NC4 stayed stable
Nearest-centre and classifier decisions did not diverge after clean interpolation.
REPRODUCIBLE ML · v1.0.0
When a network fits perfectly, what keeps moving?
Watch ten digit classes reorganize inside a neural network—then test whether cleaner geometry really means better generalization to unseen writers.
- Dataset
- UCI Optical Digits
- Evidence
- 30 neural runs
- Boundary
- One writer-disjoint split
Does neural-collapse geometry continue after zero training error—and does more collapse consistently predict better held-out performance?
CHECKPOINTS, NOT A CARTOON
Geometry theatre
Every stop is a saved model state. Motion between stops is visual interpolation only.
training
held-out
class mean
misclassified
Left: a two-dimensional projection. Right: pairwise cosines of centred class means in the full hidden space; pale lines are closer to the ideal off-diagonal value −1/9.
NC1 · variability ↓—
NC2 · simplex deviation ↓—
NC3 · self-duality gap ↓—
NC4 · decision disagreement ↓—
Held-out accuracy ↑—
PRESPECIFIED DECISIONS
A partial confirmation is the result.
Two gates passed. Two narrowly missed. Nothing was redefined after the run.
Imbalance bent the simplex
Every paired long-tail run had worse final NC2 than its clean counterpart.
NC1 kept improving
The direction was common, but not common enough for the frozen 8/10 gate.
NC2 kept improving
Simplex proximity was not seed-universal after the first zero-error epoch.
THE USEFUL CONTRADICTION
One geometry score is not a certificate.
NC1 ↔ accuracy−0.518
Moderate descriptive rank association across 30 runs.
NC2 ↔ accuracy−0.026
Almost no descriptive rank association across 30 runs.
The noisy-label MLP generalized much worse while its median NC2 was slightly lower than clean. That does not disprove neural collapse. It shows why collapse must be read as a multi-coordinate, regime-dependent phenomenon.
Read the complete interpretation →REPRODUCTION MAP
What is measured—and what is not.
- 01
Freeze
Question, data split, model, seeds, checkpoints, metrics, and gates were written before retrieval.
- 02
Stress
Clean labels, a deterministic long tail, and exactly 20% classwise symmetric corruption.
- 03
Measure
NC1–NC4 in nine dimensions; prediction quality on official unseen writers.
- 04
Stop at the boundary
Seeds describe optimization sensitivity, not a population of tasks, people, or architectures.