How random connections and motifs shape the covariance spectrum of recurrent network dynamics
Theoretical neuroscience aims to understand the relationship between neuron dynamics and connectivity in recurrent circuits. This has been intensively studied at the local level, where dynamics is described by pairwise correlations. Recent advances in simultaneous recordings of many neurons have allowed researchers to address the question at the global level, such as for the dimensionality of population dynamics. Our work contributes to this effort by analyzing the impact of connectivity statistics, including certain motifs, on the bulk and outlier covariance eigenvalues. By considering linearized dynamics around a steady state, we obtained analytically the covariance spectrum which exhibits a signature long tail robust to model variants and matches zebrafish calcium imaging data. This provides a local circuit mechanism for shaping the geometry of population dynamics and a quantitative benchmark for interpreting data. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-05-22. Recording duration: 00:53:15.
Structure, Function, and Learning in Distributed Neuronal Networks
A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of neuronal networks. In this talk, I will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from structure in neural populations and from biologically plausible learning rules. First, I will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes how easy or hard it is to discriminate between object categories based on the underlying neural manifolds’ structural properties. Next, I will describe how such methods can, in fact, open the ‘black box’ of neuronal networks, by showing how we can understand a) the role of network motifs in task implementation in neural networks and b) the role of neural noise in adversarial robustness in vision and audition. Finally, I will discuss my recent efforts to develop biologically plausible learning rules for neuronal networks, inspired by recent experimental findings in synaptic plasticity. By extending our mathematical toolkit for analyzing representations and learning rules underlying complex neuronal networks, I hope to contribute toward the long-term challenge of understanding the neuronal basis of behaviors.