arXiv:2605.28975v1 Announce Type: new Abstract: We study the log-alignment ratio (LAR), a measure of parameter-activation alignment, introduced in parameterization theory. We reformulate it as the overlap between a weight spectrum $p$ of the normalized squared singular values of a matrix and an activation spectrum $q$ of the normalized squared projections of inputs onto its singular directions. We show that unembedding LAR tracks the transition between memorization and generalization in two different settings by capturing the spread of $p$ and $q$ during training. In grokking, LAR predicts the
The continuous drive to understand and debug complex AI models mandates new diagnostic tools, and the theoretical foundation provided by parameterization theory is maturing.
A diagnostic for generalization vs. memorization during AI training could significantly improve model development, efficiency, and reliability, accelerating AI progress.
The ability to track generalization in real-time during training offers a more systematic way to optimize model architecture and training procedures.
- · AI researchers
- · Machine learning engineers
- · Deep learning framework developers
- · Companies deploying AI models
- · Trial-and-error AI development methodologies
Faster and more robust development cycles for advanced AI models.
Improved explainability and reduced 'black box' issues in AI, leading to broader adoption in critical applications.
Potentially less compute-intensive AI training if generalization can be achieved more efficiently and demonstrably.
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