{"paper":{"title":"Geometrically Principled Randomized Optimization for Efficient LLM Training","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nayeema Nonta, Sahar Rajabi, Sirisha Rambhatla","submitted_at":"2025-10-02T10:35:38Z","abstract_excerpt":"Low-rank gradient optimization for large language models is currently divided into two categories: structured methods that rigorously identify subspaces, and randomized approaches employed primarily for computational efficiency. In this work, we question the intuition behind why random projections are effective. We trace this phenomenon to the geometry of the gradient subspaces, which exhibits subspace optimization landscape has a nearly flat curvature, while a significant portion of gradient information lies outside the core subspace. Leveraging these insights, and drawing on randomized linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.01878","kind":"arxiv","version":2},"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/2510.01878/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"}