar representations across architectures, the representational properties of neural operators remain underexplored despite their growing importance in scientific computing. We compare the inference and training dynamics of SAEs, lifted-SAE, and SAE neural operators. We highlight how lifting and operator modules introduce beneficial inductive biases, enabling faster recovery, improved recovery of smooth concepts, and robust inference across varying resolutions, a property unique to neural operators.

This study addresses the challenge of inaccurate gradients in computing the empirical Fisher Information Matrix during neural network pruning. We introduce SWAP, a formulation of Entropic Wasserstein regression (EWR) for pruning, capitalizing on the geometric properties of the optimal transport problem. The ``swap'' of the commonly used linear regression with the EWR in optimization is analytically demonstrated to offer noise mitigation effects by incorporating neighborhood interpolation across data points with only marginal additional computational cost. The unique strength of SWAP is its intrinsic ability to balance noise reduction and covariance information preservation effectively. Extensive experiments performed on various networks and datasets show comparable performance of SWAP with state-of-the-art (SoTA) network pruning algorithms. Our proposed method outperforms the SoTA when the network size or the target sparsity is large, the gain is even larger with the existence of noisy gradients, possibly from noisy data, analog memory, or adversarial attacks. Notably, our proposed method achieves a gain of 6% improvement in accuracy and 8% improvement in testing loss for MobileNetV1 with less than one-fourth of the network parameters remaining.

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.

Human visual recognition is a sparse process, where only a few salient visual cues are attended to rather than traversing every detail uniformly. However, most current vision networks follow a dense paradigm, processing every single visual unit (e.g,, pixel or patch) in a uniform manner. In this paper, we challenge this dense paradigm and present a new method, coined SparseFormer, to imitate human's sparse visual recognition in an end-to-end manner. SparseFormer learns to represent images using a highly limited number of tokens (down to 49) in the latent space with sparse feature sampling procedure instead of processing dense units in the original pixel space. Therefore, SparseFormer circumvents most of dense operations on the image space and has much lower computational costs. Experiments on the ImageNet classification benchmark dataset show that SparseFormer achieves performance on par with canonical or well-established models while offering better accuracy-throughput tradeoff. Moreover, the design of our network can be easily extended to the video classification with promising performance at lower computational costs. We hope that our work can provide an alternative way for visual modeling and inspire further research on sparse neural architectures. The code will be publicly available at https://github.com/showlab/sparseformer

Deep learning approaches have demonstrated success in modeling analog audio effects. Nevertheless, challenges remain in modeling more complex effects that involve time-varying nonlinear elements, such as dynamic range compressors. Existing neural network approaches for modeling compression either ignore the device parameters, do not attain sufficient accuracy, or otherwise require large noncausal models prohibiting real-time operation. In this work, we propose a modification to temporal convolutional networks (TCNs) enabling greater efficiency without sacrificing performance. By utilizing very sparse convolutional kernels through rapidly growing dilations, our model attains a significant receptive field using fewer layers, reducing computation. Through a detailed evaluation we demonstrate our efficient and causal approach achieves state-of-the-art performance in modeling the analog LA-2A, is capable of real-time operation on CPU, and only requires 10 minutes of training data.

One of the roadblocks to a better understanding of neural networks' internals is polysemanticity, where neurons appear to activate in multiple, semantically distinct contexts. Polysemanticity prevents us from identifying concise, human-understandable explanations for what neural networks are doing internally. One hypothesised cause of polysemanticity is superposition, where neural networks represent more features than they have neurons by assigning features to an overcomplete set of directions in activation space, rather than to individual neurons. Here, we attempt to identify those directions, using sparse autoencoders to reconstruct the internal activations of a language model. These autoencoders learn sets of sparsely activating features that are more interpretable and monosemantic than directions identified by alternative approaches, where interpretability is measured by automated methods. Ablating these features enables precise model editing, for example, by removing capabilities such as pronoun prediction, while disrupting model behaviour less than prior techniques. This work indicates that it is possible to resolve superposition in language models using a scalable, unsupervised method. Our method may serve as a foundation for future mechanistic interpretability work, which we hope will enable greater model transparency and steerability.

