Modelling brain connectomes networks: Solv is a worthy competitor to hyperbolic geometry!

TL;DR

This study compares multiple geometric embeddings for brain connectomes, demonstrating that Solv geometry is a competitive alternative to hyperbolic models in representing neural networks across species.

Contribution

Introduces a Simulated Annealing-based embedding algorithm for various geometries, including Solv, and shows Solv's effectiveness in modeling connectomes.

Findings

Hyperbolic embeddings often yield the best fit.

Solv embeddings perform comparably to hyperbolic.

The new algorithm outperforms existing methods.

Abstract

Finding suitable embeddings for connectomes (spatially embedded complex networks that map neural connections in the brain) is crucial for analyzing and understanding cognitive processes. Recent studies have found two-dimensional hyperbolic embeddings superior to Euclidean embeddings in modeling connectomes across species, especially human connectomes. However, those studies had limitations: geometries other than Euclidean, hyperbolic, or spherical were not considered. Following William Thurston's suggestion that the networks of neurons in the brain could be successfully represented in Solv geometry, we study the goodness-of-fit of the embeddings for 21 connectome networks (8 species). To this end, we suggest an embedding algorithm based on Simulating Annealing that allows us to embed connectomes to Euclidean, Spherical, Hyperbolic, Solv, Nil, and product geometries. Our algorithm tends to find better embeddings than the state-of-the-art, even in the hyperbolic case. Our findings suggest that while three-dimensional hyperbolic embeddings yield the best results in many cases, Solv embeddings perform reasonably well.