{"paper":{"title":"At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Truong Xuan Khanh","submitted_at":"2026-07-07T14:44:18Z","abstract_excerpt":"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 th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06639","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06639/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}