The emergence of deep and large-scale spiking neural networks (SNNs) exhibiting high performance across diverse complex datasets has led to a need for compressing network models due to the presence of a significant number of redundant structural units, aiming to more effectively leverage their low-power consumption and biological interpretability advantages. Currently, most model compression techniques for SNNs are based on unstructured pruning of individual connections, which requires specific hardware support. Hence, we propose a structured pruning approach based on the activity levels of convolutional kernels named Spiking Channel Activity-based (SCA) network pruning framework. Inspired by synaptic plasticity mechanisms, our method dynamically adjusts the network's structure by pruning and regenerating convolutional kernels during training, enhancing the model's adaptation to the current target task. While maintaining model performance, this approach refines the network architecture, ultimately reducing computational load and accelerating the inference process. This indicates that structured dynamic sparse learning methods can better facilitate the application of deep SNNs in low-power and high-efficiency scenarios.
This paper introduces a new biologically-inspired training method named Continual Learning through Adjustment Suppression and Sparsity Promotion (CLASSP). CLASSP is based on two main principles observed in neuroscience, particularly in the context of synaptic transmission and Long-Term Potentiation (LTP). The first principle is a decay rate over the weight adjustment, which is implemented as a generalization of the AdaGrad optimization algorithm. This means that weights that have received many updates should have lower learning rates as they likely encode important information about previously seen data. However, this principle results in a diffuse distribution of updates throughout the model, as it promotes updates for weights that haven't been previously updated, while a sparse update distribution is preferred to leave weights unassigned for future tasks. Therefore, the second principle introduces a threshold on the loss gradient. This promotes sparse learning by updating a weight only if the loss gradient with respect to that weight is above a certain threshold, i.e. only updating weights with a significant impact on the current loss. Both principles reflect phenomena observed in LTP, where a threshold effect and a gradual saturation of potentiation have been observed. CLASSP is implemented in a Python/PyTorch class, making it applicable to any model. When compared with Elastic Weight Consolidation (EWC) using Computer Vision and sentiment analysis datasets, CLASSP demonstrates superior performance in terms of accuracy and memory footprint.
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and explore the mis-specified scenario where the dynamics may escape the chosen function space. We relate the Koopman operator to the conditional mean embeddings (CME) operator and then present an operator stochastic approximation algorithm to learn the Koopman operator iteratively with control over the complexity of the representation. We provide both asymptotic and finite-time last-iterate guarantees of the online sparse learning algorithm with trajectory-based sampling with an analysis that is substantially more involved than that for finite-dimensional stochastic approximation. Numerical examples confirm the effectiveness of the proposed algorithm.
We consider a mixed analog-to-digital converter (ADC) based architecture consisting of high-precision and one-bit ADCs with the antenna-varying threshold for direction of arrival (DOA) estimation using a uniform linear array (ULA), which utilizes fixed but different thresholds for one-bit ADCs across different receive antennas. The Cram{\'e}r-Rao bound (CRB) with the antenna-varying threshold is obtained. Then based on the lower bound of the CRB, we derive the asymptotic CRB of the DOA, which depends on the placement of mixed-ADC. Our analysis shows that distributing high-precision ADCs evenly around the two edges of the ULA yields improved performance. This result can be extended to a more general case where the ULA is equipped with two types of ADCs with different quantization precisions. To efficiently obtain the maximum likelihood DOA estimates, we propose a two-step algorithm. Firstly, we formulate the model as a sparse signal representation problem, and modify the sparse learning via iterative minimization (SLIM) approach to the mixed-ADC based DOA estimation. In the second step, we use the relaxation-based approach to cyclically refine the estimates of SLIM, further enhancing the DOA estimation performance. Numerical examples are presented to demonstrate the validity of the CRB analysis and the effectiveness of our methods.
This paper introduces a novel prior called Diversified Block Sparse Prior to characterize the widespread block sparsity phenomenon in real-world data. By allowing diversification on intra-block variance and inter-block correlation matrices, we effectively address the sensitivity issue of existing block sparse learning methods to pre-defined block information, which enables adaptive block estimation while mitigating the risk of overfitting. Based on this, a diversified block sparse Bayesian learning method (DivSBL) is proposed, utilizing EM algorithm and dual ascent method for hyperparameter estimation. Moreover, we establish the global and local optimality theory of our model. Experiments validate the advantages of DivSBL over existing algorithms.
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of a family of $\ell_0$-regularized problems. An efficient primal-dual algorithm is developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.
In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.
