Beyond Neural Collapse: Geometric Configurations of Deep Networks Trained with Mixup
Bibliographic record
Abstract
Neural Collapse is a phenomenon in which the last-layer activations and classifier of deep networks collapse to the geometric configuration of a simplex equiangular tight frame (ETF). The prominence of Neural Collapse prompts us to consider whether similar or alternate configurations occur with other training processes. Mixup is a straightforward data augmentation technique that involves taking convex combinations of training examples along with their labels. It has been shown to improve generalization and calibration of deep networks. However, despite much effort, it is still not fully clear how and why mixup works. In an attempt to better understand mixup, we examine the last-layer activations of training data for deep networks trained with mixup. We find that across various architecture and dataset pairs, the last-layer activations of mixup training data predominantly converges to a specific configuration. This configuration can be characterized by the clustering of same-class mixup activations (from mixed up examples of the same class) aligning with the classifier as a simplex ETF, and different-class mixup activations (from mixed up examples of different classes) forming what we refer to as ``channels" running in between the clusters of same-class activations. To corroborate our empirical findings, we also analyze this phenomenon under an unconstrained features model assumption using the mixup loss. We derive and characterize the optimal last layer features, leading to a configuration that aligns with our experimental results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".