Section 1, paragraph 4Earlier experiments (Zhou and Riis) found AlphaZero-style learning deteriorating on larger NIM boards
External cited result A published result used as background or input; not proved in Lean here.
1 Paper text
Our earlier work with Bei Zhou provides the empirical starting point. In Impartial Games: A Challenge for Reinforcement Learning, Zhou and Riis found that AlphaZero-style learning deteriorated as NIM boards grew (Zhou and Riis, 2026). Subsequent parity experiments examined how noisy labels can obstruct curriculum learning (Zhou and Riis, 2023); see also Zhou’s thesis (Zhou, 2024). These findings make parity a useful test of the gap between learning familiar patterns and discovering an exact rule that works across positions.
Generated from paper_jmlr.tex, lines 89–89.
2 Explain this
This paragraph places the paper in the author's earlier work. Zhou and Riis trained AlphaZero-style agents on impartial games and observed that performance on NIM deteriorated as boards grew. A follow-up study looked at parity tasks learned through a curriculum with noisy labels, and Zhou's thesis collects the work.
Why it matters here: those observations motivate the question of the paper, namely why a game with a short, exact solution rule can still be hard for a learner. The present paper does not re-run those experiments.
3 How this is formalised
This is a report of published empirical work, cited as background (Zhou and Riis, 2026, first preprint 2022; Zhou and Riis, 2023; Zhou, 2024). Nothing in the Lean development concerns it, and the edition does not re-examine those experiments.
| Paper anchor | c-intro-zhou (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 1, paragraph 4 |
| Claim | Earlier experiments (Zhou and Riis) found AlphaZero-style learning deteriorating on larger NIM boards |
| Coverage category | External cited result |
| Statement source | paper_jmlr.tex lines 89–89; SHA-256 of the normalised block source 786121a9079b86bf… |
| Explanations | explain/c-intro-zhou, formal/c-intro-zhou |
| Build evidence | fresh isolated rebuild, audit report |
4 Lean statement and source
No Lean statement corresponds to this claim. This is a published classical result. It is cited, not proved in this Lean development.
Build evidence: fresh isolated rebuild of all 38 bundled modules with Lean (version 4.26.0, started 2026-10-10T15:21:56Z, finished 2026-10-10T15:27:00Z: 38/38 modules compiled, 1588 axiom reports, no errors. See Build for the commands and the independent audit of 2026-10-10 (dated evidence).