Classification and probability estimation have broad applications in modern machine learning and data science applications, including biology, medicine, engineering, and computer science. The recent development of a class of weighted Support Vector Machines (wSVMs) has shown great values in robustly predicting the class probability and classification for various problems with high accuracy. The current framework is based on the $\ell^2$-norm regularized binary wSVMs optimization problem, which only works with dense features and has poor performance at sparse features with redundant noise in most real applications. The sparse learning process requires a prescreen of the important variables for each binary wSVMs for accurately estimating pairwise conditional probability. In this paper, we proposed novel wSVMs frameworks that incorporate automatic variable selection with accurate probability estimation for sparse learning problems. We developed efficient algorithms for effective variable selection for solving either the $\ell^1$-norm or elastic net regularized binary wSVMs optimization problems. The binary class probability is then estimated either by the $\ell^2$-norm regularized wSVMs framework with selected variables or by elastic net regularized wSVMs directly. The two-step approach of $\ell^1$-norm followed by $\ell^2$-norm wSVMs show a great advantage in both automatic variable selection and reliable probability estimators with the most efficient time. The elastic net regularized wSVMs offer the best performance in terms of variable selection and probability estimation with the additional advantage of variable grouping in the compensation of more computation time for high dimensional problems. The proposed wSVMs-based sparse learning methods have wide applications and can be further extended to $K$-class problems through ensemble learning.
Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for Regularized Optimization (SRO). Our SRO algorithm first generates a sketch of the original data matrix, then solves the sketched problem. Different from existing randomized algorithms, our algorithm handles general Frechet subdifferentiable regularization functions in an unified framework. We present general theoretical result for the approximation error between the optimization results of the original problem and the sketched problem for regularized least square problems which can be convex or nonconvex. For arbitrary convex regularizer, relative-error bound is proved for the approximation error. Importantly, minimax rates for sparse signal estimation by solving the sketched sparse convex or nonconvex learning problems are also obtained using our general theoretical result under mild conditions. To the best of our knowledge, our results are among the first to demonstrate minimax rates for convex or nonconvex sparse learning problem by sketching under a unified theoretical framework. We further propose an iterative sketching algorithm which reduces the approximation error exponentially by iteratively invoking the sketching algorithm. Experimental results demonstrate the effectiveness of the proposed SRO and Iterative SRO algorithms.
Explainable Graph Neural Networks (GNNs) have been developed and applied to drug-protein binding prediction to identify the key chemical structures in a drug that have active interactions with the target proteins. However, the key structures identified by the current explainable GNN models are typically chemically invalid. Furthermore, a threshold needs to be manually selected to pinpoint the key structures from the rest. To overcome the limitations of the current explainable GNN models, we propose our SLGNN, which stands for using Sparse Learning to Graph Neural Networks. Our SLGNN relies on using a chemical-substructure-based graph (where nodes are chemical substructures) to represent a drug molecule. Furthermore, SLGNN incorporates generalized fussed lasso with message-passing algorithms to identify connected subgraphs that are critical for the drug-protein binding prediction. Due to the use of the chemical-substructure-based graph, it is guaranteed that any subgraphs in a drug identified by our SLGNN are chemically valid structures. These structures can be further interpreted as the key chemical structures for the drug to bind to the target protein. We demonstrate the explanatory power of our SLGNN by first showing all the key structures identified by our SLGNN are chemically valid. In addition, we illustrate that the key structures identified by our SLGNN have more predictive power than the key structures identified by the competing methods. At last, we use known drug-protein binding data to show the key structures identified by our SLGNN contain most of the binding sites.
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.
Brain-inspired Spiking Neural Networks (SNNs) have the characteristics of event-driven and high energy-efficient, which are different from traditional Artificial Neural Networks (ANNs) when deployed on edge devices such as neuromorphic chips. Most previous work focuses on SNNs training strategies to improve model performance and brings larger and deeper network architectures. It is difficult to deploy these complex networks on resource-limited edge devices directly. To meet such demand, people compress SNNs very cautiously to balance the performance and the computation efficiency. Existing compression methods either iteratively pruned SNNs using weights norm magnitude or formulated the problem as a sparse learning optimization. We propose an improved end-to-end Minimax optimization method for this sparse learning problem to better balance the model performance and the computation efficiency. We also demonstrate that jointly applying compression and finetuning on SNNs is better than sequentially, especially for extreme compression ratios. The compressed SNN models achieved state-of-the-art (SOTA) performance on various benchmark datasets and architectures. Our code is available at https://github.com/chenjallen/Resource-Constrained-Compression-on-SNN.
We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In contrast, our method enables fully differentiable and approximation-free optimization and is thus compatible with the ubiquitous gradient descent paradigm in deep learning. The proposed optimization transfer comprises an overparameterization of selected parameters and a change of penalties. In the overparametrized problem, smooth surrogate regularization induces non-smooth, sparse regularization in the base parametrization. We prove that the surrogate objective is equivalent in the sense that it not only has identical global minima but also matching local minima, thereby avoiding the introduction of spurious solutions. Additionally, our theory establishes results of independent interest regarding matching local minima for arbitrary, potentially unregularized, objectives. We comprehensively review sparsity-inducing parametrizations across different fields that are covered by our general theory, extend their scope, and propose improvements in several aspects. Numerical experiments further demonstrate the correctness and effectiveness of our approach on several sparse learning problems ranging from high-dimensional regression to sparse neural network training.
