End-to-End Differentiable Proving

TL;DR

This paper presents a neural network architecture for end-to-end differentiable logical proving that combines symbolic reasoning with vector representations, enabling learning and inference on knowledge bases.

Contribution

It introduces a recursive neural network inspired by backward chaining, replacing unification with differentiable computations, and demonstrates improved performance and rule induction.

Findings

Outperforms ComplEx on three of four benchmarks

Learns to embed similar symbols close in vector space

Induces interpretable logical rules

Abstract

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.