# At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics

arXiv: https://arxiv.org/abs/2607.06639 · HTML: https://mlsanity.com/paper/2607.06639/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Omnigrok: Grokking Beyond Algorithmic Data](https://mlsanity.com/paper/2210.01117/) (2022)
- [Explaining grokking through circuit efficiency](https://mlsanity.com/paper/2309.02390/) (2023)
- [Grokking as the Transition from Lazy to Rich Training Dynamics](https://mlsanity.com/paper/2310.06110/) (2023)
- [Approaching Deep Learning through the Spectral Dynamics of Weights](https://mlsanity.com/paper/2408.11804/) (2024)
- [Relating Regularization and Generalization through the Intrinsic Dimension of Activations](https://mlsanity.com/paper/2211.13239/) (2022)
- [The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure](https://mlsanity.com/paper/2602.18523/) (2026)
- [Early-Warning Signals of Grokking via Loss-Landscape Geometry](https://mlsanity.com/paper/2602.16967/) (2026)
- [The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization](https://mlsanity.com/paper/2603.13331/) (2026)
- [Mechanistic Insights into Grokking from the Embedding Layer](https://mlsanity.com/paper/2505.15624/) (2025)
- [A Systematic Empirical Study of Grokking: Depth, Architecture, Activation, and Regularization](https://mlsanity.com/paper/2603.25009/) (2026)
- [Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networks](https://mlsanity.com/paper/2606.17120/) (2026)
- [Grokking as Dimensional Phase Transition in Neural Networks](https://mlsanity.com/paper/2604.04655/) (2026)
- [Late-Stage Generalization Collapse in Grokking: Detecting anti-grokking with Weightwatcher](https://mlsanity.com/paper/2602.02859/) (2026)
- [ILDR: Geometric Early Detection of Grokking](https://mlsanity.com/paper/2604.20923/) (2026)
- [Topological Signatures of Grokking](https://mlsanity.com/paper/2605.06352/) (2026)
- [Distributional Spectral Diagnostics for Localizing Grokking Transitions](https://mlsanity.com/paper/2605.08237/) (2026)
- [Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics](https://mlsanity.com/paper/2605.20441/) (2026)
- [Learned Structure Shows Up Earlier in the Task's Own Basis: A Controlled Look at a Synchronisation Precursor in Grokking](https://mlsanity.com/paper/2606.12966/) (2026)
- [Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View](https://mlsanity.com/paper/2606.04405/) (2026)

## Built on by (most cited first, 1 of 1)

- [Small Enough to Know Everything: The Fully-Enumerable Transformer as an Instrument for the Science of Delayed Generalization](https://mlsanity.com/paper/2609.20166/) (2026)

## Abstract (arXiv)

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 by 1.3-1.5x on a transformer trained to convergence; on the MLP it also erases which cells compress at all. Compression lags 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 shows what sets the lag size: adding LayerNorm to an otherwise identical transformer moves the fraction of compression done 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. 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.