Related papers: Multiscale Tensor Summation Factorization as a New…
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…
Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Tensor latent factor models can describe higher-order correlations for spatial data. However, they are computationally…
Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…
Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and…
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…
Despite their ubiquity in NLP tasks, Long Short-Term Memory (LSTM) networks suffer from computational inefficiencies caused by inherent unparallelizable recurrences, which further aggravates as LSTMs require more parameters for larger…
Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the…
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…
Embedding based models have been the state of the art in collaborative filtering for over a decade. Traditionally, the dot product or higher order equivalents have been used to combine two or more embeddings, e.g., most notably in matrix…
We present a novel method of compression of deep Convolutional Neural Networks (CNNs) by weight sharing through a new representation of convolutional filters. The proposed method reduces the number of parameters of each convolutional layer…
To overcome the computational bottleneck of various data perturbation procedures such as the bootstrap and cross validations, we propose the Generative Multiple-purpose Sampler (GMS), which constructs a generator function to produce…