Equivariant Geodesic Networks (EGN)

This repository provides the core implementation of:

“Equivariant Geodesic Networks: Geometry-Preserving Learning on Riemannian Manifolds” (ICLR 2026, under review).

The codebase focuses on learning directly on SPD manifolds and other Riemannian structures, instead of flattening them to Euclidean space.

Included components:

• equivariant_bimap.py – Equivariant bilinear mappings that respect SPD manifold structure.
• riemannian_geodesic_distance.py – Utilities for computing geodesic distances on SPD.
• geodesic_attention_layer.py and geodesic_prediction_layer.py – Attention and prediction layers that are geometry-aware.
• riemannian_mean_pool.py – Manifold-consistent pooling operator.
• eigen_activation.py, rpce_loss.py, soft_riemannian_dropout.py – Building blocks for robust, regularized training on manifold-valued data.

This project is intended as a research toolkit for SPD-based covariance descriptors, diffusion tensors, and other manifold-valued representations in computer vision and medical imaging.