Attractor-based models for sequences and pattern generation in neural circuits

TL;DR

This paper introduces attractor-based neural models for sequences and rhythmic activities, unifying static and dynamic pattern encoding in neural circuits using threshold-linear networks.

Contribution

It presents novel attractor-based models for neural functions like counting, locomotion, and sequence generation, along with new theoretical results on network architecture conditions.

Findings

Models successfully encode quadruped gaits and mollusk orientation.

Theoretical conditions for sequential attractors in neural networks.

New architecture for layered networks with minimized interference.

Abstract

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also substantial evidence that the brain encodes memories and processes information via sequences of neural activity. In this dissertation, we are focused on the general problem of how neural circuits encode rhythmic activity, as in central pattern generators (CPGs), as well as the encoding of sequences. Traditionally, rhythmic activity and CPGs have been modeled using coupled oscillators. Here we take a different approach, and present models for several different neural functions using threshold-linear networks. Our approach aims to unify attractor-based models (e.g., Hopfield networks) which encode static and dynamic patterns as attractors of the network. In the first half of this dissertation, we present several attractor-based models. These include: a network that can count the number of external inputs it receives; two models for locomotion, one encoding five different quadruped gaits and another encoding the orientation system of a swimming mollusk; and, finally, a model that connects the fixed point sequences with locomotion attractors to obtain a network that steps through a sequence of dynamic attractors. In the second half of the thesis, we present new theoretical results, some of which have already been published. There, we established conditions on network architectures to produce sequential attractors. Here we also include several new theorems relating the fixed points of composite networks to those of their component subnetworks, as well as a new architecture for layering networks which produces "fusion" attractors by minimizing interference between the attractors of individual layers.