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Feature Normalization Prevents Collapse of Noncontrastive Learning Dynamics.

Han Bao1

  • 1The Institute of Statistical Mathematics, Tokyo 190-8562, Japan bao.han@ism.ac.jp.

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|August 14, 2025
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Summary

Feature normalization is crucial for preventing collapse in noncontrastive learning. This study shows cosine loss, unlike L2 loss, induces stable dynamics, ensuring robust representation learning without negative examples.

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Computer Science

Background:

  • Contrastive learning uses positive and negative examples to learn representations.
  • Noncontrastive learning methods like BYOL and SimSiam eliminate negative examples for efficiency.
  • Previous theories suggested strong data augmentation prevents collapse in noncontrastive learning.

Purpose of the Study:

  • To analyze the dynamics of noncontrastive learning with feature normalization.
  • To extend existing theories by incorporating cosine loss and feature normalization.
  • To understand how feature normalization prevents representation collapse.

Main Methods:

  • Theoretical analysis of learning dynamics.
  • Extension of L2 loss-based theory to cosine loss.
  • Mathematical modeling of representation collapse and stable equilibria.

Main Results:

  • Cosine loss, unlike L2 loss, induces higher-order (sixth-order) dynamics.
  • Feature normalization is shown to be critical in preventing representation collapse.
  • A stable equilibrium emerges dynamically, even with initially collapsed solutions.

Conclusions:

  • Feature normalization plays a vital role in the robust prevention of collapse in noncontrastive learning.
  • The cosine loss, incorporating feature normalization, offers a more stable learning dynamic.
  • This work provides new theoretical insights into self-supervised representation learning.