Classes tighten.
Their means spread evenly.

Advance late-stage training and watch within-class features collapse toward their means, class means approach a simplex, and classifier directions align with that geometry.

Penultimate-layer features

Samples, class means, and classifier directions
MID TRAINING
Within-class variance0.62
Mean norm spread0.28
Simplex error0.58
Nearest-center agreement72%

Terminal training produces coordinated geometry.

After training error reaches zero, features may continue reorganizing. Within each class they concentrate, centered class means become equal-norm and maximally separated, classifier weights align with those means, and decisions approach nearest-class-center classification.

NC1: within-class variability collapses.

Samples from the same class approach a common feature mean relative to between-class separation.

NC2: means form a simplex ETF.

Centered class means become equal-norm with equal pairwise angles.

NC3: classifier weights align.

Last-layer directions become proportional to centered class means.

NC4: decisions simplify.

The classifier behaves like nearest-center classification in feature space.

Imbalance can break symmetry.

Minority classes may exhibit norm and angular distortions, producing minority collapse.

Measure every signature separately.

Track after interpolationCollapse is a terminal-phase phenomenon, so zero error is not the stopping point.
Center class meansSimplex claims require subtracting the global mean and checking norms and angles.
Stress imbalanceReport per-class variance, norm, accuracy, and minority behavior.

Primary sources behind the lab.

These papers establish the phenomenon, theoretical accounts, extensions beyond balanced classification, and minority-collapse behavior.

FOUNDATIONAL

Prevalence of Neural Collapse During the Terminal Phase of Deep Learning Training

Defines the four canonical collapse properties.

THEORY

A Geometric Analysis of Neural Collapse

Analyzes simplex geometry and classifier alignment.

LANDSCAPE

Neural Collapse Under MSE Loss

Studies global minimizers and collapse geometry.

IMBALANCE

Exploring Neural Collapse under Imbalanced Data

Introduces minority collapse and symmetry breaking.

Export the geometry audit.

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