{"paper":{"title":"Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Gradient descent on two-layer Kolmogorov-Arnold networks reaches optimization and generalization rates of order 1/T and 1/n with polylogarithmic width, and differential privacy makes that width necessary.","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Junyu Zhou, Marius Kloft, Philipp Liznerski, Puyu Wang","submitted_at":"2026-01-29T23:43:26Z","abstract_excerpt":"Kolmogorov--Arnold Networks (KANs) have recently emerged as a structured alternative to standard MLPs, yet a principled theory for their training dynamics, generalization, and privacy properties remains limited. In this paper, we analyze gradient descent (GD) for training two-layer KANs and derive general bounds that characterize their training dynamics, generalization, and utility under differential privacy (DP). As a concrete instantiation, we specialize our analysis to logistic loss under an NTK-separable assumption, where we show that polylogarithmic network width suffices for GD to achiev"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we show that polylogarithmic network width suffices for GD to achieve an optimization rate of order 1/T and a generalization rate of order 1/n ... obtain a utility bound of order √d/(nε) ... polylogarithmic width is not only sufficient but also necessary under differential privacy","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"NTK-separable assumption for the data under logistic loss, used to specialize the general analysis to achieve the stated rates","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Gradient descent on two-layer Kolmogorov-Arnold networks reaches optimization and generalization rates of order 1/T and 1/n with polylogarithmic width, and differential privacy makes that width necessary.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7f8359b03914bff14bedb5c96f4dab39d9d58bd27566ba238088a4b535697157"},"source":{"id":"2601.22409","kind":"arxiv","version":3},"verdict":{"id":"8b259ed7-9cb5-4b06-8cc9-6577d66dec18","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T09:31:00.048163Z","strongest_claim":"we show that polylogarithmic network width suffices for GD to achieve an optimization rate of order 1/T and a generalization rate of order 1/n ... obtain a utility bound of order √d/(nε) ... polylogarithmic width is not only sufficient but also necessary under differential privacy","one_line_summary":"For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"NTK-separable assumption for the data under logistic loss, used to specialize the general analysis to achieve the stated rates","pith_extraction_headline":"Gradient descent on two-layer Kolmogorov-Arnold networks reaches optimization and generalization rates of order 1/T and 1/n with polylogarithmic width, and differential privacy makes that width necessary."},"references":{"count":73,"sample":[{"doi":"","year":2016,"title":"Deep learning with differential privacy","work_id":"a7375ed4-55e8-4d83-a877-6694ddafac56","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"A convergence theory for deep learning via over- parameterization","work_id":"2a252a94-ee15-4740-ac95-48e4c0bfa182","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1957,"title":"On functions of three variables","work_id":"c0039bc8-c8ed-4375-a027-1d4f381c914c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks","work_id":"2f8744c1-d98b-482b-acc4-22e10362f492","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Spectrally-normalized margin bounds for neural networks.Advances in Neural Information Processing Systems, 30, 2017","work_id":"a70878f5-c8e2-48e1-8326-8c6c656e02dc","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":73,"snapshot_sha256":"85e5528b79021cf016f7d7443caee837c854c9a952d8b73bea0c1924b7dc7c5e","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"}