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Oct 11, 2023 •188 likes •304 views

HOList: An Environment for Machine Learning of Higher-Order Theorem Proving Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, Stewart Wilcox Google Research Can we create a human level AI to reason about mathematics? HOList

HOList: An Environment for Machine Learning of Higher-Order Theorem Proving Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, Stewart Wilcox Google Research
Can we create a human level AI to reason about mathematics?
HOList An Environment for Machine Learning of Higher-Order Theorem Proving ● HOList provides a simple API for ML researchers and theorem prover developers to experiment with using machine learning for mathematics. ● We use deep networks trained on an existing corpus of human proofs to guide the prover. ● We can improve our results by adding synthetic proofs (generated from supervised models and verified correct by the prover) to the training corpus.
APIs for Theorem Prover Developers and ML Researchers Proof Assistant One goal/subgoal to prove One proof step: Tactic application, relevant premises Subgoals or *proved* Proof Search Ranking of tactics and premises One goal/subgoal to prove Machine Learning
Results - Supervised Learning on Human Proofs Percent of Validation Theorems Closed Baseline : ASM_MESON_TAC 6.10% ASM_MESON_TAC + WaveNet premise selection 9.20% Wavenet 31.72% Deeper WaveNet 32.65% Wider WaveNet 27.60%
Results - Supervised Learning on Human Proofs Percent of Validation Theorems Closed Baseline : ASM_MESON_TAC 6.10% ASM_MESON_TAC + WaveNet premise selection 9.20% Wavenet 31.72% Deeper WaveNet 32.65% Wider WaveNet 27.60%
Results - Supervised Learning on Human Proofs Percent of Validation Theorems Closed Baseline : ASM_MESON_TAC 6.10% ASM_MESON_TAC + WaveNet premise selection 9.20% Wavenet 31.72% Deeper WaveNet 32.65% Wider WaveNet 27.60%
Results - Prover in the loop * Percent Closed Wavenet Loop 36.30% - Trained on loop output 36.80% Tactic Dependent Loop 38.90%
APIs for Theorem Prover Developers and ML Researchers Proof Assistant One goal/subgoal to prove One proof step: Tactic application, relevant premises Subgoals or *proved* Proof Search Ranking of tactics and premises One goal/subgoal to prove Machine Learning
APIs for Theorem Prover Developers and ML Researchers Supervised Prover Proof Search Learning - Manages the state of the Training Data: HOL-Light proof search tree. TF Examples from - Allows arbitrary nodes to Human & Synthetic Proofs Input: be explored. - Load premises Features: - Apply a tactic to a goal - Goal (or subgoal) Output: Labels: - Open goals left to prove - Tactic applied - Premises used
deephol.org ● Code is available on GitHub ● Training data ○ 30K theorems and definitions In the areas of: topology, multivariate calculus, real and complex analysis, geometric algebra, measure theory, etc., as well as the formal proof of the Kepler Conjecture. ○ 375K human proof steps ○ 830K synthesized proof steps ● Trained model checkpoints ● Docker images for the proof assistant and proof search

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