A Training-Time Diagnostic for Generalization via the Log-Alignment Ratio
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 effective dimension of the learned function: $k \approx n^{2(1-\text{LAR})}$, where $n$ is the input dimension of the matrix. In 3B-parameter la...
| Authors | Ali Shehper, Ashish Vaswani |
|---|---|
| Primary category | cs.LG |
| Published | 27 May 2026 |
| Last updated at source | 27 May 2026 |
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