{"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/latent-optimal-paths-by-gumbel-propagation","title":"Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming","arxiv_id":"2306.02568","date":"2023-06-05","proceeding":null,"authors":["Xinlei Niu","Christian Walder","Jing Zhang","Charles Patrick Martin"],"abstract":"We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at \\url{https://github.com/XinleiNIU/LatentOptimalPathsBayesianDP}.","url_abs":"https://arxiv.org/abs/2306.02568v3","url_pdf":"https://arxiv.org/pdf/2306.02568v3.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":"latent-optimal-paths-by-gumbel-propagation","repo_url":"https://github.com/xinleiniu/latentoptimalpathsbayesiandp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"latent-optimal-paths-by-gumbel-propagation","repo_url":"https://github.com/Berthaniu/LatentOptimalPathsBayesianDP","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"singing-voice-synthesis","task_name":"Singing Voice Synthesis"},{"task_slug":"text-to-speech","task_name":"Text to Speech"},{"task_slug":"text-to-speech-1","task_name":"text-to-speech"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.02568","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}