{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/enhanced-expressive-power-and-fast-training","title":"Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections","arxiv_id":"1811.09054","date":"2018-11-22","proceeding":null,"authors":["Jian-Feng Cai","Dong Li","Jiaze Sun","Ke Wang"],"abstract":"Random projections are able to perform dimension reduction efficiently for\ndatasets with nonlinear low-dimensional structures. One well-known example is\nthat random matrices embed sparse vectors into a low-dimensional subspace\nnearly isometrically, known as the restricted isometric property in compressed\nsensing. In this paper, we explore some applications of random projections in\ndeep neural networks. We provide the expressive power of fully connected neural\nnetworks when the input data are sparse vectors or form a low-dimensional\nsmooth manifold. We prove that the number of neurons required for approximating\na Lipschitz function with a prescribed precision depends on the sparsity or the\ndimension of the manifold and weakly on the dimension of the input vector. The\nkey in our proof is that random projections embed stably the set of sparse\nvectors or a low-dimensional smooth manifold into a low-dimensional subspace.\nBased on this fact, we also propose some new neural network models, where at\neach layer the input is first projected onto a low-dimensional subspace by a\nrandom projection and then the standard linear connection and non-linear\nactivation are applied. In this way, the number of parameters in neural\nnetworks is significantly reduced, and therefore the training of neural\nnetworks can be accelerated without too much performance loss.","url_abs":"http://arxiv.org/abs/1811.09054v2","url_pdf":"http://arxiv.org/pdf/1811.09054v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"enhanced-expressive-power-and-fast-training","repo_url":"https://github.com/justin941208/MPhil-Thesis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}