Md Raihan Khan

Md Raihan Khan

Lecturer in EEE at North Western University, Bangladesh. Research in deep learning for biomedical signal processing and medical imaging.

Equivariant Geodesic Networks: Geometry Preserving Learning on Riemannian Manifolds

Published in International Conference on Learning Representations (ICLR), 2026 – Under Review, 2026

This work introduces Equivariant Geodesic Networks (EGN), a geometry-aware architecture for learning on data that naturally lies on Riemannian manifolds, such as covariance matrices. The model is designed to respect the underlying manifold structure through geodesic operations and to maintain equivariance under relevant transformations.

EGN is applied to covariance-based representations in computer vision and signal processing, showing improved stability and performance compared to Euclidean baselines and naive manifold approaches. The framework offers a principled way to integrate manifold geometry into deep learning.

Recommended citation: Md Raihan Khan and Airin Akter Tania, "Equivariant Geodesic Networks: Geometry Preserving Learning on Riemannian Manifolds," ICLR 2026 (under review).
Download Paper