{"paper":{"title":"$\\ell_1$-regularized Neural Networks are Improperly Learnable in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jason D. Lee, Michael I. Jordan, Yuchen Zhang","submitted_at":"2015-10-13T04:36:09Z","abstract_excerpt":"We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based method, such that with probability at least $1 - \\delta$, it learns a predictor whose generalization error is at most $\\epsilon$ worse than that of the neural network. The sample complexity and the time complexity of the presented method are polynomial in the input dimension and in $(1/\\epsilon,\\log(1/\\delta),F(k,L))$, where $F(k,L)$ is a function depending"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03528","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":""},"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"}