{"paper":{"title":"Convergence Analysis of the Dynamics of a Special Kind of Two-Layered Neural Networks with $\\ell_1$ and $\\ell_2$ Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Zhifeng Kong","submitted_at":"2017-11-19T11:54:45Z","abstract_excerpt":"In this paper, we made an extension to the convergence analysis of the dynamics of two-layered bias-free networks with one $ReLU$ output. We took into consideration two popular regularization terms: the $\\ell_1$ and $\\ell_2$ norm of the parameter vector $w$, and added it to the square loss function with coefficient $\\lambda/2$. We proved that when $\\lambda$ is small, the weight vector $w$ converges to the optimal solution $\\hat{w}$ (with respect to the new loss function) with probability $\\geq (1-\\varepsilon)(1-A_d)/2$ under random initiations in a sphere centered at the origin, where $\\vareps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07005","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"}