57 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
The Role of Entropy in Guiding a Connection Prover
In this work we study how to learn good algorithms for selecting reasoning
steps in theorem proving. We explore this in the connection tableau calculus
implemented by leanCoP where the partial tableau provides a clean and compact
notion of a state to which a limited number of inferences can be applied. We
start by incorporating a state-of-the-art learning algorithm -- a graph neural
network (GNN) -- into the plCoP theorem prover. Then we use it to observe the
system's behaviour in a reinforcement learning setting, i.e., when learning
inference guidance from successful Monte-Carlo tree searches on many problems.
Despite its better pattern matching capability, the GNN initially performs
worse than a simpler previously used learning algorithm. We observe that the
simpler algorithm is less confident, i.e., its recommendations have higher
entropy. This leads us to explore how the entropy of the inference selection
implemented via the neural network influences the proof search. This is related
to research in human decision-making under uncertainty, and in particular the
probability matching theory. Our main result shows that a proper entropy
regularisation, i.e., training the GNN not to be overconfident, greatly
improves plCoP's performance on a large mathematical corpus
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