Disentanglement as Identifiable Pushforward Factorisation

[2410.22559] Disentanglement as Identifiable Pushforward Factorisation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2410.22559 (cs) [Submitted on 29 Oct 2024 ( v1 ), last revised 10 Apr 2026 (this version, v7)] Title: Disentanglement as Identifiable Pushforward Factorisation Authors: Carl Allen View a PDF of the paper titled Disentanglement as Identifiable Pushforward Factorisation, by Carl Allen View PDF HTML (experimental) Abstract: We characterise disentanglement in smooth generative pushforward models, such as in VAEs and GANs. For a generator/decoder $g:Z\to X$ and factorised prior $p(z)=\prod_i p_i(z_i)$, we define disentanglement as factorisation of the pushforward density $p_\mu= g_\#p$ into one-dimensional "seam" factors, where each latent dimension controls an independent generative factor of the data. We prove that $p_\mu$ factorises according to the SVD of $g$'s Jacobian; that disentanglement equates to two conditions on $g$ (C1-C2); and that under those conditions the seam factors are identifiable, up to permutation and sign. In the particular case of Gaussian ($\beta$-)VAEs, we show via an identity how diagonal posteriors promote C1-C2, in expectation, explaining why disentanglement arises modulated by $\beta$. Experiments illustrate this mechanism on Gaussian data, dSprites, and CelebA. Comments: 9 pages Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2410.22559 [cs.LG] (or arXiv:2410.22559v7 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2410.22559 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carl Allen [ view email ] [v1] Tue, 29 Oct 2024 21:54:18 UTC (714 KB) [v2] Mon, 18 Nov 2024 12:36:04 UTC (903 KB) [v3] Thu, 28 Nov 2024 16:14:44 UTC (749 KB) [v4] Thu, 6 Feb 2025 15:35:37 UTC (821 KB) [v5] Thu, 22 May 2025 14:59:51 UTC (1,419 KB) [v6] Tue, 30 Sep 2025 16:35:37 UTC (3,128 KB) [v7] Fri, 10 Apr 2026 18:10:16 UTC (12,129 KB) Full-text links: Access Paper: View a PDF of the paper titled Disentanglement as Identifiable Pushforward Factorisation, by Carl Allen View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-10 Change to browse by: cs cs.AI stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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