Related papers: Residual Matrix Product State for Machine Learning

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…

This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…

This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically…

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…

Most multilayer least squares (LS)-based neural networks are structured with two separate stages: unsupervised feature encoding and supervised pattern classification. Once the unsupervised learning is finished, the latent encoding would be…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

Detection and classification of pulmonary nodules is a challenge in medical image analysis due to the variety of shapes and sizes of nodules and their high concealment. Despite the success of traditional deep learning methods in image…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

Classical neural networks achieve only limited convergence in hard problems such as XOR or parity when the number of hidden neurons is small. With the motivation to improve the success rate of neural networks in these problems, we propose a…

We analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…