Dual Perspectives on Non-Contrastive Self-Supervised Learning
Bibliographic record
Abstract
The {\em stop gradient} and {\em exponential moving average} iterative procedures are commonly used in non-contrastive approaches to self-supervised learning to avoid representation collapse, with excellent performance in downstream applications in practice. This presentation investigates these procedures from the dual viewpoints of optimization and dynamical systems. We show that, in general, although they {\em do not} optimize the original objective, or {\em any} other smooth function, they {\em do} avoid collapse Following~\citet{Tian21}, but without any of the extra assumptions used in their proofs, we then show using a dynamical system perspective that, in the linear case, minimizing the original objective function without the use of a stop gradient or exponential moving average {\em always} leads to collapse. Conversely, we characterize explicitly the equilibria of the dynamical systems associated with these two procedures in this linear setting as algebraic varieties in their parameter space, and show that they are, in general, {\em asymptotically stable}. Our theoretical findings are illustrated by empirical experiments with real and synthetic data.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".