{"abstract":[{"lang":"eng","text":"This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory."}],"oa_version":"Preprint","publication":"Proceedings of the 40th International Conference on Machine Learning","citation":{"mla":"Zhu, Zhenyu, et al. “Benign Overfitting in Deep Neural Networks under Lazy Training.” <i>Proceedings of the 40th International Conference on Machine Learning</i>, vol. 202, ML Research Press, 2023, pp. 43105–28.","ieee":"Z. Zhu, F. Liu, G. G. Chrysos, F. Locatello, and V. Cevher, “Benign overfitting in deep neural networks under lazy training,” in <i>Proceedings of the 40th International Conference on Machine Learning</i>, Honolulu, Hawaii, United States, 2023, vol. 202, pp. 43105–43128.","chicago":"Zhu, Zhenyu, Fanghui Liu, Grigorios G Chrysos, Francesco Locatello, and Volkan Cevher. “Benign Overfitting in Deep Neural Networks under Lazy Training.” In <i>Proceedings of the 40th International Conference on Machine Learning</i>, 202:43105–28. ML Research Press, 2023.","short":"Z. Zhu, F. Liu, G.G. Chrysos, F. Locatello, V. Cevher, in:, Proceedings of the 40th International Conference on Machine Learning, ML Research Press, 2023, pp. 43105–43128.","apa":"Zhu, Z., Liu, F., Chrysos, G. G., Locatello, F., &#38; Cevher, V. (2023). Benign overfitting in deep neural networks under lazy training. In <i>Proceedings of the 40th International Conference on Machine Learning</i> (Vol. 202, pp. 43105–43128). Honolulu, Hawaii, United States: ML Research Press.","ista":"Zhu Z, Liu F, Chrysos GG, Locatello F, Cevher V. 2023. Benign overfitting in deep neural networks under lazy training. Proceedings of the 40th International Conference on Machine Learning. International Conference on Machine Learning, PMLR, vol. 202, 43105–43128.","ama":"Zhu Z, Liu F, Chrysos GG, Locatello F, Cevher V. Benign overfitting in deep neural networks under lazy training. In: <i>Proceedings of the 40th International Conference on Machine Learning</i>. Vol 202. ML Research Press; 2023:43105-43128."},"month":"05","department":[{"_id":"FrLo"}],"author":[{"first_name":"Zhenyu","last_name":"Zhu","full_name":"Zhu, Zhenyu"},{"last_name":"Liu","full_name":"Liu, Fanghui","first_name":"Fanghui"},{"first_name":"Grigorios G","last_name":"Chrysos","full_name":"Chrysos, Grigorios G"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","last_name":"Locatello"},{"first_name":"Volkan","last_name":"Cevher","full_name":"Cevher, Volkan"}],"year":"2023","language":[{"iso":"eng"}],"day":"30","external_id":{"arxiv":["2305.19377"]},"publisher":"ML Research Press","oa":1,"date_created":"2023-08-22T14:18:18Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.19377"}],"alternative_title":["PMLR"],"_id":"14208","type":"conference","volume":202,"title":"Benign overfitting in deep neural networks under lazy training","quality_controlled":"1","article_processing_charge":"No","extern":"1","date_published":"2023-05-30T00:00:00Z","date_updated":"2023-09-13T08:46:46Z","status":"public","page":"43105-43128","publication_status":"published","intvolume":"       202","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"name":"International Conference on Machine Learning","end_date":"2023-07-29","location":"Honolulu, Hawaii, United States","start_date":"2023-07-23"}}