453 research outputs found
End-to-End Differentiable Proving
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.Comment: NIPS 2017 camera-ready, NIPS 201
Learning to Prove Theorems by Learning to Generate Theorems
We consider the task of automated theorem proving, a key AI task. Deep
learning has shown promise for training theorem provers, but there are limited
human-written theorems and proofs available for supervised learning. To address
this limitation, we propose to learn a neural generator that automatically
synthesizes theorems and proofs for the purpose of training a theorem prover.
Experiments on real-world tasks demonstrate that synthetic data from our
approach improves the theorem prover and advances the state of the art of
automated theorem proving in Metamath. Code is available at
https://github.com/princeton-vl/MetaGen
- …