Grokking Metrics Overstate Compression, Lag Generalization

Truong Xuan Khanh· July 9, 2026 View original

Summary

This study reveals that common metrics for "grokking" in neural networks, such as effective rank, significantly overstate the true compression achieved at the grokking transition and lag behind the network's generalization by thousands of steps. It introduces an audit framework to accurately measure representation compression.

New research critically examines the measurement of "grokking," a phenomenon where neural networks generalize long after achieving zero training error. The study finds that metrics like effective rank, often used to quantify representation compression during grokking, are misleading. Specifically, they overstate the converged compression by a factor of 3-5x in MLPs and 1.3-1.5x in transformers when measured at the grokking transition. Furthermore, the research demonstrates that representation compression lags behind the accuracy transition by at least 10,000 steps, rather than coinciding with it. The presence of LayerNorm, for instance, significantly impacts this lag. To address these measurement issues, the authors propose a robust audit framework designed to separate the onset of generalization from actual compression, flag censoring, exclude non-generalizing cells, and ensure reference floors have plateaued.

Why it matters

Accurate measurement of grokking and representation compression is crucial for understanding how neural networks learn and generalize, impacting model design and training strategies.

How to implement this in your domain

  1. 1Apply the proposed audit framework to evaluate grokking and representation compression in your own neural network experiments.
  2. 2Re-evaluate existing research findings on grokking, considering the potential for overstated compression metrics.
  3. 3Investigate the impact of architectural choices like LayerNorm on the timing and extent of representation compression.
  4. 4Develop training strategies that explicitly account for the lag between generalization and full representation compression.

Who benefits

AI/ML ResearchSoftware DevelopmentData Science

Key takeaways

  • Grokking metrics like effective rank often overstate true representation compression.
  • Representation compression significantly lags behind a network's generalization phase.
  • Architectural components like LayerNorm can influence the timing of compression.
  • A new audit framework is proposed for more accurate measurement of grokking phenomena.

Original post by Truong Xuan Khanh

"arXiv:2607.06639v1 Announce Type: new Abstract: On modular arithmetic, a network's embedding keeps compressing for tens of thousands of steps after it has already generalized. Reading effective rank at the grokking transition overstates the converged value by 3-5x on an MLP, and…"

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