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Figure 5Saved validation curve: 1F low; 2F plateau near 0.54, then near-perfect

Empirical result Supported by saved experimental runs, not by a proof.

1 Paper text

Line plot titled "Validation accuracy vs epoch (restoration dataset)", epochs 0 to 200 on the horizontal axis, validation accuracy 0 to 1 on the vertical axis, legend "1F val acc" and "2F val acc". The 1F curve stays flat near 0.08 throughout. The 2F curve starts near 0.2, rises to a plateau near 0.54 until roughly epoch 30, rises steeply between roughly epochs 35 and 50, and stays near 1.0 from about epoch 60 to epoch 200.
Figure 5: Validation restoration accuracy vs. epoch on the restoration dataset (N=20N=20, k=4k=4, D=106D=10^6). In this saved run, the 1F model has low accuracy while the 2F model passes through an intermediate plateau around 0.54 before improving sharply towards near-perfect accuracy. The transition suggests a learning bottleneck that training eventually overcomes; it is distinct from the representational lower bound. Values use the saved batch-mean metric.

Generated from paper_jmlr.tex, lines 1110–1116.

2 Explain this

The validation curve, one point per epoch: 1F stays near 0.08; 2F rises quickly to a plateau near 0.54, stays there from about epoch 8 to about epoch 30 in the plot, then climbs steeply to near-perfect accuracy.

The plateau suggests a learning bottleneck that training eventually overcomes. It is a different thing from the representational lower bound: the 2F model can represent the solution, and eventually finds it.

3 How this is formalised

How this is covered. Empirical. The figure is a vector replot of the saved training-history CSV (400 rows; SHA-256 705b6d5d031a…) with no smoothing, subsampling or new experiment, as recorded in the figure provenance file supplied with the manuscript. The edition converts the manuscript's PDF figure to SVG without re-plotting.

Coverage record
Paper anchorfig:valacc-H20k4 (manuscript label)
Displayed asFigure 5
ClaimSaved validation curve: 1F low; 2F plateau near 0.54, then near-perfect
Coverage categoryEmpirical result
Statement sourcepaper_jmlr.tex lines 1110–1116; SHA-256 of the normalised block source 1a2357a8e3237237…
Explanationsexplain/fig:valacc-H20k4, formal/fig:valacc-H20k4
Build evidencefresh isolated rebuild, audit report

4 Lean statement and source

No Lean statement corresponds to this claim. This is an empirical statement about saved experimental runs. Lean proofs do not certify training runs, curves or checkpoints.

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).