How to reduce compute and memory requirements of neural networks (NNs) without sacrificing performance? Many recent works use sparse Mixtures of Experts (MoEs) to build resource-efficient large language models (LMs). Here we introduce several novel perspectives on MoEs, presenting a general framework that unifies various methods to approximate two-layer NNs (e.g., feedforward blocks of Transformers), including product-key memories (PKMs). Leveraging insights from this framework, we propose methods to improve both MoEs and PKMs. Unlike prior work that compares MoEs with dense baselines under the compute-equal condition, our evaluation condition is parameter-equal, which is crucial to properly evaluate LMs. We show that our MoEs are competitive with the dense Transformer-XL on both the WikiText-103 and enwiki8 datasets at two different scales, while being much more resource efficient. This demonstrates that MoEs are relevant not only to extremely large LMs but also to any-scale resource-efficient LMs. Our code is public.

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

Sparsely-gated Mixture of Experts networks (MoEs) have demonstrated excellent scalability in Natural Language Processing. In Computer Vision, however, almost all performant networks are "dense", that is, every input is processed by every parameter. We present a Vision MoE (V-MoE), a sparse version of the Vision Transformer, that is scalable and competitive with the largest dense networks. When applied to image recognition, V-MoE matches the performance of state-of-the-art networks, while requiring as little as half of the compute at inference time. Further, we propose an extension to the routing algorithm that can prioritize subsets of each input across the entire batch, leading to adaptive per-image compute. This allows V-MoE to trade-off performance and compute smoothly at test-time. Finally, we demonstrate the potential of V-MoE to scale vision models, and train a 15B parameter model that attains 90.35% on ImageNet.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

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.

Spiking Neural Networks (SNNs) provide an energy-efficient way to extract 3D spatio-temporal features. Point clouds are sparse 3D spatial data, which suggests that SNNs should be well-suited for processing them. However, when applying SNNs to point clouds, they often exhibit limited performance and fewer application scenarios. We attribute this to inappropriate preprocessing and feature extraction methods. To address this issue, we first introduce the Spike Voxel Coding (SVC) scheme, which encodes the 3D point clouds into a sparse spike train space, reducing the storage requirements and saving time on point cloud preprocessing. Then, we propose a Spike Sparse Convolution (SSC) model for efficiently extracting 3D sparse point cloud features. Combining SVC and SSC, we design an efficient 3D SNN backbone (E-3DSNN), which is friendly with neuromorphic hardware. For instance, SSC can be implemented on neuromorphic chips with only minor modifications to the addressing function of vanilla spike convolution. Experiments on ModelNet40, KITTI, and Semantic KITTI datasets demonstrate that E-3DSNN achieves state-of-the-art (SOTA) results with remarkable efficiency. Notably, our E-3DSNN (1.87M) obtained 91.7\% top-1 accuracy on ModelNet40, surpassing the current best SNN baselines (14.3M) by 3.0\%. To our best knowledge, it is the first direct training 3D SNN backbone that can simultaneously handle various 3D computer vision tasks (e.g., classification, detection, and segmentation) with an event-driven nature. Code is available: https://github.com/bollossom/E-3DSNN/.

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.

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

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.

Sparse Autoencoders (SAEs) can efficiently identify candidate monosemantic features from pretrained neural networks for galaxy morphology. We demonstrate this on Euclid Q1 images using both supervised (Zoobot) and new self-supervised (MAE) models. Our publicly released MAE achieves superhuman image reconstruction performance. While a Principal Component Analysis (PCA) on the supervised model primarily identifies features already aligned with the Galaxy Zoo decision tree, SAEs can identify interpretable features outside of this framework. SAE features also show stronger alignment than PCA with Galaxy Zoo labels. Although challenges in interpretability remain, SAEs provide a powerful engine for discovering astrophysical phenomena beyond the confines of human-defined classification.

