Graph embeddings for identifying symmetries in Connectomes.

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Connectomics

Background:

• Neural circuit models often organize synaptic connections based on processed variables.
• Canonical models for head direction, spatial navigation, and orientation selectivity exhibit symmetries related to angular and spatial variables.

Purpose of the Study:

• To develop a graph embedding algorithm for identifying symmetries in neural connectomes.
• To differentiate between cell-type-specific structure and circuit symmetries.

Main Methods:

• A novel graph embedding algorithm was developed.
• The algorithm was applied to the Drosophila brain connectome and a synthetic grid cell network.

Main Results:

• The method successfully identified rotational and translational symmetries in Drosophila heading direction and visual projection neuron circuits.
• Toroidal symmetry was identified in a synthetic medial entorhinal cortex grid cell connectome.
• The embedding geometries revealed latent variables processed by the circuits.

Conclusions:

• The developed algorithm effectively identifies symmetries in neural circuits.
• This approach can uncover the latent variables and cell types underlying neural computations.
• It offers a new tool for analyzing complex neural network architectures.