The feature-spread experiment published September 14 found that correcting the anti-collapse statistic restored feature spread but did not restore dimensional rank. The corrected-statistic-only variant achieved standard deviation near 1.1, but effective rank stayed at 1.01 to 1.02: features varied, but they varied along a single direction.

What the corrected statistic changed

The original anti-collapse statistic scaled by batch size and used a one-sided trapezoid integral over [0.2, 4]. The corrected version matches the upstream formulation: batch-scaled, full-width integral over [0, 3]. This made the regularization strength consistent across variants, so the same coefficient value applied fairly.

After correction, the feature-spread-only variant showed mean standard deviation of 1.09 to 1.25 across seeds. But effective rank stayed at 1.01 to 1.02. Features varied, but they varied along a single direction.

What the corrected statistic did not change

  • Rank: still near 1 in every seed.
  • Prediction: still worse than constant-predictor and shuffled-target controls.
  • Encoder regularizer: still exceeded the collapsed-reference threshold.

The correction fixed the regularization scale, but it did not add the projector and normalization package that upstream uses. Parameter count stayed at 29,304, not 35,888. Without that package, the model lacks the channel-wise normalization and projection that give features multiple independent directions to vary along.

Why rank matters separately

Standard deviation measures how much features vary; rank measures how broadly that variation is distributed. Several coordinates can vary together along almost the same direction, so high spread coexists with rank near one. Conversely, a higher rank can be an artifact of noise rather than structured diversity. Both statistics are needed to assess whether a model has recovered from collapse.

Reproduction

The experiment used four variants, seeds 17, 29, 43, batch size 32, 600 CPU updates. Development examples changed numeric parameters within four authored arithmetic families. Results are from saved verifier records; the full experiment package (diagnostic code, checkpoints) is not distributed with this note. No new training or evaluation was run for this publication.

Publication disclosure

Implementation, investigation and writing were AI-assisted. Publication review checked hashes of the 12 saved result records and their reported values without loading checkpoints. The evidence summary is at /assets/publications/training-debugging.json. The complete private investigation package remains outside this repository. This note documents a bounded engineering check, not a trained-model result or a new evaluation method.