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End-to-end Differentiable Proving
Tim Rocktäschel · Sebastian Riedel

Wed Dec 06 10:50 AM -- 11:05 AM (PST) @ Hall C

We introduce deep neural networks for end-to-end differentiable theorem proving that operate on dense vector representations of symbols. These neural networks are recursively constructed by following 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. The resulting neural network can be trained to infer facts from a given incomplete knowledge base using gradient descent. By doing so, 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) it can use provided and induced logical rules for complex multi-hop reasoning. On four benchmark knowledge bases we demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, while at the same time inducing interpretable function-free first-order logic rules.

Author Information

Tim Rocktäschel (University of Oxford)

Tim is a Researcher at Facebook AI Research (FAIR) London, an Associate Professor at the Centre for Artificial Intelligence in the Department of Computer Science at University College London (UCL), and a Scholar of the European Laboratory for Learning and Intelligent Systems (ELLIS). Prior to that, he was a Postdoctoral Researcher in Reinforcement Learning at the University of Oxford, a Junior Research Fellow in Computer Science at Jesus College, and a Stipendiary Lecturer in Computer Science at Hertford College. Tim obtained his Ph.D. from UCL under the supervision of Sebastian Riedel, and he was awarded a Microsoft Research Ph.D. Scholarship in 2013 and a Google Ph.D. Fellowship in 2017. His work focuses on reinforcement learning in open-ended environments that require intrinsically motivated agents capable of transferring commonsense, world and domain knowledge in order to systematically generalize to novel situations.

Sebastian Riedel (University College London)

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