Related papers: Generalized Nonnegative Structured Kruskal Tensor …

Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…

Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…

Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like…

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…

Recently, it can be noticed that most models based on spiking neural networks (SNNs) only use a same level temporal resolution to deal with speech classification problems, which makes these models cannot learn the information of input data…

In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

While the next-token prediction (NTP) paradigm enables large language models (LLMs) to express their intrinsic knowledge, its sequential nature constrains performance on specialized, non-generative tasks. We attribute this performance…

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training…

This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional…

Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct…

Modern data sources are typically of large scale and multi-modal natures, and acquired on irregular domains, which poses serious challenges to traditional deep learning models. These issues are partially mitigated by either extending…

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…

Regression analysis-based approaches have been widely studied for face recognition (FR) in the past several years. More recently, to better deal with some difficult conditions such as occlusions and illumination, nuclear norm based matrix…