{"paper":{"title":"Depth Dependence of $\\mu$P Learning Rates in ReLU MLPs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Boris Hanin, Samy Jelassi, Sanjiv Kumar, Sashank J. Reddi, Srinadh Bhojanapalli, Ziwei Ji","submitted_at":"2023-05-13T01:10:49Z","abstract_excerpt":"In this short note we consider random fully connected ReLU networks of width $n$ and depth $L$ equipped with a mean-field weight initialization. Our purpose is to study the dependence on $n$ and $L$ of the maximal update ($\\mu$P) learning rate, the largest learning rate for which the mean squared change in pre-activations after one step of gradient descent remains uniformly bounded at large $n,L$. As in prior work on $\\mu$P of Yang et. al., we find that this maximal update learning rate is independent of $n$ for all but the first and last layer weights. However, we find that it has a non-trivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.07810","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.07810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}