{"paper":{"title":"Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Converging to common minima across data sources during pretraining improves downstream generalization even at identical loss values.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Huanran Chen, Huaqing Zhang, Jun Zhu, Ke Shen, Xiao Li, Yinpeng Dong","submitted_at":"2026-04-10T12:17:18Z","abstract_excerpt":"The foundational capabilities of large language models are acquired during pretraining on internet-scale, highly heterogeneous data mixtures. In this work, we investigate an interesting geometric question regarding the converged state of pretraining: Does the model converge to a common minimizer across all data sources (e.g., \\cref{fig:cwa_illustration:close}), or merely a minimizer of the summed loss (e.g., \\cref{fig:cwa_illustration:distant})? We hypothesize that the geometric \"closeness\" of task-specific minima is intrinsically linked to downstream generalization. We reveal that standard op"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Nexus significantly boosts downstream performance, despite achieving the same pretraining loss. Notably, on the 3B model, Nexus reduces the out-of-distribution loss by 0.012 and yields up to a 15.0% accuracy improvement on complex reasoning tasks (e.g., GSM8k).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The geometric closeness of task-specific minima is intrinsically linked to downstream generalization, and that maximizing gradient similarity during optimization produces this closeness.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Nexus optimizer improves LLM downstream performance by converging to common minima across data sources despite identical pretraining loss.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Converging to common minima across data sources during pretraining improves downstream generalization even at identical loss values.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a584887b95800e03e044bfd266dd9f91be2c62b2cc57f44f5fd665782b17d358"},"source":{"id":"2604.09258","kind":"arxiv","version":2},"verdict":{"id":"d3ba602d-47e6-4b65-9d4a-d0b8d58839f6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:50:26.241619Z","strongest_claim":"Nexus significantly boosts downstream performance, despite achieving the same pretraining loss. Notably, on the 3B model, Nexus reduces the out-of-distribution loss by 0.012 and yields up to a 15.0% accuracy improvement on complex reasoning tasks (e.g., GSM8k).","one_line_summary":"Nexus optimizer improves LLM downstream performance by converging to common minima across data sources despite identical pretraining loss.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The geometric closeness of task-specific minima is intrinsically linked to downstream generalization, and that maximizing gradient similarity during optimization produces this closeness.","pith_extraction_headline":"Converging to common minima across data sources during pretraining improves downstream generalization even at identical loss values."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.09258/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":2,"snapshot_sha256":"061188b7996e67bdbad99c3626f52832ce173c1e1b7cc37dd2c29826c484c4aa"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}