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The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse recovery performance. How can this be explained? To answer…

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…

Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…

Overfitting is one of the most common problems when training deep neural networks on comparatively small datasets. Here, we demonstrate that neural network activation sparsity is a reliable indicator for overfitting which we utilize to…

Sparse recovery is ubiquitous in machine learning and signal processing. Due to the NP-hard nature of sparse recovery, existing methods are known to suffer either from restrictive (or even unknown) applicability conditions, or high…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

Inspired by the robustness and efficiency of sparse representation in sparse coding based image restoration models, we investigate the sparsity of neurons in deep networks. Our method structurally enforces sparsity constraints upon hidden…

We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…

Sparse autoencoders (SAEs) are widely used in mechanistic interpretability to project LLM activations onto sparse latent spaces. However, sparsity alone is an imperfect proxy for interpretability, and current training objectives often…

Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…

$L_p$-norm regularization schemes such as $L_0$, $L_1$, and $L_2$-norm regularization and $L_p$-norm-based regularization techniques such as weight decay, LASSO, and elastic net compute a quantity which depends on model weights considered…

In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class…

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed…

We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…

We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…

Deep neural networks achieve outstanding performance across vision and language tasks, yet their large parameter counts limit deployment in resource-constrained settings. One-shot pruning reduces model size without retraining, but models…

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…