We introduce neural networks for end-to-end differentiable theorem proving that operate 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 facts, (iii) induce logical rules, and (iv) use provided and induced logical rules for complex multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.
For instance, end-to-end differentiable proving REF replaces traditional unification with a trained neural network and demonstrates the efficacy of this approach for knowledge base completion.
End-to-end Differentiable Proving
ArXiv
ArXiv
Computer Science