Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
Abstract:Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collapse, or have position-dependent geometry. We introduce factor-space structure, combining factor domains, generator-induced identifications, and position-dependent scales to distinguish topologically equivalent spaces with different factor geometries. We show that statistically independent factors need not be geometrically separable: hue and scale produce effects that grow at different rates, yielding anisotropy that no fixed rescaling removes. We propose the Factor-Space Topographic Map (FactoMap), which learns interpretable prototypes indexed by a factor-space lattice. Topographic learning transfers the lattice's periodicity, collapses, and non-uniform extent to the representation. Experiments show that matching this structure preserves factor continuity and enables disentanglement of the underlying factors.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2608.24762 [cs.LG] |
| (or arXiv:2608.24762v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.24762
arXiv-issued DOI via DataCite (pending registration)
|
Submission history
From: Bahareh Tolooshams [view email][v1] Tue, 25 Aug 2026 15:59:59 UTC (2,754 KB)
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
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.
More from arXiv — Machine Learning
-
Algebraic Integer Quantization for Machine Learning Applications
Oct 12
-
CircuitTree: Composing Circuits into A Syllable Transcriber
Oct 12
-
Behind-the-Meter Photovoltaic Visibility from Net Smart Meters: Deployment Regimes and Operational Insights
Oct 12
-
GlucoPRISM: Protocol-Supervised Pretraining for Cross-Cohort Glucose Transfer
Oct 12
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.