Related papers: Lower and Upper Bounds on the VC-Dimension of Tens…

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…

In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we…

$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…

Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…

We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We…

Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…

SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft,…

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank…

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…

We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…