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.

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

Shift operation is an efficient alternative over depthwise separable convolution. However, it is still bottlenecked by its implementation manner, namely memory movement. To put this direction forward, a new and novel basic component named Sparse Shift Layer (SSL) is introduced in this paper to construct efficient convolutional neural networks. In this family of architectures, the basic block is only composed by 1x1 convolutional layers with only a few shift operations applied to the intermediate feature maps. To make this idea feasible, we introduce shift operation penalty during optimization and further propose a quantization-aware shift learning method to impose the learned displacement more friendly for inference. Extensive ablation studies indicate that only a few shift operations are sufficient to provide spatial information communication. Furthermore, to maximize the role of SSL, we redesign an improved network architecture to Fully Exploit the limited capacity of neural Network (FE-Net). Equipped with SSL, this network can achieve 75.0% top-1 accuracy on ImageNet with only 563M M-Adds. It surpasses other counterparts constructed by depthwise separable convolution and the networks searched by NAS in terms of accuracy and practical speed.

It is widely acknowledged that the performance of Transformer models is exponentially related to their number of parameters and computational complexity. While approaches like Mixture of Experts (MoE) decouple parameter count from computational complexity, they still face challenges in inference due to high memory access costs. This work introduces UltraMem, incorporating large-scale, ultra-sparse memory layer to address these limitations. Our approach significantly reduces inference latency while maintaining model performance. We also investigate the scaling laws of this new architecture, demonstrating that it not only exhibits favorable scaling properties but outperforms traditional models. In our experiments, we train networks with up to 20 million memory slots. The results show that our method achieves state-of-the-art inference speed and model performance within a given computational budget.

The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice, however, there are significant algorithmic and performance challenges. In this work, we address these challenges and finally realize the promise of conditional computation, achieving greater than 1000x improvements in model capacity with only minor losses in computational efficiency on modern GPU clusters. We introduce a Sparsely-Gated Mixture-of-Experts layer (MoE), consisting of up to thousands of feed-forward sub-networks. A trainable gating network determines a sparse combination of these experts to use for each example. We apply the MoE to the tasks of language modeling and machine translation, where model capacity is critical for absorbing the vast quantities of knowledge available in the training corpora. We present model architectures in which a MoE with up to 137 billion parameters is applied convolutionally between stacked LSTM layers. On large language modeling and machine translation benchmarks, these models achieve significantly better results than state-of-the-art at lower computational cost.

Learning predictive models from observations using deep neural networks (DNNs) is a promising new approach to many real-world planning and control problems. However, common DNNs are too unstructured for effective planning, and current control methods typically rely on extensive sampling or local gradient descent. In this paper, we propose a new framework for integrated model learning and predictive control that is amenable to efficient optimization algorithms. Specifically, we start with a ReLU neural model of the system dynamics and, with minimal losses in prediction accuracy, we gradually sparsify it by removing redundant neurons. This discrete sparsification process is approximated as a continuous problem, enabling an end-to-end optimization of both the model architecture and the weight parameters. The sparsified model is subsequently used by a mixed-integer predictive controller, which represents the neuron activations as binary variables and employs efficient branch-and-bound algorithms. Our framework is applicable to a wide variety of DNNs, from simple multilayer perceptrons to complex graph neural dynamics. It can efficiently handle tasks involving complicated contact dynamics, such as object pushing, compositional object sorting, and manipulation of deformable objects. Numerical and hardware experiments show that, despite the aggressive sparsification, our framework can deliver better closed-loop performance than existing state-of-the-art methods.

