Enhancing Knowledge Graph Embedding's via Logic Regularized Graph Neural Networks

Abstract

In (high)-dimensional data, deep learning-based Knowledge Graph Embedding (KGE) models have shown better capacity in learning the true pattern of latent features. However, they are typically used as "black boxes", where statistical correlation is preferred over explicit logical inference. These are geometrically feasible but semantically invalid predictions, do not satisfy self-explaining constraints. In this paper, we present an Logic Regularized Graph Neural Network (LRGNN) as a neuro-symbolic framework to bridge the gap between the expressive power of deep learning and formal logic's semantic-accuracy. In contrast to traditional non-differentiable logic based approaches where logic and learning are separated, we introduce a new child-sum product T-norm loss that is differentiable into the learning objectives. We wish to extract high confidences compositional rules (e.g. triangle patterns) explicitly from data, and use them as constraints to control the optimization landscape – this is because it seems impossible for humans to learn all patterns and effects purely by observation of training data. As one can see from the experiments on the FB15k-237 benchmark, even after removing all previous feature information for shallow logic inference, LR-GNN still keeps a competitive training convergence (Loss: 0.0349) and sufficiently testified that the logic with confidence (99.56%). these findings affirm that neuro symbolic regularization in practice prunes the embedding space of logically invalid relations, yielding a robust and interpretable alternative to fully data driven models.