{"paper":{"title":"Turning Stale Gradients into Stable Gradients: Coherent Coordinate Descent with Implicit Landscape Smoothing for Lightweight Zeroth-Order Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Coherent Coordinate Descent reuses historical gradients as warm starts to achieve O(1) query cost while keeping global descent directions in zeroth-order optimization.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Chen Liang, Daniel Rakita, Qian Wang, Xiatao Sun","submitted_at":"2026-05-14T04:52:24Z","abstract_excerpt":"Zeroth-Order (ZO) optimization is pivotal for scenarios where backpropagation is unavailable, such as memory-constrained on-device learning and black-box optimization. However, existing methods face a stark trade-off: they are either sample-inefficient (e.g., standard finite differences) or suffer from high variance due to randomized estimation (e.g., random subspace methods). In this work, we propose Coherent Coordinate Descent (CoCD), a deterministic, sample-efficient, and budget-aware ZO optimizer. Theoretically, we formalize the notion of gradient coherence and demonstrate that CoCD is equ"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"CoCD is equivalent to Block Cyclic Coordinate Descent with warm starts, enabling O(1) query complexity per step while maintaining global descent directions; larger finite-difference step sizes induce implicit smoothing by reducing the effective smoothness constant.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Historical gradients remain sufficiently coherent across iterations to provide reliable descent directions without significant landscape drift or loss of global information.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CoCD converts stale gradients into stable descent directions for zeroth-order optimization through coherent coordinate updates and implicit landscape smoothing from larger finite-difference steps.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Coherent Coordinate Descent reuses historical gradients as warm starts to achieve O(1) query cost while keeping global descent directions in zeroth-order optimization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d8694eb94551951c57f618bdc744adf00773aa92ae4dc790f52fe0f75aed57af"},"source":{"id":"2605.14373","kind":"arxiv","version":1},"verdict":{"id":"b49b0968-e78e-471a-a011-47d93936aa19","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:44:56.481353Z","strongest_claim":"CoCD is equivalent to Block Cyclic Coordinate Descent with warm starts, enabling O(1) query complexity per step while maintaining global descent directions; larger finite-difference step sizes induce implicit smoothing by reducing the effective smoothness constant.","one_line_summary":"CoCD converts stale gradients into stable descent directions for zeroth-order optimization through coherent coordinate updates and implicit landscape smoothing from larger finite-difference steps.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Historical gradients remain sufficiently coherent across iterations to provide reliable descent directions without significant landscape drift or loss of global information.","pith_extraction_headline":"Coherent Coordinate Descent reuses historical gradients as warm starts to achieve O(1) query cost while keeping global descent directions in zeroth-order optimization."},"references":{"count":35,"sample":[{"doi":"","year":null,"title":"arXiv preprint arXiv:2504.18790 , year=","work_id":"3c7632fc-90d6-4779-9216-c2b09698a372","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"IEEE Signal Processing Magazine , volume=","work_id":"762edb74-3ffb-42f2-b862-20ce9c7b53c6","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"International Conference on Artificial Intelligence and Statistics , pages=","work_id":"e768ec45-ba21-4b9d-9138-244159f02861","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"International Conference on Learning Representations , year=","work_id":"21014bdc-df06-4015-bfc6-a07ae0632bef","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"International Conference on Machine Learning , pages=","work_id":"e702eb44-94af-4897-b2fe-71e567898432","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"d5b0ab5462bfa0c62a22d8bddd40d1338a565af7fd510bd6d408f54a87764cc9","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"3118bb8ec2aee895e0a30d0023add0e8459c1e9758ea85d8885de6d47a165d08"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}