Multiscale representations of community structures in attractor neural networks.

Our cognition relies on the ability of the brain to segment hierarchically structured events on multiple scales. Recent evidence suggests that the brain performs this event segmentation based on the structure of state-transition graphs behind sequential experiences. However, the underlying circuit mechanisms are poorly understood. In this paper we propose an extended attractor network model for graph-based hierarchical computation which we call the Laplacian associative memory. This model generates multiscale representations for communities (clusters) of associative links between memory items, and the scale is regulated by the heterogenous modulation of inhibitory circuits. We analytically and numerically show that these representations correspond to graph Laplacian eigenvectors, a popular method for graph segmentation and dimensionality reduction. Finally, we demonstrate that our model exhibits chunked sequential activity patterns resembling hippocampal theta sequences. Our model connects graph theory and attractor dynamics to provide a biologically plausible mechanism for abstraction in the brain.