{"paper":{"title":"On the Connection Between Learning Two-Layers Neural Networks and Tensor Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrea Montanari, Marco Mondelli","submitted_at":"2018-02-20T19:40:32Z","abstract_excerpt":"We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\\boldsymbol x \\in \\mathbb R^d$, $r$ hidden units with weights $\\{\\boldsymbol w_i\\}_{1\\le i \\le r}$ and output $y\\in \\mathbb R$, i.e., $y=\\sum_{i=1}^r \\sigma( \\boldsymbol w_i^{\\mathsf T}\\boldsymbol x)$, with activation functions given by low-degree polynomials. In particular, if $\\sigma(x) = a_0+a_1x+a_3x^3$, we prove that no polynomial-time learning algorithm can outperform the trivial predictor that assigns to each example the response variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07301","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"}