U Oregon Neuro

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We use random matrix theory to show how gating robustly produces marginal stability and line attractors – important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation-time of the dynamics. Gating is also shown to give rise to a novel, discontinuous transition to chaos, where the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity), contrary to a seminal result for additive RNNs. Critical surfaces and regions of marginal stability in the parameter space are indicated in phase diagrams, thus providing a map for principled parameter choices for ML practitioners. Finally, we develop a field-theory for gradients that arise in training, by incorporating the adjoint sensitivity framework from control theory in the DMFT. This paves the way for the use of powerful field-theoretic techniques to study training/gradients in large RNNs.

The mechanisms by which neural circuits generate an extensible library of motor motifs and flexibly string them into arbitrary sequences are unclear. We developed a model in which inhibitory basal ganglia output neurons project to thalamic units that are themselves bidirectionally connected to a recurrent cortical network. During movement sequences, electrophysiological recordings of basal ganglia output neurons show sustained activity patterns that switch at the boundaries between motifs. Thus, we model these inhibitory patterns as silencing some thalamic neurons while leaving others disinhibited and free to interact with cortex during specific motifs. We show that a small number of disinhibited thalamic neurons can control cortical dynamics to generate specific motor output in a noise robust way. If the thalamic units associated with each motif are segregated, many motor outputs can be learned without interference and then combined in arbitrary orders for the flexible production of long and complex motor sequences.

Olfactory navigation is essential for the survival of living beings from unicellular organisms to mammals. In the wild, rodents combine odor information with an internal spatial representation of the environment for foraging and navigation. What are the neural circuits in the brain that implement these behaviours? My research addresses this question by examining the synaptic circuits and neural population activity in the olfactory cortex to understand the integration of olfactory and spatial information. Primary olfactory (piriform) cortex (PCx) has long been recognized as a highly associative brain structure. What is the behavioural and functional role of these associative synapses in PCx? We designed an odor-cued navigation task, where rats must use both olfactory and spatial information to obtain water rewards. We recorded from populations of posterior piriform cortex (pPCx) neurons during behaviour and found that individual neurons were not only odor-selective, but also fired differentially to the same odor sampled at different locations, forming an “olfactory place map”. Spatial locations can be decoded from simultaneously recorded pPCx population, and spatial selectivity is maintained in the absence of odors, across behavioural contexts. This novel olfactory place map is consistent with our finding for a dominant role of associative excitatory synapses in shaping PCx representations, and suggest a role for PCx spatial representations in supporting olfactory navigation. This work not only provides insight into the neural basis for how odors can be used for navigation, but also reveals PCx as a prime site for addressing the general question of how sensory information is anchored within memory systems and combined with cognitive maps to guide flexible behaviour.

The electrosensory lobe (ELL) in mormyrid electric fish is a cerebellar-like structure that cancels the sensory effects of self-generated electric fields, allowing prey to be detected. Like the cerebellum, the ELL involves two stages of processing, analogous to the Purkinje cells and cells of the deep cerebellar nuclei. Through the work of Curtis Bell and others, a model was previously developed to describe the output stage of the ELL, but the role of the Purkinje-cell analogs, the medium ganglion (MG) cells, in the circuit had remained mysterious. I will present a complete, multi-layer circuit description of the ELL, developed in collaboration with Nate Sawtell and Salomon Muller, that reveals a novel role for the MG cells. The resulting model provides an example of how a biological system solves well-known problems associated with learning in multi-layer networks, and it reveals that ELL circuitry is organization on the basis of learning rather than by the response properties of neurons.