{"paper":{"title":"Momentum Streams for Optimizer-Inspired Transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Jiayun Wu, Jingchu Gai, Nai-Chieh Huang","submitted_at":"2026-05-23T06:40:27Z","abstract_excerpt":"The residual update of a pre-norm Transformer layer admits an interpretation as one step of a first-order optimizer acting on a surrogate token energy, wherein the attention and MLP sublayers function as gradient oracles. Based on this observation, we build a family of optimizer-inspired Transformers (triple-momentum, Adam/AdamW, Muon, SOAP) and compare them under matched compute. In our main pretraining experiment, the triple-momentum TMMFormer achieves the lowest validation loss, outperforming the vanilla Transformer and prior architectural variants. A controlled ablation and supporting theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24425","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/2605.24425/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"}