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In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit…

In the era of deep learning, word embeddings are essential when dealing with text tasks. However, storing and accessing these embeddings requires a large amount of space. This is not conducive to the deployment of these models on…

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM…

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

Overparameterized transformer networks have obtained state of the art results in various natural language processing tasks, such as machine translation, language modeling, and question answering. These models contain hundreds of millions of…

A novel generalization of the Prouhet-Thue-Morse sequence to binary $\pm 1$-weight sequences is presented. Derived from Rademacher functions, these weight sequences are shown to satisfy interesting orthogonality and recurrence relations. In…

A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse…

The paper develops an optimal regulator for a general class of multi-input affine nonlinear systems minimizing a nonlinear cost functional with infinite horizon. The cost functional is general enough to enforce saturation limits on the…

In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence…

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…

This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…

There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…

The DEtection TRansformer (DETR) is a powerful end-to-end object detector, yet its one-to-one matching strategy suffers from slow convergence and low recall. A common approach to address this issue is to use one-to-many label assignment to…

Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficient sampling strategy for two primary tensor CUR…