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[CS.AI] Revealing the Truth about Grokking: A Validity Audit of Representation Metrics

Published at: 2026-07-10 22:00 Last updated: 2026-07-13 08:24
#algorithm #optimization #Neural

In modular arithmetic, a network's embedding continues to compress for tens of thousands of steps even after it has already generalized. Reading the effective rank at the grokking transition overstates the converged value by 3-5x on an MLP and by 1.3-1.5x on a transformer trained to convergence. On the MLP, it also erases which cells are compressing at all. Compression lags behind the accuracy transition by an amount on the order of the time-to-grok, at least 10,000 steps, rather than coinciding with it. A one-variable ablation study shows what sets the lag size: adding LayerNorm to an otherwise identical transformer reduces the fraction of compression completed by the grok step from 0.87 to 0.25, and a pre-registered control rules out scale invariance as the mechanism. We package this as an audit that separates onset from compression, flags censoring, excludes boundary cells that never fully generalize, and checks that the reference floor has plateaued, with an adversarial suite that caught a false-confidence bug in our own branch. Additionally, a secondary, MLP-specific depth law linking norm budget to converged floor fails a generality test on a transformer and flips sign under free weight decay. Code and the toolkit are released.

Original Source: https://arxiv.org/abs/2607.06639

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