{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/limitations-of-lazy-training-of-two-layers-1","title":"Limitations of Lazy Training of Two-layers Neural Network","arxiv_id":null,"date":"2019-12-01","proceeding":"NeurIPS 2019 12","authors":["Song Mei","Theodor Misiakiewicz","Behrooz Ghorbani","Andrea Montanari"],"abstract":"We study the supervised learning problem under either of the following two models:\n(1) Feature vectors x_i are d-dimensional Gaussian and responses are y_i = f_*(x_i) for f_* an unknown quadratic function;\n(2) Feature vectors x_i are distributed as a mixture of two d-dimensional centered Gaussians, and y_i's are the corresponding class labels. \nWe use two-layers neural networks with quadratic activations, and compare three  different learning regimes: the random features (RF) regime in which we only train the second-layer weights; the neural tangent (NT) regime in which we train a linearization of the neural network around its initialization; the fully trained neural network (NN) regime in  which we train all the weights in the network. We prove that, even for the simple quadratic model of point (1), there is a potentially unbounded gap between the prediction risk achieved in these three training regimes, when the number of neurons is smaller than the ambient dimension. When the number of neurons is larger than the number of dimensions, the problem is significantly easier and both NT and NN learning achieve zero risk.","url_abs":"http://papers.nips.cc/paper/9111-limitations-of-lazy-training-of-two-layers-neural-network","url_pdf":"http://papers.nips.cc/paper/9111-limitations-of-lazy-training-of-two-layers-neural-network.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"limitations-of-lazy-training-of-two-layers-1","repo_url":"https://github.com/bGhorbani/Lazy-Training-Neural-Nets","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}