Image quality is a critical factor in delivering visually appealing content on web platforms. However, images often suffer from degradation due to lossy operations applied by online social networks (OSNs), negatively affecting user experience. Image restoration is the process of recovering a clean high-quality image from a given degraded input. Recently, multi-task (all-in-one) image restoration models have gained significant attention, due to their ability to simultaneously handle different types of image degradations. However, these models often come with an excessively high number of trainable parameters, making them computationally inefficient. In this paper, we propose a strategy for compressing multi-task image restoration models. We aim to discover highly sparse subnetworks within overparameterized deep models that can match or even surpass the performance of their dense counterparts. The proposed model, namely MIR-L, utilizes an iterative pruning strategy that removes low-magnitude weights across multiple rounds, while resetting the remaining weights to their original initialization. This iterative process is important for the multi-task image restoration model's optimization, effectively uncovering "winning tickets" that maintain or exceed state-of-the-art performance at high sparsity levels. Experimental evaluation on benchmark datasets for the deraining, dehazing, and denoising tasks shows that MIR-L retains only 10% of the trainable parameters while maintaining high image restoration performance. Our code, datasets and pre-trained models are made publicly available at https://github.com/Thomkat/MIR-L.

AI led chess systems to a superhuman level, yet these systems heavily rely on black-box algorithms. This is unsustainable in ensuring transparency to the end-user, particularly when these systems are responsible for sensitive decision-making. Recent interpretability work has shown that the inner representations of Deep Neural Networks (DNNs) were fathomable and contained human-understandable concepts. Yet, these methods are seldom contextualised and are often based on a single hidden state, which makes them unable to interpret multi-step reasoning, e.g. planning. In this respect, we propose contrastive sparse autoencoders (CSAE), a novel framework for studying pairs of game trajectories. Using CSAE, we are able to extract and interpret concepts that are meaningful to the chess-agent plans. We primarily focused on a qualitative analysis of the CSAE features before proposing an automated feature taxonomy. Furthermore, to evaluate the quality of our trained CSAE, we devise sanity checks to wave spurious correlations in our results.

Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and expressiveness of PCs. However, PC training performance plateaus as model size increases. We discover that most capacity in existing large PC structures is wasted: fully-connected parameter layers are only sparsely used. We propose two operations: pruning and growing, that exploit the sparsity of PC structures. Specifically, the pruning operation removes unimportant sub-networks of the PC for model compression and comes with theoretical guarantees. The growing operation increases model capacity by increasing the size of the latent space. By alternatingly applying pruning and growing, we increase the capacity that is meaningfully used, allowing us to significantly scale up PC learning. Empirically, our learner achieves state-of-the-art likelihoods on MNIST-family image datasets and on Penn Tree Bank language data compared to other PC learners and less tractable deep generative models such as flow-based models and variational autoencoders (VAEs).

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.

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

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.

Recovering camera poses from a set of images is a foundational task in 3D computer vision, which powers key applications such as 3D scene/object reconstructions. Classic methods often depend on feature correspondence, such as keypoints, which require the input images to have large overlap and small viewpoint changes. Such requirements present considerable challenges in scenarios with sparse views. Recent data-driven approaches aim to directly output camera poses, either through regressing the 6DoF camera poses or formulating rotation as a probability distribution. However, each approach has its limitations. On one hand, directly regressing the camera poses can be ill-posed, since it assumes a single mode, which is not true under symmetry and leads to sub-optimal solutions. On the other hand, probabilistic approaches are capable of modeling the symmetry ambiguity, yet they sample the entire space of rotation uniformly by brute-force. This leads to an inevitable trade-off between high sample density, which improves model precision, and sample efficiency that determines the runtime. In this paper, we propose ADen to unify the two frameworks by employing a generator and a discriminator: the generator is trained to output multiple hypotheses of 6DoF camera pose to represent a distribution and handle multi-mode ambiguity, and the discriminator is trained to identify the hypothesis that best explains the data. This allows ADen to combine the best of both worlds, achieving substantially higher precision as well as lower runtime than previous methods in empirical evaluations.

