Proof of a perfect platonic representation hypothesis

arxiv:2507.01098

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Representation alignment · 2025-07-01

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1. Part 1
2. Part 2
3. Part 3
4. Part 4

Contents

• Proof of a perfect platonic representation hypothesis
• Abstract
• 1 Introduction
• 2 Problem Setting
• Notation.
• Platonic Representation Hypothesis.
• Definition 1 .
• Model.
• Data and loss function.
• Entropic loss due to SGD training.
• Main result.
• Theorem 1 .
• 3 Most global minima are not platonic
• 4 Proof
• Remark .
• 5 What breaks the perfect plato?
• Weight Decay Breaks PRH.
• Gradient Flow Breaks PRH.
• Label Transformations Breaks PRH.
• Convergence to Saddle or Local Minima Breaks the PRH.
• Data Discrepancy / Heterogeneity Breaks the PRH.
• Edge of Stability (EOS) breaks PRH.
• 6 Discussion
• Cause of the Platonic Representation Hypothesis.
• Imperfect Platonic Representation Hypothesis.
• Emergent Invariances in Learning Algorithms.
• Universal Phenomena and Unified Theories.
• Feature Learning and Infinitesimal Learning Rate.
• More Technical Implications.
• Acknowledgement