{"paper":{"title":"Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Boris Hanin","submitted_at":"2018-01-11T13:17:22Z","abstract_excerpt":"We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network N with ReLU activations. Our results show that the empirical variance of the squares of the entries in the input-output Jacobian of N is exponential in a simple architecture-dependent constant beta, given by the sum of the reciprocals of the hidden layer widths. When beta is large, the gradients computed by N at initialization vary wildly. Our approach complements the mean field theory analysis of random networks. From this point of view, we rigorously compute finite width cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03744","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}