相关论文: Temiar Reduplication in One-Level Prosodic Morphol…

We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…

We provide explicit expressions of ABCD tensors for the most classical classes of spectral curves. And we discuss algorithmic implementation of Topological Recursion.

We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification,…

Handling the ever-increasing scale of contemporary deep learning and transformer-based models poses a significant challenge. Overparameterized Transformer networks outperform prior art in Natural Language processing and Computer Vision.…

Handwritten mathematical expression recognition (HMER) is a challenging task that has many potential applications. Recent methods for HMER have achieved outstanding performance with an encoder-decoder architecture. However, these methods…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

Retrieving known items from vague descriptions, Tip-of-the-Tongue (ToT) retrieval, remains a significant challenge. We propose using a single call to a generic 8B-parameter LLM for query reformulation, bridging the gap between ill-formed…

We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…

Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon…

We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…

The Matrix Decomposition techniques have been a vital computational approach to analyzing the hierarchy of functional connectivity in the human brain. However, there are still four shortcomings of these methodologies: 1). Large training…

Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…

\emph{Reductions} combine collections of input values with an associative (and usually also commutative) operator to produce either a single, or a collection of outputs. They are ubiquitous in computing, especially with big data and deep…

Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…

Repetitive DNA sequences underpin genome architecture and evolutionary processes, yet they remain challenging to classify accurately. Terrier is a deep learning model designed to overcome these challenges by classifying repetitive DNA…