Self-supervised learning (SSL) has become an important approach in pretraining large neural networks, enabling unprecedented scaling of model and dataset sizes. While recent advances like I-JEPA have shown promising results for Vision Transformers, adapting such methods to Convolutional Neural Networks (CNNs) presents unique challenges. In this paper, we introduce CNN-JEPA, a novel SSL method that successfully applies the joint embedding predictive architecture approach to CNNs. Our method incorporates a sparse CNN encoder to handle masked inputs, a fully convolutional predictor using depthwise separable convolutions, and an improved masking strategy. We demonstrate that CNN-JEPA outperforms I-JEPA with ViT architectures on ImageNet-100, achieving a 73.3% linear top-1 accuracy using a standard ResNet-50 encoder. Compared to other CNN-based SSL methods, CNN-JEPA requires 17-35% less training time for the same number of epochs and approaches the linear and k-NN top-1 accuracies of BYOL, SimCLR, and VICReg. Our approach offers a simpler, more efficient alternative to existing SSL methods for CNNs, requiring minimal augmentations and no separate projector network.

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

In recent years, there has been a significant increase in the utilization of deep learning methods, particularly convolutional neural networks (CNNs), which have emerged as the dominant approach in various domains that involve structured grid data, such as picture analysis and processing. Nevertheless, the exponential growth in the utilization of LiDAR and 3D sensors across many domains has resulted in an increased need for the analysis of 3D point clouds. The utilization of 3D point clouds is crucial in various applications, including object recognition and segmentation, as they offer a spatial depiction of things within a three-dimensional environment. In contrast to photos, point clouds exhibit sparsity and lack a regular grid, hence posing distinct processing and computational issues.

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.

Sparse autoencoders (SAEs) have shown promise in extracting interpretable features from complex neural networks. We present one of the first applications of SAEs to dense text embeddings from large language models, demonstrating their effectiveness in disentangling semantic concepts. By training SAEs on embeddings of over 420,000 scientific paper abstracts from computer science and astronomy, we show that the resulting sparse representations maintain semantic fidelity while offering interpretability. We analyse these learned features, exploring their behaviour across different model capacities and introducing a novel method for identifying ``feature families'' that represent related concepts at varying levels of abstraction. To demonstrate the practical utility of our approach, we show how these interpretable features can be used to precisely steer semantic search, allowing for fine-grained control over query semantics. This work bridges the gap between the semantic richness of dense embeddings and the interpretability of sparse representations. We open source our embeddings, trained sparse autoencoders, and interpreted features, as well as a web app for exploring them.

Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often relies on discrete steps that optimize the architecture and then train the parameters. We introduce a novel neural network training framework that fundamentally transforms the process by learning architecture and parameters simultaneously with gradient descent. With the appropriate setting of the loss function, it can discover sparse and compact neural networks for given datasets. Central to our approach is a multi-scale encoder-decoder, in which the encoder embeds pairs of neural networks with similar functionalities close to each other (irrespective of their architectures and weights). To train a neural network with a given dataset, we randomly sample a neural network embedding in the embedding space and then perform gradient descent using our custom loss function, which incorporates a sparsity penalty to encourage compactness. The decoder generates a neural network corresponding to the embedding. Experiments demonstrate that our framework can discover sparse and compact neural networks maintaining a high performance.

Information sharing is critical in time-sensitive and realistic multi-robot exploration, especially for smaller robotic teams in large-scale environments where connectivity may be sparse and intermittent. Existing methods often overlook such communication constraints by assuming unrealistic global connectivity. Other works account for communication constraints (by maintaining close proximity or line of sight during information exchange), but are often inefficient. For instance, preplanned rendezvous approaches typically involve unnecessary detours resulting from poorly timed rendezvous, while pursuit-based approaches often result in short-sighted decisions due to their greedy nature. We present IR2, a deep reinforcement learning approach to information sharing for multi-robot exploration. Leveraging attention-based neural networks trained via reinforcement and curriculum learning, IR2 allows robots to effectively reason about the longer-term trade-offs between disconnecting for solo exploration and reconnecting for information sharing. In addition, we propose a hierarchical graph formulation to maintain a sparse yet informative graph, enabling our approach to scale to large-scale environments. We present simulation results in three large-scale Gazebo environments, which show that our approach yields 6.6-34.1% shorter exploration paths when compared to state-of-the-art baselines, and lastly deploy our learned policy on hardware. Our simulation training and testing code is available at https://ir2-explore.github.io.