We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the extended Kramers-Moyal expansion to express the drift and diffusion terms of an SPDE in terms of state responses and use Spike-and-Slab priors with sparse learning techniques to efficiently and accurately discover the underlying SPDEs. The proposed approach has been applied to three canonical SPDEs, (a) stochastic heat equation, (b) stochastic Allen-Cahn equation, and (c) stochastic Nagumo equation. Our results demonstrate that the proposed approach can accurately identify the underlying SPDEs with limited data. This is the first attempt at discovering SPDEs from data, and it has significant implications for various scientific applications, such as climate modeling, financial forecasting, and chemical kinetics.
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning, we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to understand what kind of RKBSs can promote sparsity for learning solutions. We consider two typical learning models in an RKBS: the minimum norm interpolation (MNI) problem and the regularization problem. We first establish an explicit representer theorem for solutions of these problems, which represents the extreme points of the solution set by a linear combination of the extreme points of the subdifferential set, of the norm function, which is data-dependent. We then propose sufficient conditions on the RKBS that can transform the explicit representation of the solutions to a sparse kernel representation having fewer terms than the number of the observed data. Under the proposed sufficient conditions, we investigate the role of the regularization parameter on sparsity of the regularized solutions. We further show that two specific RKBSs: the sequence space $\ell_1(\mathbb{N})$ and the measure space can have sparse representer theorems for both MNI and regularization models.
Transfer learning is an essential tool for improving the performance of primary tasks by leveraging information from auxiliary data resources. In this work, we propose Adaptive Robust Transfer Learning (ART), a flexible pipeline of performing transfer learning with generic machine learning algorithms. We establish the non-asymptotic learning theory of ART, providing a provable theoretical guarantee for achieving adaptive transfer while preventing negative transfer. Additionally, we introduce an ART-integrated-aggregating machine that produces a single final model when multiple candidate algorithms are considered. We demonstrate the promising performance of ART through extensive empirical studies on regression, classification, and sparse learning. We further present a real-data analysis for a mortality study.
The underwater propagation environment for visible light signals is affected by complex factors such as absorption, shadowing, and reflection, making it very challengeable to achieve effective underwater visible light communication (UVLC) channel estimation. It is difficult for the UVLC channel to be sparse represented in the time and frequency domains, which limits the chance of using sparse signal processing techniques to achieve better performance of channel estimation. To this end, a compressed sensing (CS) based framework is established in this paper by fully exploiting the sparsity of the underwater visible light channel in the distance domain of the propagation links. In order to solve the sparse recovery problem and achieve more accurate UVLC channel estimation, a sparse learning based underwater visible light channel estimation (SL-UVCE) scheme is proposed. Specifically, a deep-unfolding neural network mimicking the classical iterative sparse recovery algorithm of approximate message passing (AMP) is employed, which decomposes the iterations of AMP into a series of layers with different learnable parameters. Compared with the existing non-CS-based and CS-based schemes, the proposed scheme shows better performance of accuracy in channel estimation, especially in severe conditions such as insufficient measurement pilots and large number of multipath components.
Super-Resolution from a single motion Blurred image (SRB) is a severely ill-posed problem due to the joint degradation of motion blurs and low spatial resolution. In this paper, we employ events to alleviate the burden of SRB and propose an Event-enhanced SRB (E-SRB) algorithm, which can generate a sequence of sharp and clear images with High Resolution (HR) from a single blurry image with Low Resolution (LR). To achieve this end, we formulate an event-enhanced degeneration model to consider the low spatial resolution, motion blurs, and event noises simultaneously. We then build an event-enhanced Sparse Learning Network (eSL-Net++) upon a dual sparse learning scheme where both events and intensity frames are modeled with sparse representations. Furthermore, we propose an event shuffle-and-merge scheme to extend the single-frame SRB to the sequence-frame SRB without any additional training process. Experimental results on synthetic and real-world datasets show that the proposed eSL-Net++ outperforms state-of-the-art methods by a large margin. Datasets, codes, and more results are available at https://github.com/ShinyWang33/eSL-Net-Plusplus.
While recent progress in video-text retrieval has been advanced by the exploration of better representation learning, in this paper, we present a novel multi-grained sparse learning framework, S3MA, to learn an aligned sparse space shared between the video and the text for video-text retrieval. The shared sparse space is initialized with a finite number of sparse concepts, each of which refers to a number of words. With the text data at hand, we learn and update the shared sparse space in a supervised manner using the proposed similarity and alignment losses. Moreover, to enable multi-grained alignment, we incorporate frame representations for better modeling the video modality and calculating fine-grained and coarse-grained similarities. Benefiting from the learned shared sparse space and multi-grained similarities, extensive experiments on several video-text retrieval benchmarks demonstrate the superiority of S3MA over existing methods. Our code is available at https://github.com/yimuwangcs/Better_Cross_Modal_Retrieval.