Related papers: Faster Tensor Canonicalization
We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine.…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations…
Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
Tensor expression simplification is an "ancient" topic in computer algebra, a representative of which is the canonicalization of Riemann tensor polynomials. Practically fast algorithms exist for monoterm canonicalization, but not for…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
Computations with tensors are ubiquitous in fundamental physics, and so is the usage of Einstein's dummy index convention for the contraction of indices. For instance, $T_{ia}U_{aj}$ is readily recognized as the same as $T_{ib}U_{bj}$, but…
We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
The popular subword tokenizers of current language models, such as Byte-Pair Encoding (BPE), are known not to respect morpheme boundaries, which affects the downstream performance of the models. While many improved tokenization algorithms…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
In this work, we introduce pixel wise tensor normalization, which is inserted after rectifier linear units and, together with batch normalization, provides a significant improvement in the accuracy of modern deep neural networks. In…
Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…