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

• URL: http://arxiv.org/abs/2511.18940v1
• Date: Mon, 24 Nov 2025 09:46:55 GMT
• Title: Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery
• Authors: Sanjeev Manivannan, Chandrashekar Lakshminarayan,
• Abstract summary: Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces.<n>We introduce novel geometry-aware preprocessing modules and deep congruence networks.<n>Our framework improves cross-subject accuracy by 3-4% over the strongest classical baselines.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces due to strong subject variability and the curved geometry of covariance matrices on the symmetric positive definite (SPD) manifold. We address the zero-shot cross-subject setting, where no target-subject labels or adaptation are allowed, by introducing novel geometry-aware preprocessing modules and deep congruence networks that operate directly on SPD covariance matrices. Our preprocessing modules, DCR and RiFU, extend Riemannian Alignment by improving action separation while reducing subject-specific distortions. We further propose two manifold classifiers, SPD-DCNet and RiFUNet, which use hierarchical congruence transforms to learn discriminative, subject-invariant covariance representations. On the BCI-IV 2a benchmark, our framework improves cross-subject accuracy by 3-4% over the strongest classical baselines, demonstrating the value of geometry-aware transformations for robust EEG decoding.

Related papers

• ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning [2.757490632589873]
  We propose Arbitrary Geometry-encoded Transformer (ArGEnT), a geometry-aware attention-based architecture for operator learning on arbitrary domains.<n>By combining flexible geometry encoding with operator-learning capabilities, ArGEnT provides a scalable surrogate modeling framework for optimization, uncertainty, and data-driven modeling of complex physical systems.
  arXiv  Detail & Related papers  (2026-02-12T06:22:59Z)
• Dense Semantic Matching with VGGT Prior [49.42199006453071]
  We propose an approach that retains VGGT's intrinsic strengths by reusing early feature stages, fine-tuning later ones, and adding a semantic head for bidirectional correspondences.<n>Our approach achieves superior geometry awareness, matching reliability, and manifold preservation, outperforming previous baselines.
  arXiv  Detail & Related papers  (2025-09-25T14:56:11Z)
• PAID: Pairwise Angular-Invariant Decomposition for Continual Test-Time Adaptation [70.98107766265636]
  This paper takes the geometric attributes of pre-trained weights as a starting point, systematically analyzing three key components: magnitude, absolute angle, and pairwise angular structure.<n>We find that the pairwise angular structure remains stable across diverse corrupted domains and encodes domain-invariant semantic information, suggesting it should be preserved during adaptation.
  arXiv  Detail & Related papers  (2025-06-03T05:18:15Z)
• A Recipe for Geometry-Aware 3D Mesh Transformers [2.0992612407358293]
  We study an approach for embedding features at the patch level, accommodating patches with variable node counts. Our research highlights critical insights: 1) the importance of structural and positional embeddings facilitated by heat diffusion in general 3D mesh transformers; 2) the effectiveness of novel components such as geodesic masking and feature interaction via cross-attention in enhancing learning; and 3) the superior performance and efficiency of our proposed methods in challenging segmentation and classification tasks.
  arXiv  Detail & Related papers  (2024-10-31T19:13:31Z)
• EqNIO: Subequivariant Neural Inertial Odometry [33.96552018734359]
  We show that IMU data transforms equivariantly, when rotated around the gravity vector and reflected with respect to arbitrary planes parallel to gravity. We then map the IMU data into this frame, thereby achieving an invariant canonicalization that can be directly used with off-the-shelf inertial odometry networks.
  arXiv  Detail & Related papers  (2024-08-12T17:42:46Z)
• Riemannian Self-Attention Mechanism for SPD Networks [34.794770395408335]
  An SPD manifold self-attention mechanism (SMSA) is proposed in this paper. An SMSA-based geometric learning module (SMSA-GL) is designed for the sake of improving the discrimination of structured representations.
  arXiv  Detail & Related papers  (2023-11-28T12:34:46Z)
• GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformers [63.41460219156508]
  We argue that existing positional encoding schemes are suboptimal for 3D vision tasks. We propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation. We show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models.
  arXiv  Detail & Related papers  (2023-10-16T13:16:09Z)
• Deep Diversity-Enhanced Feature Representation of Hyperspectral Images [87.47202258194719]
  We rectify 3D convolution by modifying its topology to enhance the rank upper-bound. We also propose a novel diversity-aware regularization (DA-Reg) term that acts on the feature maps to maximize independence among elements. To demonstrate the superiority of the proposed Re$3$-ConvSet and DA-Reg, we apply them to various HS image processing and analysis tasks.
  arXiv  Detail & Related papers  (2023-01-15T16:19:18Z)
• Deep Optimal Transport for Domain Adaptation on SPD Manifolds [9.552869120136005]
  We introduce a new geometric deep learning framework that combines optimal transport theory with the geometry of SPD manifold.<n>Our approach aligns data distributions while respecting the manifold structure, effectively reducing both marginal and conditional discrepancies.<n>We validate our method on three cross-session brain computer interface datasets, KU, BNCI2014001, and BNCI2015001.
  arXiv  Detail & Related papers  (2022-01-15T03:13:02Z)
• Self-supervised Geometric Perception [96.89966337518854]
  Self-supervised geometric perception is a framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels. We show that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.
  arXiv  Detail & Related papers  (2021-03-04T15:34:43Z)
• MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning [90.20563679417567]
  This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. We show that such networks converge faster than unstructured networks on CartPole, a grid world and Pong.
  arXiv  Detail & Related papers  (2020-06-30T15:38:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.