arXiv Machine Learning

Discovering Data Manifold Geometry through Geometric Properties

arXiv Computer Vision
2d ago

PAGER: Partial-to-global Alignment via Geometric and Relational Distillation

arXiv:2610.01589v1 Announce Type: new Abstract: Pretrained 3D encoders are typically developed on globally reconstructed scenes expressed in a consistent world coordinate frame, whereas embodied syst...

By Akira-Miranda Adeyomi Adeniran-Lowe, Binod Singh, Lars Arnold Dethlefsen, Lazaros Nalpantidis, Theodora Kontogianni
arXiv Computer Vision
Sep 22

GeoBalance: Geometry-Aware Monitoring and Reconstruction with Asymmetric Optimization for Balanced Multimodal Learning

arXiv:2609.23533v1 Announce Type: new Abstract: Multimodal classifiers can converge to modality-dominant solutions in which one modality dominates the joint prediction, suppressing the learning of ot...

By Zechang Xiong, Da Li, Rong Yin, Kexin Tang, Biao Yang, Pengyuan Li, Wenkang Kong, Yulan Hu, Shengyu Zhu, Hao Peng
arXiv Machine Learning
Sep 7

Nested Inductive Bias Framework for SPD Manifold Learning

The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.

By Tushar Das