Neural-Symbolic Integration with Evolvable Policies

TL;DR

This paper introduces an evolutionary framework for neural-symbolic systems that can learn non-differentiable symbolic policies alongside neural weights, enabling applications without predefined symbolic knowledge.

Contribution

It extends NeSy architectures to evolve symbolic policies and neural weights simultaneously using mutation-based evolution, removing the need for differentiability or predefined policies.

Findings

Successfully approximates hidden non-differentiable policies

Median correct performance approaches 100%

Demonstrates effectiveness with empty policies and random weights

Abstract

Neural-Symbolic (NeSy) Artificial Intelligence has emerged as a promising approach for combining the learning capabilities of neural networks with the interpretable reasoning of symbolic systems. However, existing NeSy frameworks typically require either predefined symbolic policies or policies that are differentiable, limiting their applicability when domain expertise is unavailable or when policies are inherently non-differentiable. We propose a framework that addresses this limitation by enabling the concurrent learning of both non-differentiable symbolic policies and neural network weights through an evolutionary process. Our approach casts NeSy systems as organisms in a population that evolve through mutations (both symbolic rule additions and neural weight changes), with fitness-based selection guiding convergence toward hidden target policies. The framework extends the NEUROLOG architecture to make symbolic policies trainable, adapts Valiant's Evolvability framework to the NeSy context, and employs Machine Coaching semantics for mutable symbolic representations. Neural networks are trained through abductive reasoning from the symbolic component, eliminating differentiability requirements. Through extensive experimentation, we demonstrate that NeSy systems starting with empty policies and random neural weights can successfully approximate hidden non-differentiable target policies, achieving median correct performance approaching 100%. This work represents a step toward enabling NeSy research in domains where the acquisition of symbolic knowledge from experts is challenging or infeasible.