{"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/hyperbolic-vae-via-latent-gaussian-1","title":"Hyperbolic VAE via Latent Gaussian Distributions","arxiv_id":"2209.15217","date":"2022-09-30","proceeding":"NeurIPS 2023 11","authors":["Seunghyuk Cho","Juyong Lee","Dongwoo Kim"],"abstract":"We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space consists of a set of Gaussian distributions. It is known that the set of the univariate Gaussian distributions with the Fisher information metric form a hyperbolic space, which we call a Gaussian manifold. To learn the VAE endowed with the Gaussian manifolds, we propose a pseudo-Gaussian manifold normal distribution based on the Kullback-Leibler divergence, a local approximation of the squared Fisher-Rao distance, to define a density over the latent space. In experiments, we demonstrate the efficacy of GM-VAE on two different tasks: density estimation of image datasets and environment modeling in model-based reinforcement learning. GM-VAE outperforms the other variants of hyperbolic- and Euclidean-VAEs on density estimation tasks and shows competitive performance in model-based reinforcement learning. We observe that our model provides strong numerical stability, addressing a common limitation reported in previous hyperbolic-VAEs.","url_abs":"https://arxiv.org/abs/2209.15217v3","url_pdf":"https://arxiv.org/pdf/2209.15217v3.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":"hyperbolic-vae-via-latent-gaussian-1","repo_url":"https://github.com/ml-postech/gm-vae","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"model-based-reinforcement-learning","task_name":"Model-based Reinforcement Learning"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2209.15217","atlas_url":"https://app.syntology.ai/?focus=2209.15217","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}