{"paper":{"title":"Accelerating Zeroth-Order Spectral Optimization with Partial Orthogonalization from Power Iteration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Partial orthogonalization via power iteration accelerates zeroth-order fine-tuning of large language models.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jiahe Chen, Ziye Ma","submitted_at":"2026-05-09T16:16:45Z","abstract_excerpt":"Zeroth-order (ZO) optimization has become increasingly popular and important in fine-tuning large language models (LLMs), especially on edge devices due to its ability to adjust the model to local data without the need for memory-intensive back-propagation. Recent works try to reduce ZO variance through low-dimensional subspace search, but subspace restriction alone leaves key optimization geometry under-exploited, motivating additional acceleration. In this work, we focus on the hidden layer training problem in which spectral optimizers like Muon outperform AdamW due to its ability to exploit"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Experiments on LLM fine-tuning show that our method can achieve from 1.5x to 4x the convergence speed of ZO-Muon, the current SOTA algorithm, across SuperGlue datasets in the OPT-13B model.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that projecting the search space onto a momentum-derived subspace sufficiently lowers gradient variance to stabilize the streaming power-iteration procedure and enable effective partial orthogonalization in the zeroth-order regime (abstract, paragraph on streaming variant).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ZO-MOPI accelerates zeroth-order LLM fine-tuning by applying partial spectral orthogonalization from power iteration inside a momentum-projected subspace to reduce variance and exploit dominant directions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Partial orthogonalization via power iteration accelerates zeroth-order fine-tuning of large language models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4d7a9efff25927d6fe9bd319bf8316ea0d31673a41574332e9d1b313f506d991"},"source":{"id":"2605.09034","kind":"arxiv","version":2},"verdict":{"id":"f74a27e0-851c-469c-8b5e-23f6c21784bd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:29:05.372590Z","strongest_claim":"Experiments on LLM fine-tuning show that our method can achieve from 1.5x to 4x the convergence speed of ZO-Muon, the current SOTA algorithm, across SuperGlue datasets in the OPT-13B model.","one_line_summary":"ZO-MOPI accelerates zeroth-order LLM fine-tuning by applying partial spectral orthogonalization from power iteration inside a momentum-projected subspace to reduce variance and exploit dominant directions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that projecting the search space onto a momentum-derived subspace sufficiently lowers gradient variance to stabilize the streaming power-iteration procedure and enable effective partial orthogonalization in the zeroth-order regime (abstract, paragraph on streaming variant).","pith_extraction_headline":"Partial orthogonalization via power iteration accelerates zeroth-order fine-tuning of large language 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