Journal of Symbolic Computation最新文献_第5页

Effects of reducing redundant parameters in parameter optimization for symbolic regression using genetic programming 遗传规划在符号回归参数优化中减少冗余参数的效果

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-12-02 DOI: 10.1016/j.jsc.2024.102413

Gabriel Kronberger , Fabrício Olivetti de França

{"title":"Effects of reducing redundant parameters in parameter optimization for symbolic regression using genetic programming","authors":"Gabriel Kronberger , Fabrício Olivetti de França","doi":"10.1016/j.jsc.2024.102413","DOIUrl":"10.1016/j.jsc.2024.102413","url":null,"abstract":"<div><div>Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression (SR) – a machine learning method for symbolic equation learning. Correspondingly, several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms for local optimization of parameters. An issue that has however mostly been ignored in SR and GP literature is overparameterization of SR expressions, and as a consequence, bad conditioning of NLS optimization problem. The aim of this study is to analyze the effects of overparameterization on the NLS results and convergence speed, whereby we use Operon as an example GP/SR implementation. First, we demonstrate that numeric rank approximation can be used to detect overparameterization using a set of six selected benchmark problems. In the second part, we analyze whether the NLS results or convergence speed can be improved by simplifying expressions to remove redundant parameters with equality saturation. This analysis is done with the much larger Feynman symbolic regression benchmark set after collecting all expressions visited by GP, as the simplification procedure is not fast enough to use it within GP fitness evaluation. We observe that Operon frequently visits overparameterized solutions but the number of redundant parameters is small on average. We analyzed the Pareto-optimal expressions of the first and last generation of GP, and found that for 70% to 80% of the simplified expressions, the success rate of reaching the optimum was better or equal than for the overparameterized form. The effect was smaller for the number of NLS iterations until convergence, where we found fewer or equal iterations for 51% to 63% of the expressions after simplification.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102413"},"PeriodicalIF":0.6,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limits of real bivariate rational functions 实二元有理函数的极限

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-27 DOI: 10.1016/j.jsc.2024.102405

Sĩ Tiệp Đinh , Feng Guo , Hồng Đức Nguyễn , Tiến-Sơn Phạm

引用次数: 0

Computing component groups of stabilizers of nilpotent orbit representatives 幂零轨道代表的稳定器组成群的计算

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-26 DOI: 10.1016/j.jsc.2024.102404

Emanuele Di Bella, Willem A. de Graaf

引用次数: 0

Exact moment representation in polynomial optimization 多项式优化中的精确矩表示

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-26 DOI: 10.1016/j.jsc.2024.102403

Lorenzo Baldi, Bernard Mourrain

{"title":"Exact moment representation in polynomial optimization","authors":"Lorenzo Baldi, Bernard Mourrain","doi":"10.1016/j.jsc.2024.102403","DOIUrl":"10.1016/j.jsc.2024.102403","url":null,"abstract":"<div><div>We investigate the problem of representing moment sequences by measures in the context of Polynomial Optimization Problems, that consist in finding the infimum of a real polynomial on a real semialgebraic set defined by polynomial inequalities. We analyze the exactness of Moment Matrix (MoM) hierarchies, dual to the Sum of Squares (SoS) hierarchies, which are sequences of convex cones introduced by Lasserre to approximate measures and positive polynomials. We investigate in particular flat truncation properties, which allow testing effectively when MoM exactness holds and recovering the minimizers.</div><div>We show that the dual of the MoM hierarchy coincides with the SoS hierarchy extended with the real radical of the support of the defining quadratic module <em>Q</em>. We deduce that flat truncation happens if and only if the support of the quadratic module associated with the minimizers is of dimension zero. We also bound the order of the hierarchy at which flat truncation holds.</div><div>As corollaries, we show that flat truncation and MoM exactness hold when regularity conditions, known as Boundary Hessian Conditions, hold (and thus that MoM exactness holds generically); and when the support of the quadratic module <em>Q</em> is zero-dimensional. Effective numerical computations illustrate these flat truncation properties.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102403"},"PeriodicalIF":0.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sections of Dupin cyclides and their focal properties 杜邦自行车的部分和他们的焦点性质

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-26 DOI: 10.1016/j.jsc.2024.102402

Eriola Hoxhaj , Jean Michel Menjanahary , Rimvydas Krasauskas

引用次数: 0

Computing the homology of universal covers via effective homology and discrete vector fields 通过有效同源性和离散向量场计算普遍盖的同源性

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-14 DOI: 10.1016/j.jsc.2024.102401

Miguel A. Marco-Buzunáriz , Ana Romero

{"title":"Computing the homology of universal covers via effective homology and discrete vector fields","authors":"Miguel A. Marco-Buzunáriz , Ana Romero","doi":"10.1016/j.jsc.2024.102401","DOIUrl":"10.1016/j.jsc.2024.102401","url":null,"abstract":"<div><div>Effective homology techniques allow us to compute homology groups of a wide family of topological spaces. By the Whitehead tower method, this can also be used to compute higher homotopy groups. However, some of these techniques (in particular, the Whitehead tower) rely on the assumption that the starting space is simply connected. For some applications, this problem could be circumvented by replacing the space by its universal cover, which is a simply connected space that shares the higher homotopy groups of the initial space. In this paper, we formalize a simplicial construction for the universal cover, and represent it as a twisted Cartesian product.</div><div>As we show with some examples, the universal cover of a space with effective homology does not necessarily have effective homology in general. We show two independent sufficient conditions that can ensure it: one is based on a nilpotency property of the fundamental group, and the other one on discrete vector fields.</div><div>Some examples showing our implementation of these constructions in both SageMath and Kenzo are shown, together with an approach to compute the homology of the universal cover when the group is Abelian even in some cases where there is no effective homology, using the twisted homology of the space.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102401"},"PeriodicalIF":0.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local dual spaces and primary decomposition 局部对偶空间和一级分解

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-13 DOI: 10.1016/j.jsc.2024.102400

Justin Chen, Marc Härkönen, Anton Leykin

引用次数: 0

On the existence and convergence of formal power series solutions of nonlinear Mahler equations 论非线性马勒方程的形式幂级数解的存在性和收敛性

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-11-08 DOI: 10.1016/j.jsc.2024.102399

Renat Gontsov , Irina Goryuchkina

引用次数: 0

Absolute concentration robustness: Algebra and geometry 绝对浓度稳健性代数与几何

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-30 DOI: 10.1016/j.jsc.2024.102398

Luis David García Puente , Elizabeth Gross , Heather A. Harrington , Matthew Johnston , Nicolette Meshkat , Mercedes Pérez Millán , Anne Shiu

引用次数: 0

Persistent components in Canny's generalized characteristic polynomial 坎尼广义特征多项式中的持久成分

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-30 DOI: 10.1016/j.jsc.2024.102397

Gleb Pogudin

引用次数: 0