Related papers: Automatic Discovery of Geometry Theorems Using Min…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
In this study, we propose a method for extracting the hidden algebraic structures of model parameters that are uniquely determined by observed time-series data and unidentifiable state-space models, explicitly and exhaustively. State-space…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of…
A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each…
Property prediction plays an important role in material discovery. As an initial step to eventually develop a foundation model for material science, we introduce a new autoencoder called the MHG-GNN, which combines graph neural network…
The detection of small road hazards, such as lost cargo, is a vital capability for self-driving cars. We tackle this challenging and rarely addressed problem with a vision system that leverages appearance, contextual as well as geometric…
Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…
A characteristic pair is a pair (G,C) of polynomial sets in which G is a reduced lexicographic Groebner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be…
Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation…
In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
Knowledge graph completion (KGC) aims to solve the incompleteness of knowledge graphs (KGs) by predicting missing links from known triples, numbers of knowledge graph embedding (KGE) models have been proposed to perform KGC by learning…
We study from a physics viewpoint a class of generative neural nets, Gibbs machines, designed for gradual learning. While including variational auto-encoders, they offer a broader universal platform for incrementally adding newly learned…
Let T(x) in k[x] be a monic non-constant polynomial and write R=k[x] / (T) the quotient ring. Consider two bivariate polynomials a(x, y), b(x, y) in R[y]. In a first part, T = p^e is assumed to be the power of an irreducible polynomial p. A…
Markov Chain Monte Carlo (MCMC) method is a widely used algorithm design scheme with many applications. To make efficient use of this method, the key step is to prove that the Markov chain is rapid mixing. Canonical paths is one of the two…
With the rapid advancement of large language models, there has been a growing interest in their capabilities in mathematical reasoning. However, existing research has primarily focused on text-based algebra problems, neglecting the study of…