fmri-dictionary-learning-optimal-transport

name	fmri-dictionary-learning-optimal-transport
description	Novel approach to dictionary learning on fMRI data that explicitly accounts for individual brain geometry variability using optimal transport (Fused Gromov-Wasserstein distance) with amortized optimization for computational efficiency.
arxiv_id	2605.20883
published	2026-05-20
authors	Sonia Mazelet, Rémi Flamary, Bertrand Thirion
tags	["dictionary-learning","fmri","optimal-transport","brain-geometry","fgw-distance","individual-variability","functional-alignment"]

Learning fMRI Activation Dictionaries Across Individual Geometries via Optimal Transport

Core Concept

Introduces a novel dictionary learning approach for fMRI data that explicitly accounts for individual brain geometry variability using optimal transport (Fused Gromov-Wasserstein distance) instead of projecting all brains onto a common template. Uses amortized optimization to learn a neural network that predicts optimal transport plans at substantially reduced computational cost.

Key Contributions

1. Geometry-Aware Dictionary Learning: Unlike standard approaches that warp individual brains to a common template (losing subject-specific information), this method preserves individual geometry by comparing brains via optimal transport.

2. Fused Gromov-Wasserstein Distance: Uses FGW distance to compare fMRI graphs with different geometries and features, balancing feature alignment (node attributes) with structural consistency (graph topology).

3. Amortized Optimization: Learns a neural network to predict approximations of optimal transport plans, making FGW-based dictionary learning computationally feasible for large-scale fMRI graphs.

4. Controllable Geometric Abstraction: Dictionary atoms can be learned at different levels of geometric variability by varying the FGW trade-off parameter, controlling the balance between feature alignment and structural consistency.

Methodology

Framework

1. Input: fMRI data from multiple subjects with individual brain geometries (3D coordinates, connectivity)
2. Graph Construction: Each subject's brain → graph with node features (fMRI activations) and edge structure (spatial/functional connectivity)
3. FGW Dictionary Learning:
   • Compare graphs across individuals using FGW distance
   • Learn dictionary atoms that balance feature alignment vs. structural consistency
   • Trade-off parameter α controls this balance
4. Amortized Transport: Neural network predicts optimal transport plans, avoiding expensive per-pair FGW computations

Key Innovation

Instead of: Project individual → common template → dictionary learning The method does: Dictionary learning directly on individual geometries, connected via optimal transport

Validation

• Dataset: HCP (Human Connectome Project) dataset
• Results: Captures different levels of geometric variability; preserves essential information for downstream tasks

Applications

• Population-level fMRI analysis: Identifying shared activation patterns while preserving individual geometry
• Brain state classification: Learned dictionaries provide interpretable representations
• Individual differences research: Understanding how brain geometry variability relates to functional differences
• Multi-subject fMRI alignment: Alternative to standard template-based registration

Relationship to Existing Methods

• Vs. Template-based registration: Preserves individual geometry rather than discarding it
• Vs. Hyperalignment: Different mathematical foundation (optimal transport vs. Procrustes)
• Vs. Shared response model: More flexible geometry handling

Activation Keywords

• fmri-dictionary-learning, optimal-transport-fmri, fgw-brain, individual-brain-geometry, fmri-alignment, amortized-transport, dictionary-learning-fmri, brain-graph-optimal-transport, fmri-subject-variability, fused-gromov-wasserstein-brain