arXiv:2608. 04234v1 Announce Type: cross Abstract: We study the problem of aligning data from multiple modalities into a shared representation space, focusing on settings where strong pretrained unimodal encoders are available but cross-modal paired data are scarce.
By Yixuan Florence Wu, Yilun Zhu, Naichen Shi
arXiv:2604.02535v2 Announce Type: replace
Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
By Zeyang Huang, Angelos Chatzimparmpas, Thomas H\"ollt, Takanori Fujiwara
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
By Dhruv Kohli, Sawyer J. Robertson, Gal Mishne, Alexander Cloninger
arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
By Keyi Li, Yuval Kluger, Boris Landa
DMT‑Dens is a parametric manifold‑visualization technique that uses a latent‑token Transformer encoder to produce two‑dimensional embeddings of high‑dimensional biological data. It preserves sampling density by aligning rank‑based manifold structures and optimizing a Pearson‑correlation loss on k‑nearest‑neighbor log‑radius estimates. Benchmark tests show that DMT‑Dens maintains density fidelity while achieving competitive label separability on biological datasets.
By Ruizhe Wang, Yixuan Dong, Bolin Yang, Bingo Wing-Kuen Ling, Fuji Yang, Zelin Zang
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
By Yizhu Wang, Mu Niu, Xiaochen Yang