Related papers: Pointers in Recursion: Exploring the Tropics
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
This paper presents rerankers, a Python library which provides an easy-to-use interface to the most commonly used re-ranking approaches. Re-ranking is an integral component of many retrieval pipelines; however, there exist numerous…
Recurrence equations lie at the heart of many computational paradigms including dynamic programming, graph analysis, and linear solvers. These equations are often expensive to compute and much work has gone into optimizing them for…
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…
We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and…
The typical multi-task learning methods for spatio-temporal data prediction involve low-rank tensor computation. However, such a method have relatively weak performance when the task number is small, and we cannot integrate it into…
We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is…
We reconstruct some of the development in Richard Bird's [2008] paper Zippy Tabulations of Recursive Functions, using dependent types and string diagrams rather than mere simple types. This paper serves as an intuitive introduction to and…
We introduce a new, demand-driven variant of Spector's bar recursion in the spirit of the Berardi-Bezem-Coquand functional. The recursion takes place over finite partial functions $u$, where the control parameter $\varphi$, used in…
Because of their occasional need to return to shallow points in a search tree, existing backtracking methods can sometimes erase meaningful progress toward solving a search problem. In this paper, we present a method by which backtrack…
We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on…