{"paper":{"title":"Rethinking Neural Network Learning Rates: A Stackelberg Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Assigning a smaller learning rate to body layers and a larger learning rate to the final layer is equivalent to two-time-scale alternating gradient descent on a Stackelberg reformulation of neural network training.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Sihan Zeng, Sujay Bhatt, Sumitra Ganesh","submitted_at":"2026-05-15T01:59:10Z","abstract_excerpt":"Neural networks are typically trained with a single learning rate across all layers. While recent empirical evidence suggests that assigning layer-specific learning rates can accelerate training, a principled understanding of the conditions and mechanisms under which non-uniform learning rates are beneficial remains limited. In this work, we investigate non-uniform learning rates through the lens of Stackelberg optimization. Specifically, we demonstrate that training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpret"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpreted as a two-time-scale alternating gradient descent algorithm applied to a Stackelberg reformulation of the original objective. We establish finite-time convergence guarantees for the algorithm under broad conditions that accommodate constraint sets and non-smooth activation functions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The training dynamics of a neural network can be accurately captured by a Stackelberg game in which the final layer is the leader whose objective is defined on the followers' best response; this reformulation must preserve the original optimization landscape sufficiently for the convergence and curvature claims to transfer back to standard training.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-uniform learning rates correspond to a Stackelberg reformulation of the training objective whose two-time-scale alternating gradient descent yields finite-time convergence and can accelerate training through stronger optimization structure and sharper early curvature.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Assigning a smaller learning rate to body layers and a larger learning rate to the final layer is equivalent to two-time-scale alternating gradient descent on a Stackelberg reformulation of neural network training.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"552582ffead687d51ef7ff6a22d007369719c1c86fa2ab838e14e9e6b1bd09b3"},"source":{"id":"2605.15530","kind":"arxiv","version":1},"verdict":{"id":"147a7b78-4206-491d-ba15-662e0ef9a049","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T14:37:19.333466Z","strongest_claim":"training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpreted as a two-time-scale alternating gradient descent algorithm applied to a Stackelberg reformulation of the original objective. We establish finite-time convergence guarantees for the algorithm under broad conditions that accommodate constraint sets and non-smooth activation functions.","one_line_summary":"Non-uniform learning rates correspond to a Stackelberg reformulation of the training objective whose two-time-scale alternating gradient descent yields finite-time convergence and can accelerate training through stronger optimization structure and sharper early curvature.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The training dynamics of a neural network can be accurately captured by a Stackelberg game in which the final layer is the leader whose objective is defined on the followers' best response; this reformulation must preserve the original optimization landscape sufficiently for the convergence and curvature claims to transfer back to standard training.","pith_extraction_headline":"Assigning a smaller learning rate to body layers and a larger learning rate to the final layer is equivalent to two-time-scale alternating gradient descent on a Stackelberg reformulation of neural network training."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15530/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T15:01:17.518879Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:49:57.554234Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T14:22:02.212584Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.037972Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T13:49:41.835827Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T13:49:41.373268Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.621376Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f64f3827a010f6bcf03542a0597378fe7c2aa3307f2f5d6f42b2d86b067bb0ba"},"references":{"count":16,"sample":[{"doi":"","year":null,"title":"Ultra-fast fea- ture learning for the training of two-layer neural net- works in the two-timescale regime.arXiv preprint arXiv:2504.18208,","work_id":"74802858-d44a-4c3c-9f04-b14627b4cfb3","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Closed-Form Last Layer Optimization","work_id":"71a57628-f71c-479b-b8eb-9e3d74dc91d9","ref_index":2,"cited_arxiv_id":"2510.04606","is_internal_anchor":true},{"doi":"","year":1905,"title":"Stochastic gradient methods with layer- wise adaptive moments for training of deep networks","work_id":"65c65157-0510-4070-94a6-5c7dadaa998f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Noise- adaptive layerwise learning rates: Accelerating geometry- aware optimization for deep neural network training","work_id":"43915281-2b91-46ce-9436-f6f81a79cf7a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Large batch training does not need warmup.arXiv preprint arXiv:2002.01576,","work_id":"ca8ff354-b95e-4dc9-a3ba-892034201629","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"d1da5c8fe04af6fd364e2c67fba1c27bf064927f332a83421fc80acee9a401c5","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"3f919971fd094e41245d7b6c18966afa32fd50efe90bb44d7888f460ed6ab9d6"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}