Catastrophic forgetting remains a significant challenge to continual learning for decades. While recent works have proposed effective methods to mitigate this problem, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse representations and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions, we can significantly improve the resilience of neural networks to catastrophic forgetting. Our method has broad applicability and benefits for continual learning in regression, class incremental learning, and reinforcement learning tasks. Specifically, we achieves excellent performance on Split MNIST dataset in just one single pass, without using replay buffer, task boundary information, or pre-training.

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at https://github.com/Ma-Lab-Berkeley/CRATE.

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.

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.

We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.

Sparse autoencoders (SAEs) bricken2023monosemanticity,gao2024scalingevaluatingsparseautoencoders rely on dictionary learning to extract interpretable features from neural networks at scale in an unsupervised manner, with applications to representation engineering and information retrieval. SAEs are, however, computationally expensive lieberum2024gemmascopeopensparse, especially when multiple SAEs of different sizes are needed. We show that dictionary importance in vanilla SAEs follows a power law. We compare progressive coding based on subset pruning of SAEs -- to jointly training nested SAEs, or so-called {\em Matryoshka} SAEs bussmann2024learning,nabeshima2024Matryoshka -- on a language modeling task. We show Matryoshka SAEs exhibit lower reconstruction loss and recaptured language modeling loss, as well as higher representational similarity. Pruned vanilla SAEs are more interpretable, however. We discuss the origins and implications of this trade-off.

We propose an efficient radiance field rendering algorithm that incorporates a rasterization process on adaptive sparse voxels without neural networks or 3D Gaussians. There are two key contributions coupled with the proposed system. The first is to adaptively and explicitly allocate sparse voxels to different levels of detail within scenes, faithfully reproducing scene details with 65536^3 grid resolution while achieving high rendering frame rates. Second, we customize a rasterizer for efficient adaptive sparse voxels rendering. We render voxels in the correct depth order by using ray direction-dependent Morton ordering, which avoids the well-known popping artifact found in Gaussian splatting. Our method improves the previous neural-free voxel model by over 4db PSNR and more than 10x FPS speedup, achieving state-of-the-art comparable novel-view synthesis results. Additionally, our voxel representation is seamlessly compatible with grid-based 3D processing techniques such as Volume Fusion, Voxel Pooling, and Marching Cubes, enabling a wide range of future extensions and applications.

Training deep neural networks (DNNs) is costly. Fortunately, Nvidia Ampere and Hopper GPUs can accelerate matrix multiplications twice as fast as a dense equivalent by implementing 2:4 sparsity. However, previous STE-based 2:4 pre-training methods (e.g. STE with hard-thresholding, SR-STE) suffer from optimization difficulties because of discontinuous pruning function. In this study, we comprehensively analyse the bottleneck of traditional N:M sparse training and recognize three drawbacks with discontinuity: incorrect descending direction, inability to predict the amount of descent and sparse mask oscillation. In light of this, we propose S-STE, a simple yet powerful 2:4 training method that contains two parts: to continuously project weights to be 2:4 sparse, and to rescale sparse weights with a per-tensor fixed scaling factor. Besides, we adopt minimum-variance unbiased estimation for activation gradient and FP8 quantization for whole process. Results show that our method surpasses previous 2:4 pre-training recipes and is comparable even with full parameter models. Our toolkit is available at https://github.com/huyz2023/2by4-pretrain.

