arXiv AI By Truong Xuan Khanh

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

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arXiv:2607. 06639v1 Announce Type: cross Abstract: On modular arithmetic, a network's embedding keeps compressing for tens of thousands of steps after it has already generalized.

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Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers

Grokking -- where a transformer on modular arithmetic suddenly transitions from near-chance to near-perfect validation accuracy -- is attributed to a Fourier circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior circuit knowledge.