LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs

Key points

• Mathematicians value proofs for more than correctness: among correct proofs, simplicity, purity and the computational cost of finding them vary widely.1
• LEVER scores partial proofs over an AND/OR proof graph, combining realized objective values with predictions for open subgoals, so the objective guides search before a proof is complete.1
• The same mechanism optimizes computational cost, proof length, topical impurity, and even their weighted combinations, while the Lean kernel enforces correctness.1
• Overall, LEVER is a performant, cost-efficient and tunable proof search algorithm for navigating the space of correct proofs.1

Sources (1)

• [1]LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 12:40 PM

  We propose LEVER, a proof search algorithm that makes the objective over correct proofs programmable and optimizes it during search.

  Mathematicians value proofs for more than correctness: among correct proofs, simplicity, purity and the computational cost of finding them vary widely.

Extractive summary: sentences quoted from the sources.