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Found 18 papers, 7 papers with code
Tensor Network-Constrained Kernel Machines as Gaussian Processes
We analyze the convergence of both CPD and TT-constrained models, and show how TT yields models exhibiting more GP behavior compared to CPD, for the same number of model parameters.
A divide-and-conquer approach for sparse recovery of high dimensional signals
Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals.
Projecting basis functions with tensor networks for Gaussian process regression
The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace.
Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models
Unless one considers the dual formulation of the learning problem, which renders exact large-scale learning unfeasible, the exponential increase of model parameters in the dimensionality of the data caused by their tensor-product structure prohibits to tackle high-dimensional problems.
How Informative is the Approximation Error from Tensor Decomposition for Neural Network Compression?
While scaling the approximation error commonly is used to account for the different sizes of layers, the average correlation across layers is smaller than across all choices (i. e. layers, decompositions, and level of compression) before fine-tuning.
Towards Green AI with tensor networks -- Sustainability and innovation enabled by efficient algorithms
Furthermore, we argue that better algorithms should be evaluated in terms of both accuracy and efficiency.
Tensor Network Kalman Filtering for Large-Scale LS-SVMs
Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification.
Large-Scale Learning with Fourier Features and Tensor Decompositions
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods.
Alternating linear scheme in a Bayesian framework for low-rank tensor approximation
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition.
Nonlinear system identification with regularized Tensor Network B-splines
This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach.
Kernelized Support Tensor Train Machines
In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for image classification.
Matrix Product Operator Restricted Boltzmann Machines
This work presents the matrix product operator RBM (MPORBM) that utilizes a tensor network generalization of Mv/TvRBM, preserves input formats in both the visible and hidden layers, and results in higher expressive power.
Deep Compression of Sum-Product Networks on Tensor Networks
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models.
Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
We propose a new tensor completion method based on tensor trains.
A Support Tensor Train Machine
There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms.
Parallelized Tensor Train Learning of Polynomial Classifiers
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces.
A Tensor Network Kalman filter with an application in recursive MIMO Volterra system identification
This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them.
Systems and Control
A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms
We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products.
Numerical Analysis Numerical Analysis
