{"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/spatial-variational-auto-encoding-via-matrix","title":"Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions","arxiv_id":"1705.06821","date":"2017-05-18","proceeding":null,"authors":["Zhengyang Wang","Hao Yuan","Shuiwang Ji"],"abstract":"The key idea of variational auto-encoders (VAEs) resembles that of\ntraditional auto-encoder models in which spatial information is supposed to be\nexplicitly encoded in the latent space. However, the latent variables in VAEs\nare vectors, which can be interpreted as multiple feature maps of size 1x1.\nSuch representations can only convey spatial information implicitly when\ncoupled with powerful decoders. In this work, we propose spatial VAEs that use\nfeature maps of larger size as latent variables to explicitly capture spatial\ninformation. This is achieved by allowing the latent variables to be sampled\nfrom matrix-variate normal (MVN) distributions whose parameters are computed\nfrom the encoder network. To increase dependencies among locations on latent\nfeature maps and reduce the number of parameters, we further propose spatial\nVAEs via low-rank MVN distributions. Experimental results show that the\nproposed spatial VAEs outperform original VAEs in capturing rich structural and\nspatial information.","url_abs":"http://arxiv.org/abs/1705.06821v2","url_pdf":"http://arxiv.org/pdf/1705.06821v2.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":"spatial-variational-auto-encoding-via-matrix","repo_url":"https://github.com/divelab/svae","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"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}