Related papers: Tensor Cookbook: Mastering Tensors through Diagram…
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…
A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
In mathematics, many notations have been invented for the concise representation of mathematical formulae. Tensor index notation is one of such notations and has been playing a crucial role in describing formulae in mathematical physics.…
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
Axon is a language that enables shape and rank inference for tensors in a Deep Learning graphs. It aims to make shapes implicit and inferred, in a similar manner to how types are implicit and inferred in many functional programming…
Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks.…
Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential…
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,…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…
Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches…
Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…