Related papers: A Simple and Efficient Tensor Calculus for Machine…
Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…
In this paper we study $p$-order methods for unconstrained minimization of convex functions that are $p$-times differentiable ($p\geq 2$) with $\nu$-H\"{o}lder continuous $p$th derivatives. We propose tensor schemes with and without…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing the minimum number of…
The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models.…
In 2011, einsum was introduced to NumPy as a practical and convenient notation for tensor expressions in machine learning, quantum circuit simulation, and other fields. It has since been implemented in additional Python frameworks such as…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…
In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…
This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which…
Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…