Unified Generative Latent Representation for Functional Brain Graphs

TL;DR

This work addresses the challenge of summarizing functional brain graphs by learning a unified, geometry-aware latent representation that jointly captures spectral gradients and topological structure in dense, weighted FC graphs. It introduces a graph transformer autoencoder with an edge-conditioned encoder, a memory-augmented cross-attention decoder, and latent diffusion on the graph-level latent $z_g$, guided by spectral geometry. The learned latent space meaningfully separates working-memory states and decoded stimuli, and diffusion-based sampling yields biologically plausible synthetic graphs with statistics aligned to real data, enabling data augmentation and mechanistic explorations of connectivity-to-computation. Overall, the approach provides a principled pathway to map smooth variations in brain graph structure to cognitive states and to generate plausible connectomes for further analysis and modeling.

Abstract

Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional connectivity graphs occupy a low-dimensional latent geometry along which both topological and spectral structures display graded variations. Here, we estimated this unified graph representation and enabled generation of dense functional brain graphs through a graph transformer autoencoder with latent diffusion, with spectral geometry providing an inductive bias to guide learning. This geometry-aware latent representation, although unsupervised, meaningfully separated working-memory states and decoded visual stimuli, with performance further enhanced by incorporating neural dynamics. From the diffusion modeled distribution, we were able to sample biologically plausible and structurally grounded synthetic dense graphs.

Figures (5)

• Figure 1: (A) Resting-state FC graph reconstruction comparing spectral, graph features, edge-only encodings and baseline. (B) Latent space color coded by spectral prominence (of association-sensory and visual-sensorimotor gradients) and global graph properties. (C) Task-fMRI FC reconstruction across different feature encodings. (D) UMAP showing cognitive load and stimulus type separation in $z_g$.
• Figure 2: (A) Latent space of resting-state FC colored by association-sensory gradient ($\psi_{AS}$) prominence and diffusion-learned distribution $p(z_g)$. (B) Example generation of low- and high-$\psi_{AS}$ prominence spectral embeddings and connectivity matrices. (C) Distribution alignment of graph statistics (mean degree, degree variability, modularity) between test and generated sets.
• Figure 3: Diffusion-map embeddings (first two gradients). The $\psi_{AS}$ continuously spans from transmodal association to unimodal sensory networks, while $\psi_{VS}$ separates lower-order visual and somatosensory/motor systems.
• Figure 4: (A) Latent space embedding $z_g$ of FC graphs from seven cognitive tasks. (B) Confusion matrix for linear classifier on test set $z_g$. (C) Radial integration--segregation origination in $z_g$.
• Figure 5: (A) Linear noise scheduler showing the signal retention $\sqrt{\bar{\alpha}_t}$ across diffusion steps $t$, with the corresponding forward noising process in latent space. (B) The covariance structure of latent dimensions in the original training and generated sets.