spectralot-functional-alignment

name	spectralot-functional-alignment
description	Method for geometry-aware functional alignment of fMRI data using SpectralOT to improve cross-subject decoding by embedding cortical geometry into Laplace-Beltrami eigenmodes.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2607.10931","authors":["Pierre-Louis Barbarant","Florent Meyniel","Bertrand Thirion"],"submitted":"2026-07-12","comment":"Proceedings of the 9th Conference on Cognitive Computational Neuroscience, New York, NY, USA, 2026"}

SpectralOT Functional Alignment

When to Use This Skill

Use this skill when you need to:

• Perform functional alignment of fMRI data across subjects for improved cross-subject decoding
• Incorporate cortical geometry into functional alignment procedures
• Work with surface-based fMRI data (cortical surfaces) and functional maps
• Implement geometry-aware regularization in neuroimaging analysis pipelines

Overview

SpectralOT introduces a novel functional alignment method for fMRI data that embeds cortical geometry into Laplace-Beltrami eigenmodes to regularize the alignment process. This approach balances functional feature alignment with anatomical structure preservation while maintaining computational efficiency. The method improves cross-subject decoding performance by leveraging the spectral decomposition of the Laplace-Beltrami operator on the cortical surface.

Methodology

Core Concept

The method addresses the challenge of inter-individual variability in brain response patterns by aligning functional data across individuals before training population-level decoders. Unlike traditional approaches that may distort anatomical structure, SpectralOT incorporates geometric constraints directly into the alignment framework.

Mathematical Formulation

1. Laplace-Beltrami Eigenmodes: Compute eigenmodes of the Laplace-Beltrami operator on each subject's cortical surface mesh, capturing intrinsic geometric properties.

2. Spectral Embedding: Project functional data (e.g., fMRI activation maps) onto the Laplace-Beltrami eigenbasis to obtain spectral coefficients that represent functional patterns in a geometry-aware basis.

3. Optimal Transport Alignment: Solve an optimal transport problem in the spectral domain to find the mapping that minimizes discrepancies between subjects' functional representations while respecting geometric constraints.

4. Geometric Regularization: The use of Laplace-Beltrami eigenmodes inherently regularizes the alignment to preserve cortical topology, preventing excessive warping that could distort anatomical correspondence.

Workflow

1. Preprocessing:

   • Extract cortical surface meshes from structural MRI for each subject
   • Preprocess fMRI data to obtain functional maps on the cortical surface

2. Spectral Decomposition:

   • Compute Laplace-Beltrami eigenmodes for each surface mesh
   • Project functional maps onto the eigenbasis to obtain spectral coefficients

3. Alignment Optimization:

   • Formulate optimal transport problem between spectral coefficients of source and target subjects
   • Solve for optimal coupling matrix using Sinkhorn algorithm or similar
   • Apply the learned transformation to align functional data

4. Validation:

   • Evaluate alignment quality using cross-subject decoding accuracy
   • Assess preservation of anatomical landmarks and functional boundaries

Implementation Notes

• Requires surface reconstruction tools (e.g., FreeSurfer) to obtain cortical meshes
• Functional data should be sampled on the cortical surface (e.g., via surface-based smoothing)
• Choice of truncation level for Laplace-Beltrami eigenbasis affects trade-off between geometric detail and computational cost
• The method is compatible with various functional modalities (fMRI, EEG source localization, etc.) when mapped to cortical surface

Expected Outcomes

When applied correctly, this skill should enable:

• Improved cross-subject decoding accuracy compared to alignment-free or geometry-unaware methods
• Better preservation of topographically organized functional areas
• Reduced inter-subject variability in functional responses post-alignment
• Computationally efficient alignment suitable for large datasets

References

• Barbarant, P.-L., Meyniel, F., & Thirion, B. (2026). Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding. arXiv:2607.10931.
• Proceedings of the 9th Conference on Cognitive Computational Neuroscience, New York, NY, USA, 2026.

Activation Keywords

• spectralot
• functional alignment
• laplace beltrami
• cortical geometry
• fmri alignment
• cross-subject decoding
• geometry-aware