arXiv research

Recovering matrix valued potentials from wave equation data on stationary spacetimes.

We investigate solutions of the elliptic sinh-Gordon equation of spectral genus g<3. These solutions are parametrized by complex matrix-valued polynomials called potentials. On the space of these potentials there act two commuting flows. The orbits of these flows are called Polynomial Killing fields and are double peri…

A new method clusters rows of a matrix of point processes.

Autoencoders are popular among neural-network-based matrix completion models due to their ability to retrieve potential latent factors from the partially observed matrices. Nevertheless, when training data is scarce their performance is significantly degraded due to overfitting. In this paper, we mit- igate overfitting…

Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To cir…

In the probabilistic topic models, the quantity of interest---a low-rank matrix consisting of topic vectors---is hidden in the text corpus matrix, masked by noise, and the Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank m…

SNN architecture shows gradient descent converges to regularized solution in matrix sensing problems.

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.

Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.

New method quantifies classifier uncertainty, revealing large variability in performance metrics.

Study of metrics on positive-definite matrices from power potential, linking to power means.

Discovering the underlying low dimensional structure of high dimensional data has attracted a significant amount of researches recently and has shown to have a wide range of applications. As an effective dimension reduction tool, singular value decomposition is often used to analyze high dimensional matrices, which are…

Paper improves matrix-valued data classification using nonparametric LDA.

The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…

A new method speeds up ALS for recommender systems by subsampling key elements.

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that …

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct appl…

Study evaluates thresholds for removing noise from DNN weights using random matrix theory.

Current auto loans converge to super-prime credit despite remaining underwater.

Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.

Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.

Study finds weak solutions for complex map flows with optimal lifespan.

The US Census Bureau corrupts data to protect privacy, but we show how to clean and analyze it effectively.

Paper develops a new test for high-dimensional matrix-valued data.

Holomorphic functions from knot complements link to quantum modular forms.

Two multifidelity trust-region methods use low-fidelity models for efficient optimization.

New nonconvex regularizer speeds up low-rank matrix completion.

The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the (unobservable)_denoising_ problem of how to best approximate a low-rank signal matrix bur…

This paper reviews methods for discovering patient subgroups from EHR data.

New technique stabilizes singular values in concatenated matrices.

A new method STMF improves missing value prediction using tropical semiring.

New analysis reveals masked self-supervised learning's effectiveness in extracting data structure.

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and non-Lipschitz problem, we develop a non-monotone alternating updating method based o…

Develops a gradient flow for Muon optimizer, a method for optimization.

Improved singular value approximation for convolutional layers.

We extend Kyle's model to include stochastic liquidity and multiple assets.

We give a geometric construction of the multivariable Conway potential function for colored links. In the case of a single color, it is Kauffman's definition of the Conway polynomial in terms of a Seifert matrix.

A new algorithm speeds up matrix operations in Neural Networks.

This work analyzes self-attention matrices using random matrix theory.

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. …

We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to so…

Optimal rank-adaptive matrix estimation from linear measurements.

Unified approach for robust low rank matrix estimation with adversaries.

New framework for higher-order singular-value derivatives of rectangular matrices.

SNS accelerates Sinkhorn algorithm with sparse Newton iterations.