{"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/phase-diagram-of-training-dynamics-in-deep","title":"Phase diagram of early training dynamics in deep neural networks: effect of the learning rate, depth, and width","arxiv_id":"2302.12250","date":"2023-02-23","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"We systematically analyze optimization dynamics in deep neural networks (DNNs) trained with stochastic gradient descent (SGD) and study the effect of learning rate $\\eta$, depth $d$, and width $w$ of the neural network. By analyzing the maximum eigenvalue $\\lambda^H_t$ of the Hessian of the loss, which is a measure of sharpness of the loss landscape, we find that the dynamics can show four distinct regimes: (i) an early time transient regime, (ii) an intermediate saturation regime, (iii) a progressive sharpening regime, and (iv) a late time ``edge of stability\" regime. The early and intermediate regimes (i) and (ii) exhibit a rich phase diagram depending on $\\eta \\equiv c / \\lambda_0^H $, $d$, and $w$. We identify several critical values of $c$, which separate qualitatively distinct phenomena in the early time dynamics of training loss and sharpness. Notably, we discover the opening up of a ``sharpness reduction\" phase, where sharpness decreases at early times, as $d$ and $1/w$ are increased.","url_abs":"https://arxiv.org/abs/2302.12250v2","url_pdf":"https://arxiv.org/pdf/2302.12250v2.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":[],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2302.12250","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.12250"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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