{"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/volume-preserving-neural-networks-a-solution","title":"Volume-preserving Neural Networks","arxiv_id":"1911.09576","date":"2019-11-21","proceeding":null,"authors":["Gordon MacDonald","Andrew Godbout","Bryn Gillcash","Stephanie Cairns"],"abstract":"We propose a novel approach to addressing the vanishing (or exploding) gradient problem in deep neural networks. We construct a new architecture for deep neural networks where all layers (except the output layer) of the network are a combination of rotation, permutation, diagonal, and activation sublayers which are all volume preserving. Our approach replaces the standard weight matrix of a neural network with a combination of diagonal, rotational and permutation matrices, all of which are volume-preserving. We introduce a coupled activation function allowing us to preserve volume even in the activation function portion of a neural network layer. This control on the volume forces the gradient (on average) to maintain equilibrium and not explode or vanish. To demonstrate our architecture we apply our volume-preserving neural network model to two standard datasets.","url_abs":"https://arxiv.org/abs/1911.09576v3","url_pdf":"https://arxiv.org/pdf/1911.09576v3.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":"volume-preserving-neural-networks-a-solution","repo_url":"https://github.com/andrewgodbout/VPNN_pytorch","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"all","task_name":"All"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}