{"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/neural-network-renormalization-group","title":"Neural Network Renormalization Group","arxiv_id":"1802.02840","date":"2018-02-08","proceeding":null,"authors":["Shuo-Hui Li","Lei Wang"],"abstract":"We present a variational renormalization group (RG) approach using a deep\ngenerative model based on normalizing flows. The model performs hierarchical\nchange-of-variables transformations from the physical space to a latent space\nwith reduced mutual information. Conversely, the neural net directly maps\nindependent Gaussian noises to physical configurations following the inverse RG\nflow. The model has an exact and tractable likelihood, which allows unbiased\ntraining and direct access to the renormalized energy function of the latent\nvariables. To train the model, we employ probability density distillation for\nthe bare energy function of the physical problem, in which the training loss\nprovides a variational upper bound of the physical free energy. We demonstrate\npractical usage of the approach by identifying mutually independent collective\nvariables of the Ising model and performing accelerated hybrid Monte Carlo\nsampling in the latent space. Lastly, we comment on the connection of the\npresent approach to the wavelet formulation of RG and the modern pursuit of\ninformation preserving RG.","url_abs":"http://arxiv.org/abs/1802.02840v4","url_pdf":"http://arxiv.org/pdf/1802.02840v4.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":"neural-network-renormalization-group","repo_url":"https://github.com/li012589/NeuralRG","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"neural-network-renormalization-group","repo_url":"https://github.com/wangleiphy/MongeAmpereFlow","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.02840","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}