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arxiv: 2605.20883 · v1 · pith:PMNNKPJBnew · submitted 2026-05-20 · 💻 cs.LG

Learning fMRI activations dictionaries across individual geometries via optimal transport

Sonia Mazelet , R\'emi Flamary , Bertrand Thirion This is my paper

Pith reviewed 2026-05-21 06:35 UTC · model grok-4.3

classification 💻 cs.LG
keywords dictionary learningfMRIoptimal transportGromov-Wassersteinbrain geometryamortized optimizationgraph representations
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The pith

A dictionary learning method for fMRI uses optimal transport to handle differences in individual brain geometries without projecting to a template.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a way to learn dictionaries of brain activity patterns from fMRI scans that respects the unique shape of each person's brain. Standard approaches map every brain onto one average template, which discards personal geometric details. Instead, this method compares brain graphs using the Fused Gromov-Wasserstein distance and approximates the required transport plans with a neural network to keep computation feasible. Dictionary atoms are made to vary with the balance between matching features and matching structure. Experiments on the HCP dataset indicate that the resulting representations capture varying degrees of geometric difference while retaining key information for tasks like classification.

Core claim

By combining the Fused Gromov-Wasserstein distance with amortized neural approximation of transport plans, dictionary atoms that depend on the FGW trade-off parameter can be learned for graphs with different geometries and features; numerical experiments on the HCP dataset show that the approach captures different levels of geometric variability in the data and provides representations that preserve essential information.

What carries the argument

The Fused Gromov-Wasserstein distance, which compares graphs with different geometries and features by balancing feature alignment and structural consistency, together with amortized optimization that trains a neural network to predict approximate optimal transport plans.

If this is right

  • Dictionary atoms depend on the trade-off parameter that controls the balance between feature alignment and structural consistency.
  • The amortized neural approximation makes repeated FGW computations feasible on large fMRI graphs.
  • The learned representations capture different levels of geometric variability across subjects.
  • Essential information for downstream tasks such as classification is preserved in the representations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Retaining subject-specific geometry could improve accuracy in population-level analyses that currently lose individual detail through template alignment.
  • The same amortized transport approximation might reduce cost when applying dictionary learning to other mismatched graph datasets, such as connectomes from different species.
  • Downstream models trained on these representations may generalize better to new subjects because geometric variability is explicitly modeled rather than removed.

Load-bearing premise

That the Fused Gromov-Wasserstein distance combined with amortized neural approximation of transport plans is sufficient to learn dictionaries whose atoms meaningfully depend on the trade-off parameter while remaining computationally tractable for fMRI-scale graphs.

What would settle it

An experiment showing that the learned dictionary atoms do not change meaningfully with the FGW trade-off parameter or that the resulting representations fail to preserve essential information better than those obtained by projecting brains to a common template.

Figures

Figures reproduced from arXiv: 2605.20883 by Bertrand Thirion, R\'emi Flamary, Sonia Mazelet.

Figure 1
Figure 1. Figure 1: Visualization of the learned dictionary atoms for different values of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Original contrast (top) and its reconstruction (bottom) for a given subject and contrast story - math. AGDL We train AGDL with both the linear interpolation (6) and the MLP (7) on the HCP dataset by minimizing the loss in Eq. (5), using a batch size of 32, a learning rate of 0.001, and training for 1000 epochs. We train the model stochastically by sampling 100 graphs per epoch. The atoms are initialized wi… view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of the reconstructions obtained by moving along the first two principal [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 9
Figure 9. Figure 9: 30 20 10 0 10 20 30 t-SNE dimension 1 30 20 10 0 10 20 30 40 t-SNE dimension 2 t-SNE visualization of AGDL dictionary coefficients colored by contrast GAMBLING win - loss EMOTION fear - neut MOTOR rf - avg rh - avg RELATIONAL match - relation WM bk2_avg - bk0_avg SOCIAL mental - rnd LANGUAGE story - math [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 3
Figure 3. Figure 3: t-SNE visualization of the learned em￾beddings for α = 0.22 (best contrast classification performance). Each point corresponds to a graph, colored according to its contrast. PCA in the embedding space To further il￾lustrate subject variability in the learned rep￾resentation, we choose two classical contrasts right hand - average and fear - neutral and per￾form PCA in the embedding space across many subject… view at source ↗
Figure 5
Figure 5. Figure 5: Performance for contrast classification (left) and subject classification (right) for different [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: t-SNE visualization of the training set SVC scores for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of the activations for the first [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FUGW loss on validation dataset for ULOT training along epochs [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: All learned dictionary atoms with AGDL for [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: t-SNE visualization of the learned embeddings for all contrasts for [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: t-SNE visualization of the learned atoms, where each point corresponds to an atom. The [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
read the original abstract

Dictionary learning is a powerful tool for creating interpretable representations. When applied to functional magnetic resonance imaging (fMRI) data, the resulting patterns of brain activity can be used for various downstream tasks, such as brain state classification or population-level analysis. However, a major challenge is the variability in brain geometry across individuals. This is usually addressed by projecting each individual brain geometry onto a common template, which removes subject-specific information. In this work, we introduce a novel approach to dictionary learning on fMRI data that explicitly accounts for this variability. We use the optimal transport-based Fused Gromov-Wasserstein (FGW) distance to compare graphs with different geometries and features. To address the challenge of computing multiple FGW distances for large graphs such as those arising from fMRI data, we rely on amortized optimization to learn a neural network that predicts an approximation of the optimal transport plans, which substantially reduces the computational cost. Additionally, we learn dictionary atoms that depend on the FGW trade-off parameter, which controls the balance between feature alignment and structural consistency. Numerical experiments on the HCP dataset demonstrate that the proposed approach captures different levels of geometric variability in the data and provides representations that preserve essential information.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a dictionary learning method for fMRI data that uses the Fused Gromov-Wasserstein (FGW) distance to compare graphs with varying individual brain geometries and node features. It addresses computational cost on large HCP-scale graphs via amortized neural-network approximation of transport plans and makes dictionary atoms explicitly dependent on the FGW trade-off parameter that balances feature alignment against structural consistency. Experiments on the HCP dataset are claimed to show that the resulting representations capture different levels of geometric variability while preserving essential information for downstream tasks.

