Section 7.2.5, paragraph 3Staged acquisition at the output level; no internal mechanism and no 8/15 explanation are established
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
Thus the later improvement is accounted for at the output level by learning to select moves with the correct lowest bit while retaining the already accurate upper bits. This supports staged acquisition of the restoration behaviour. It does not identify an internal representation or explain why optimisation follows this order. Nor does the plateau’s proximity to establish a random-bit guessing mechanism: that baseline assumes a particular distribution and prediction rule. Internal probes, interventions and independent training runs are needed to explain the transition and test its reproducibility.
Generated from paper_jmlr.tex, lines 1131–1131.
2 Explain this
At the level of outputs, the later improvement consists of getting the lowest bit of the change right while keeping the upper bits. That supports "staged acquisition". The paper is careful about what it does not conclude:
- it does not identify an internal representation or explain why optimisation follows this order;
- the plateau's closeness to does not establish a random-bit guessing mechanism (that number assumes a particular distribution and prediction rule);
- probes, interventions and independent runs would be needed.
3 How this is formalised
Interpretation of empirical data. The arithmetic fact (the fraction of nonzero 4-bit nim-sums with lowest bit ) is checked (Section 7.3, paragraph 3 (arithmetic)); whether it has anything to do with the plateau is not established.
| Paper anchor | par-learning-in-stages-the-plateau-and-subsequent-improvement-p3 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 7.2.5, paragraph 3 |
| Claim | Staged acquisition at the output level; no internal mechanism and no 8/15 explanation are established |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 1131–1131; SHA-256 of the normalised block source 6fd5cea90e31d3d6… |
| Depends on | Section 7.2.5, paragraph 2, Section 7.3, paragraph 3 (arithmetic) |
| Explanations | explain/c-plateau-interpretation, formal/c-plateau-interpretation |
| 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).