Constraint satisfaction approach in structuring neural network architectures

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-10-08 DOI:10.1016/j.cam.2025.117140

Vittorio Bauduin , Salvatore Cuomo , Vincenzo Schiano Di Cola

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引用次数: 0

Abstract

This work presents a novel numerical and quantitative methodology grounded in Constraint Satisfaction Problem (CSP) theory, aimed at developing a specialized tool for the structural analysis of fully connected, feed-forward Neural Networks (NNs). The proposed approach enables a systematic exploration of neuron configurations within the hidden layers.

A backtracking search algorithm was specifically designed to traverse the space of admissible architectural parameters, thereby implementing a constrained combinatorial strategy for neural network architecture exploration. This study introduces a practical tool for researchers aiming to identify diverse neuronal organizational patterns within hidden layers, subject to predefined hyperparameter constraints.

The proposed algorithm was subsequently validated by exhaustively exploring all feasible architectural configurations for solving a two-dimensional Poisson equation using a Physics-Informed Neural Network (PINN).

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构造神经网络结构的约束满足方法

这项工作提出了一种新的基于约束满足问题（CSP）理论的数值和定量方法，旨在开发一种专门的工具，用于全连接的前馈神经网络（NNs）的结构分析。提出的方法能够系统地探索隐藏层内的神经元配置。设计了一种回溯搜索算法来遍历可允许的结构参数空间，从而实现了神经网络结构探索的约束组合策略。本研究为研究人员提供了一个实用的工具，旨在识别隐藏层中受预定义超参数约束的不同神经元组织模式。随后，通过使用物理信息神经网络（PINN）详尽地探索所有可行的结构配置来解决二维泊松方程，验证了所提出的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.