{"paper":{"title":"Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on H\\\"older Class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","cs.NE","math.NA"],"primary_cat":"cs.LG","authors_text":"Fengru Wang, Jerry Zhijian Yang, Xiliang Lu, Yanming Lai, Yuanyuan Yang, Yuling Jiao","submitted_at":"2021-02-28T15:57:42Z","abstract_excerpt":"In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions. For general continuous $f$ defined on $[0,1]^d$ with continuity modulus $\\omega_f(\\cdot)$, we construct ReLU-sine-$2^x$ networks that enjoy an approximation rate $\\mathcal{O}(\\omega_f(\\sqrt{d})\\cdot2^{-M}+\\omega_{f}\\left(\\frac{\\sqrt{d}}{N}\\right))$, where $M,N\\in \\mathbb{N}^{+}$ denote the hyperparameters related to widths of the networks. As a consequence, we can construct ReLU-sine-$2^x$ network with the depth $5$ and width $\\max\\left\\{\\left\\lceil2d^{3/2}\\left(\\frac{3\\mu}{\\epsilon}\\right)^{1/{\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.00542","kind":"arxiv","version":6},"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/2103.00542/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"}