A Logical Approach to Interpret Neural Network: Formalizing Hopfield Network Dynamics

Xiaoxuan Fu, Ke Wu

Keywords: Propositional dynamic logic; Hopfield network; Neuro-Symbolic

Abstract: This paper introduces a formal framework for interpreting neural network behavior, focusing on Hopfield networks, using propositional dynamic logic (PDL). By connecting Leitgeb's discursive interpretation of neural networks with a formal system, we provide a clear method for analyzing the dynamic evolution of network states. Utilizing PDL, we describe the process of convergence to stable memory patterns and the stability of neural network states. This work offers a rigorous logical foundation for understanding neural network dynamics, bridging the gap between symbolic interpretation and formal analysis. The proposed framework not only enhances the interpretability of Hopfield networks but also lays the groundwork for extending these methods to other neural network architectures, contributing to the broader field of explainable AI.

Submission Number: 36