# Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery

arXiv: https://arxiv.org/abs/2511.18940 · HTML: https://mlsanity.com/paper/2511.18940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Transfer Learning in Brain-Computer Interfaces](https://mlsanity.com/paper/1512.00296/) (2015)

## Abstract (arXiv)

Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.