Section 8.5, paragraph 2Empirical evidence of a remaining learning bottleneck alongside the representational theorem
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
The restoration experiment makes this distinction tangible. Even with transition information and correct supervision, learning passes through an intermediate plateau before reaching near-perfect measured accuracy. The checkpoint diagnostic in Section 7.2 associates the later improvement with the lowest bit of the selected move’s XOR change. We therefore have empirical evidence of a remaining learning bottleneck that is largely overcome in this run, alongside a theorem about a different, representational obstruction. The data do not establish how many distinct learning mechanisms produce the stages or why the transitions occur.
Generated from paper_jmlr.tex, lines 1259–1259.
2 Explain this
The restoration experiment illustrates the gap: even with transition information and correct labels, learning passes through a plateau before becoming near-perfect, and the diagnostic ties the later improvement to the lowest bit of the selected move's change. So there is empirical evidence of a remaining learning bottleneck, alongside a theorem about a different, representational obstruction. How many mechanisms produce the stages, and why, is not established.
3 How this is formalised
An interpretation of the empirical records Section 7.2.5, “Learning in stages: the plateau and subsequent improvement” and Section 7.2.5, paragraph 2.
| Paper anchor | sec:opt-gap-p2 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 8.5, paragraph 2 |
| Claim | Empirical evidence of a remaining learning bottleneck alongside the representational theorem |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 1259–1259; SHA-256 of the normalised block source 0acee1d20e77ffe4… |
| Depends on | Section 7.2.5, “Learning in stages: the plateau and subsequent improvement”, Section 7.2.5, paragraph 2 |
| Explanations | explain/c-opt-gap-evidence, formal/c-opt-gap-evidence |
| 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).