{"paper":{"title":"$\\alpha$-Stable convergence of heavy-tailed infinitely-wide neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Hoil Lee, Hongseok Yang, Jiho Lee, Paul Jung","submitted_at":"2021-06-18T01:36:41Z","abstract_excerpt":"We consider infinitely-wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with i.i.d. samples from either a light-tailed (finite variance) or heavy-tailed distribution in the domain of attraction of a symmetric $\\alpha$-stable distribution, where $\\alpha\\in(0,2]$ may depend on the layer. For the bias terms of the layer, we assume i.i.d. initializations with a symmetric $\\alpha$-stable distribution having the same $\\alpha$ parameter of that layer. We then extend a recent result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.11064","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/2106.11064/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"}