CTN: Ivan Davidovich

Title: Uncovering latent low-dimensional structure in network connectivity

Abstract: Network connectivity constrains the patterns of neural activity in the brain. These constraints are often observed as low-dimensional manifolds in neural activity space. Continuous Attractor Networks (CANs) are a prime example of this type of network phenomenon. Interestingly, there are examples of CANs where the structure or topology of the manifold observed in the space of neural activity does not match the corresponding structure or topology of the connection weights in the network. To learn more about this relationship, we need to go beyond studying the structure of neural activity and investigate the structure in the connectivity of those systems. To this end, we wish to identify a minimal set of parameters, or coordinates, that are enough to characterize the connectivity weights between any pair of neurons given their coordinate values. In the simplest cases, this is equivalent to finding an appropriate ordering (labelling) of cells that will reveal the underlying structure in the connectivity weights. Traditional approaches use properties of neural activity, such as neural selectivity, to identify such an ordering. However, there are many situations that are not amenable to this treatment, either because neural activity data is not available, for example in connectome data sets, because tuning curves are disordered, or because of the particular architecture of the network. To address this issue, we employ tools from Dimensionality Reduction and Topological Data Analysis to uncover structure directly from the connectivity weights in different examples of CAN models. I will show that this approach can uncover connectivity structure that is different from the one observed in activity space, and in some cases works even when a fairly large fraction of neurons in the system is not observed. We argue that this perspective towards the study of structure in network connectivity can lead to the discovery of organization in cases where no obvious structure is present in the activity of the neural population, or where connectomics data is available without corresponding activity recordings.