{"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/adversarial-autoencoders-with-constant","title":"Adversarial Autoencoders with Constant-Curvature Latent Manifolds","arxiv_id":"1812.04314","date":"2018-12-11","proceeding":null,"authors":["Daniele Grattarola","Lorenzo Livi","Cesare Alippi"],"abstract":"Constant-curvature Riemannian manifolds (CCMs) have been shown to be ideal\nembedding spaces in many application domains, as their non-Euclidean geometry\ncan naturally account for some relevant properties of data, like hierarchy and\ncircularity. In this work, we introduce the CCM adversarial autoencoder\n(CCM-AAE), a probabilistic generative model trained to represent a data\ndistribution on a CCM. Our method works by matching the aggregated posterior of\nthe CCM-AAE with a probability distribution defined on a CCM, so that the\nencoder implicitly learns to represent data on the CCM to fool the\ndiscriminator network. The geometric constraint is also explicitly imposed by\njointly training the CCM-AAE to maximise the membership degree of the\nembeddings to the CCM. While a few works in recent literature make use of\neither hyperspherical or hyperbolic manifolds for different learning tasks,\nours is the first unified framework to seamlessly deal with CCMs of different\ncurvatures. We show the effectiveness of our model on three different datasets\ncharacterised by non-trivial geometry: semi-supervised classification on MNIST,\nlink prediction on two popular citation datasets, and graph-based molecule\ngeneration using the QM9 chemical database. Results show that our method\nimproves upon other autoencoders based on Euclidean and non-Euclidean\ngeometries on all tasks taken into account.","url_abs":"http://arxiv.org/abs/1812.04314v2","url_pdf":"http://arxiv.org/pdf/1812.04314v2.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":"adversarial-autoencoders-with-constant","repo_url":"https://github.com/danielegrattarola/ccm-aae","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"link-prediction","task_name":"Link Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1812.04314","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1812.04314"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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