{"paper":{"title":"Per-Token Fixed-Point Convergence in Depth-Recurrent Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Joe Logan","submitted_at":"2026-07-15T23:38:44Z","abstract_excerpt":"A depth-recurrent transformer applies a weight-tied core a variable number of times, and prior work has shown that training with a randomized recursion count yields one checkpoint usable across a range of inference depths. We ask what such a model actually computes per token, and measure it directly. On a 135M-class model trained on FineWeb-Edu, the recurrent state converges to a per-token fixed point: mean successive-output KL divergence falls from 3.9e-1 at the second loop to 8.5e-6 by the sixteenth, and per-token state change decays in step. Crucially, this convergence is not uniform across"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14427","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/2607.14427/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"}