Significance. If the numerical claims hold, the work provides a principled way to retain subject-specific geometric information in fMRI dictionary learning instead of projecting onto a common template, which could improve interpretability and performance in population-level analyses and brain-state classification. The combination of FGW with amortization is a technically interesting extension of optimal-transport tools to neuroimaging graphs.

major comments (2)
  1. [§3.2] §3.2 (amortized FGW approximation): the central claim that dictionary atoms 'meaningfully depend on the trade-off parameter' while remaining tractable requires that the neural-network predictor preserves sensitivity to the FGW balance parameter. No approximation-error bounds, ablation against exact FGW solvers, or sensitivity plots on representative HCP graph sizes are reported, leaving open the possibility that amortization bias erases the intended dependence on the trade-off parameter.
  2. [§4] §4 (numerical experiments on HCP): the abstract asserts that the method 'captures different levels of geometric variability,' yet the provided description contains no quantitative metrics, error bars, ablation studies, or baseline comparisons (e.g., against template-based dictionary learning). Without these, it is impossible to assess whether the learned atoms actually vary controllably with the trade-off parameter or merely reflect post-hoc choices.
minor comments (2)
  1. [§2] The notation for the FGW objective and the precise manner in which the trade-off parameter enters the dictionary-learning loss should be stated explicitly, ideally with an equation reference.
  2. [§4] Figure captions and axis labels in the experimental section should indicate which values of the trade-off parameter are shown and how variability is quantified.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed comments, which help clarify how to better demonstrate the properties of the amortized FGW approximation and the experimental results. We address each major point below and will revise the manuscript to incorporate additional evidence where feasible.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (amortized FGW approximation): the central claim that dictionary atoms 'meaningfully depend on the trade-off parameter' while remaining tractable requires that the neural-network predictor preserves sensitivity to the FGW balance parameter. No approximation-error bounds, ablation against exact FGW solvers, or sensitivity plots on representative HCP graph sizes are reported, leaving open the possibility that amortization bias erases the intended dependence on the trade-off parameter.

    Authors: We agree that explicit verification of sensitivity is important. The neural network is conditioned on the trade-off parameter α as an explicit input, and the training objective directly minimizes discrepancy to exact FGW plans; this design choice is intended to retain dependence on α. However, we acknowledge the absence of dedicated sensitivity analysis and ablations in the current version. In the revision we will add (i) sensitivity plots of atom variation across α for both the amortized predictor and exact FGW on representative HCP subgraph sizes, and (ii) an ablation comparing reconstruction and downstream performance when using the amortized versus exact solver on smaller instances. Theoretical approximation-error bounds are not currently available and would require substantial additional analysis beyond the scope of the present work. revision: partial

  2. Referee: [§4] §4 (numerical experiments on HCP): the abstract asserts that the method 'captures different levels of geometric variability,' yet the provided description contains no quantitative metrics, error bars, ablation studies, or baseline comparisons (e.g., against template-based dictionary learning). Without these, it is impossible to assess whether the learned atoms actually vary controllably with the trade-off parameter or merely reflect post-hoc choices.

    Authors: The current manuscript presents qualitative visualizations of atoms at different α values together with qualitative downstream-task preservation, but we concur that quantitative support is needed to substantiate the claims. In the revised version we will include (i) quantitative metrics such as atom stability across α, reconstruction error on held-out subjects, and brain-state classification accuracy with error bars, (ii) direct comparisons against a standard template-based dictionary-learning baseline, and (iii) ablation results showing performance as a function of the trade-off parameter. These additions will make the controllability of geometric variability explicit and allow readers to evaluate the claims quantitatively. revision: yes

standing simulated objections not resolved
  • Theoretical approximation-error bounds for the neural-network FGW predictor

Circularity Check

0 steps flagged

No circularity; established OT machinery applied to new domain with independent amortization

full rationale

The derivation relies on the pre-existing Fused Gromov-Wasserstein distance (external to this paper) to compare graphs, with an amortized neural network introduced as a separate computational approximation to enable scaling. Dictionary atoms are explicitly parameterized by the trade-off parameter as a controllable input rather than derived tautologically from fitted outputs. Experiments on the external HCP dataset provide validation outside the method's own equations. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations appear in the chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that FGW distance is an appropriate metric for comparing fMRI graphs with mismatched geometries and that the neural approximation preserves enough accuracy for dictionary learning. No new physical entities are postulated.

free parameters (1)
  • FGW trade-off parameter
    Controls the balance between feature alignment and structural consistency; dictionary atoms are learned to depend on it.
axioms (1)
  • domain assumption Optimal transport plans exist and can be approximated by a neural network for the graph sizes arising in fMRI parcellations.
    Invoked to justify the amortized optimization step that makes the method tractable.

pith-pipeline@v0.9.0 · 5743 in / 1406 out tokens · 48024 ms · 2026-05-21T06:35:28.579237+00:00 · methodology

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Reference graph

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