相关论文: Interaction Decompositions for Tensor Network Regr…

Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…

Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…

Tensor decompositions have been successfully applied to compress neural networks. The compression algorithms using tensor decompositions commonly minimize the approximation error on the weights. Recent work assumes the approximation error…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…

Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…

In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…

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…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…