Constraint satisfaction approach in structuring neural network architectures

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). • Analyzing Width and Depth in Neural Network Architectures via Constraint Satisfaction Problems. • Numerical-Quantitative approach in the Approximation Theory of Neural Networks. • Neuronal Distribution Analysis Conducted through an Automated Machine Learning (AutoML) Framework.