相关论文: Asymptotic Singular Value Distribution of Linear C…

Dropout as a regularization technique is widely used in fully connected layers while is less effective in convolutional layers. Therefore more structured forms of dropout have been proposed to regularize convolutional networks. The…

Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…

Depth prediction is one of the fundamental problems in computer vision. In this paper, we propose a simple yet effective convolutional spatial propagation network (CSPN) to learn the affinity matrix for various depth estimation tasks.…

We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value…

Existing graph convolutional networks focus on the neighborhood aggregation scheme. When applied to semi-supervised learning, they often suffer from the overfitting problem as the networks are trained with the cross-entropy loss on a small…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…

The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…

Deep neural networks using state space models as layers are well suited for long-range sequence tasks but can be challenging to compress after training. We use that regularizing the sum of Hankel singular values of state space models leads…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…

The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a…

We present a real-time propagation method for computing linear and nonlinear optical properties of molecules based on the Bethe-Salpeter equation. The method follows the time evolution of the one-particle density matrix under an external…

We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the…

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This…

In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation).…

Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…