Reduced Implication-Bias Logic Loss for Neuro-Symbolic Learning

Abstract

Integrating logical reasoning and machine learning by approximating logical inference with differentiable operators is a widely used technique in the field of Neuro-Symbolic Learning. However, some differentiable operators could introduce significant biases during backpropagation, which can degrade the performance of Neuro-Symbolic systems. In this paper, we demonstrate that the loss functions derived from fuzzy logic operators commonly exhibit a bias, referred to as Implication Bias. To mitigate this bias, we propose a simple yet efficient method to transform the biased loss functions into Reduced Implication-bias Logic Loss (RILL). Empirical studies demonstrate that RILL outperforms the biased logic loss functions, especially when the knowledge base is incomplete or the supervised training data is insufficient.