{"paper":{"title":"On the Residual Scaling of Looped Transformers: Stability and Transferability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bingrui Li, Ge Zhang, Jian Li, Shaowen Wang, Shen Yan, Wenhao Huang","submitted_at":"2026-06-16T22:39:13Z","abstract_excerpt":"Looped (weight-tied) Transformers apply a shared residual block $N$ times ($h \\leftarrow h + \\varepsilon\\,f(h)$, same $f$ at each step), increasing effective depth without adding parameters. Prior depth-scaling analyses prescribe $\\varepsilon = 1/\\!\\sqrt{L}$ for depth-$L$ residual networks. We show that this is insufficient for looped architectures: weight sharing makes residual updates correlated across iterations, requiring the stronger scaling $\\varepsilon = 1/N$. For multi-layer blocks ($L$ unique layers looped $N$ times), we derive a factored parameterization $\\varepsilon = \\lambda/(N\\!\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18524","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/2606.18524/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"}