Section 5.3.1, paragraph 3The significance of two frames for learning is representational
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
The significance for learnability is representational. A two-frame policy network can condition its response on and hence on the locally computable , while a single-frame policy must reconstruct the relevant global information from alone. The experiments in Section 7 examine this contrast through supervised restoration learning and imitation-trained rollout policies. The reported networks are policy-only; these results do not establish that self-play discovers the constructions.
Generated from paper_jmlr.tex, lines 612–612.
2 Explain this
The advantage of two frames is about what a network can represent: a two-frame policy can condition on the locally computable difference, while a single-frame policy must reconstruct the global invariant from one board.
3 How this is formalised
An interpretive paragraph; the formal contrast is Proposition 5.5 versus Theorem 5.2 (barrier).
The reported Section 7 results concern supervised restoration and imitation-trained rollout policies, with no value head (Section 7.1). They do not establish self-play discovery. An auxiliary MCTS tournament exists in the restoration notebook, but it is separate from those reported results and is not self-play training. The manuscript's earlier reference to experimental policy/value networks was corrected in the focused revision.
| Paper anchor | par-interpretation-mirror-the-delta-p3 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 5.3.1, paragraph 3 |
| Claim | The significance of two frames for learning is representational |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 612–612; SHA-256 of the normalised block source 5b4c91a026ba8def… |
| Depends on | Proposition 5.5, Theorem 5.2 (barrier) |
| Explanations | explain/c-mcts-sentence, formal/c-mcts-sentence |
| Build evidence | fresh isolated rebuild, audit report |
4 Lean statement and source
No Lean statement corresponds to this claim. This is interpretation or motivation, not a formal mathematical claim.
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).