Neural-Symbolic Integration with Evolvable Policies

TL;DR

Neural-Symbolic Integration with Evolvable Policies tackles learning non-differentiable symbolic policies alongside neural weights without predefined knowledge. It frames NeSy systems as evolving organisms and uses Machine Coaching semantics, Evolvability theory, and abductive reasoning to train both components concurrently. Experiments across 150 runs with 30 random target policies show median correct performance near 100%, illustrating viability though with higher computational cost than end-to-end baselines. The work advances NeSy research in domains lacking expert symbolic knowledge by enabling interpretable policy induction through evolution.

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.

Figures (20)

• Figure 1: Example symbolic policy structure using Machine Coaching semantics. The policy consists of prioritized rules (increasing in priority from top to bottom), where each rule has a body (sequence of literals) and head (single literal). This example demonstrates the type of non-differentiable shallow propositional policies that our evolutionary framework learns to approximate. This policy is used throughout the paper to demonstrate the framework's operation.
• Figure 2: The NeuroLog NeSy architecture, as proposed by tsamoura2021Neurolog.
• Figure 3: The extended NeuroLog architecture enabling concurrent neural and symbolic learning. Black arrows show forward reasoning (deduction): the deduce() methods of NeuralModule and SymbolicModule are chained via the Translator to produce predictions. Red arrows show neural induction: the NeuralModule trains via backpropagation using abductive feedback from the SymbolicModule's abduce() method, which generates training signals from symbolic rules. Blue arrows show symbolic induction: new rules are added to the SymbolicModule's policy via its induce() method during evolutionary mutations.
• Figure 4: Example of forward reasoning in the extended NeuroLog architecture with a concrete target policy. The input MNIST image sequence is processed by the NeuralModule (CNN), producing symbolic atom predictions via the Translator, which the SymbolicModule uses with its policy (the same policy shown in \ref{['fig:kbExample']}) to generate the final output. This policy represents one of the randomly generated target policies used in the experiments.
• Figure 5: Two training instances from a $\widehat{p\xspace}\xspace_{train}$ dataset labeled by the symbolic policy in \ref{['fig:kbExample']}. Each instance consists of a sequence of 8 MNIST digit images representing atoms: digits with value $1$ () represent positive atoms, digits with value $2$ () represent negative atoms. The label (head or -head) is determined by applying the symbolic policy's rules to the atom sequence.