Spiking Neural Networks (SNNs) are well known as a promising energy-efficient alternative to conventional artificial neural networks. Subject to the preconceived impression that SNNs are sparse firing, the analysis and optimization of inherent redundancy in SNNs have been largely overlooked, thus the potential advantages of spike-based neuromorphic computing in accuracy and energy efficiency are interfered. In this work, we pose and focus on three key questions regarding the inherent redundancy in SNNs. We argue that the redundancy is induced by the spatio-temporal invariance of SNNs, which enhances the efficiency of parameter utilization but also invites lots of noise spikes. Further, we analyze the effect of spatio-temporal invariance on the spatio-temporal dynamics and spike firing of SNNs. Then, motivated by these analyses, we propose an Advance Spatial Attention (ASA) module to harness SNNs' redundancy, which can adaptively optimize their membrane potential distribution by a pair of individual spatial attention sub-modules. In this way, noise spike features are accurately regulated. Experimental results demonstrate that the proposed method can significantly drop the spike firing with better performance than state-of-the-art SNN baselines. Our code is available in https://github.com/BICLab/ASA-SNN.

Traditionally, convolutional neural networks (CNN) and vision transformers (ViT) have dominated computer vision. However, recently proposed vision graph neural networks (ViG) provide a new avenue for exploration. Unfortunately, for mobile applications, ViGs are computationally expensive due to the overhead of representing images as graph structures. In this work, we propose a new graph-based sparse attention mechanism, Sparse Vision Graph Attention (SVGA), that is designed for ViGs running on mobile devices. Additionally, we propose the first hybrid CNN-GNN architecture for vision tasks on mobile devices, MobileViG, which uses SVGA. Extensive experiments show that MobileViG beats existing ViG models and existing mobile CNN and ViT architectures in terms of accuracy and/or speed on image classification, object detection, and instance segmentation tasks. Our fastest model, MobileViG-Ti, achieves 75.7% top-1 accuracy on ImageNet-1K with 0.78 ms inference latency on iPhone 13 Mini NPU (compiled with CoreML), which is faster than MobileNetV2x1.4 (1.02 ms, 74.7% top-1) and MobileNetV2x1.0 (0.81 ms, 71.8% top-1). Our largest model, MobileViG-B obtains 82.6% top-1 accuracy with only 2.30 ms latency, which is faster and more accurate than the similarly sized EfficientFormer-L3 model (2.77 ms, 82.4%). Our work proves that well designed hybrid CNN-GNN architectures can be a new avenue of exploration for designing models that are extremely fast and accurate on mobile devices. Our code is publicly available at https://github.com/SLDGroup/MobileViG.

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.

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

Graph neural networks (GNNs) have shown great power in modeling graph structured data. However, similar to other machine learning models, GNNs may make predictions biased on protected sensitive attributes, e.g., skin color and gender. Because machine learning algorithms including GNNs are trained to reflect the distribution of the training data which often contains historical bias towards sensitive attributes. In addition, the discrimination in GNNs can be magnified by graph structures and the message-passing mechanism. As a result, the applications of GNNs in sensitive domains such as crime rate prediction would be largely limited. Though extensive studies of fair classification have been conducted on i.i.d data, methods to address the problem of discrimination on non-i.i.d data are rather limited. Furthermore, the practical scenario of sparse annotations in sensitive attributes is rarely considered in existing works. Therefore, we study the novel and important problem of learning fair GNNs with limited sensitive attribute information. FairGNN is proposed to eliminate the bias of GNNs whilst maintaining high node classification accuracy by leveraging graph structures and limited sensitive information. Our theoretical analysis shows that FairGNN can ensure the fairness of GNNs under mild conditions given limited nodes with known sensitive attributes. Extensive experiments on real-world datasets also demonstrate the effectiveness of FairGNN in debiasing and keeping high accuracy.

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.