Related papers: Evaluating Singular Value Thresholds for DNN Weigh…

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…

Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work,…

After decades of attention, emergence continues to lack a centralized mathematical definition that leads to a rigorous emergence test applicable to physical flocks and swarms, particularly those containing both deterministic elements (eg,…

Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an $m \times n$ matrix $\widehat{{\mathbf M}}$, the prototypical RSVD algorithm…

Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a…

We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis…

This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The…

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore,…

Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…

The mainstream AI community has seen a rise in large-scale open-source classifiers, often pre-trained on vast datasets and tested on standard benchmarks; however, users facing diverse needs and limited, expensive test data may be…

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

Singular value thresholding (SVT) plays an important role in the well-known robust principal component analysis (RPCA) algorithms which have many applications in computer vision and recommendation systems. In this paper, we formulate and…

In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…

The proper initialization of weights is crucial for the effective training and fast convergence of deep neural networks (DNNs). Prior work in this area has mostly focused on balancing the variance among weights per layer to maintain…

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…

We introduce a methodology for designing and training deep neural networks (DNN) that we call "Deep Regression Ensembles" (DRE). It bridges the gap between DNN and two-layer neural networks trained with random feature regression. Each layer…

Theoretical analysis of the error landscape of deep neural networks has garnered significant interest in recent years. In this work, we theoretically study the importance of noise in the trajectories of gradient descent towards optimal…