The Sequence Knowledge - Issue #968: Learning RSI: Mathematics as a Laboratory for Recursive Improvement
AlphaProof and the importance of a trustworthy learning signal
TL;DR
- Language models can produce substantial mathematical output given difficult theorems and sufficient time.
- A major challenge is identifying which generated mathematics is valid and deserves to be retained.
- Systems like AlphaProof, Goedel-Prover-V2, and DeepSeekMath-V2 use a generator-checker framework for recursive improvement.
- This framework involves a generator proposing proof candidates and a checker validating them for training material.
- The feedback mechanism must remain informative as the candidate-generating proposer strengthens.
- Mathematics serves as a useful laboratory because proposals can be independently checked.
- The article touches on Lean's kernel, AlphaProof's approach to exploration and training, and the discoverability of useful theorems.
- It also considers changes when verification itself is learned and the boundary a checker cannot cross (ensuring the stated theorem is the intended one).