Related papers: A continuous analogue of the tensor-train decompos…
A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option…
Kohn-Sham density functional theory (DFT) is the workhorse of quantum chemistry, offering an attractive balance between accuracy and computational cost. Although exact in principle, DFT in practice relies on an approximation to the unknown…
Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were…
Because tensor data appear more and more frequently in various scientific researches and real-world applications, analyzing the relationship between tensor features and the univariate outcome becomes an elementary task in many fields. To…
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…
Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…
Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task…
A widely used approach to compute the action $f(A)v$ of a matrix function $f(A)$ on a vector $v$ is to use a rational approximation $r$ for $f$ and compute $r(A)v$ instead. If $r$ is not computed adaptively as in rational Krylov methods,…
Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…
We introduce Tangent Attention Fine-Tuning (TAFT), a method for fine-tuning linearized transformers obtained by computing a First-order Taylor Expansion around a pre-trained initialization. We show that the Jacobian-Vector Product resulting…
In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Recent research in deep learning (DL) has investigated the use of the Fast Fourier Transform (FFT) to accelerate the computations involved in Convolutional Neural Networks (CNNs) by replacing spatial convolution with element-wise…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
We describe a model element able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum form. The implementation of this model in the form of a multi-barrier, multiple-slit…
Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations…
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting)…
This paper describes a new method for representing embedding tables of graph neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We consider the scenario where (a) the graph data that lack node features, thereby…