Related papers: Deep Tree Tensor Networks for Image Recognition

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

This work proposes a domain-informed neural network architecture for experimental particle physics, using particle interaction localization with the time-projection chamber (TPC) technology for dark matter research as an example…

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods…

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…

The large variation of datasets is a huge barrier for image classification tasks. In this paper, we embraced this observation and introduce the finite temperature tensor network (FTTN), which imports the thermal perturbation into the matrix…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Graph Neural Networks (GNNs) excel at learning from graph-structured data but are limited to modeling pairwise interactions, insufficient for capturing higher-order relationships present in many real-world systems. Topological Deep Learning…

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,…

We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural…

Advanced tensor decomposition, such as Tensor train (TT) and Tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs). However, compressing convolutional…

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…

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 combine density-functional tight-binding (DFTB) with deep tensor neural networks (DTNN) to maximize the strengths of both approaches in predicting structural, energetic, and vibrational molecular properties. The DTNN is used to learn a…

We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…