Learning Axioms to Compute Verifiable Symbolic Expression Equivalence Proofs Using Graph-to-Sequence Networks

We target the problem of proving the semantic equivalence between two complex expressions represented as typed trees, and demonstrate our system on expressions from a rich multi-type symbolic language for linear algebra. We propose the first graph-to-sequence deep learning system to generate axiomatic proofs of equivalence between program pairs. We generate expressions which include scalars, vectors and matrices and 16 distinct operators combining them, with 147 distinct axioms of equivalence. We study the robustness of the system to generate proofs of increasing length, demonstrating how incremental graph-to-sequence networks can learn to represent complex and verifiable symbolic reasoning. It achieves 93% average true positive coverage on 10,000 test cases while ensuring zero false positives by design.