What is the meaning of the dynamics of a neuronal circuit? The activity of individual neurons and networks changes and fluctuates on the scale of tens of milliseconds or even less, yet the outside world that it presumably represents changes far more slowly on a typical scale of seconds. How can this discrepancy be reconciled? Are these dynamics the result of biological messiness, or are they the hard-to-interpret substrate of circuit computations?
My research goal is to understand how dynamics in neuronal circuits relate and constrain the representation of information and computations upon it. Traditionally, neural dynamics has been studied by dynamical systems physicists, but mostly as a phenomenon in and of itself, separate from representation. Similarly, representation and coding have been studied in the context of statistics, information theory, and machine learning, but mostly in the static regime. Yet, the nature of the brain is the union of both aspects. Its structure and biophysics cause strong dynamical activity, and this activity in turn must ultimately represent information. Therefore, my lab aims to bring together these two disparate approaches and further our understanding of the unique form of computation that occurs in neural circuits.
How does one determine the role of dynamics in neural computation? In the lab, we adopt three synergistic strategies. First, we are interested in directly analyzing the dynamics of neural circuits to better understand the relation between neural dynamics and behavior in well-understood tasks such as sensory discrimination or working memory. Second, we theoretically explore the types of dynamics that could be associated with particular network computations. Third, we analyze the structural properties of neural circuits in an effort to understand how these properties constrain circuit dynamics and the types of computations that circuits can perform.
For instance, in previous work, we have shown the consequences of two ubiquitous properties of cortical structures for the relation between dynamics and representation. These properties are the large ratio of cortical neurons to thalamic neurons and the numerous lateral connections between cortical neurons. The former means that different neurons must encode partially overlapping properties, technically referred to as an "overcomplete" representation. The latter implies that different neurons have the opportunity to shape each other’s activity. We have shown that these properties taken together raise the possibility of network architectures in which the activity of each neuron is constantly changing, yet the representation of the network as a whole remains constant. Such networks may explain the very diverse activity of neurons in working memory tasks, in which the representation must remain stable.
Now is an exciting time to be in theoretical neuroscience. The convergence of multiple experimental techniques is increasingly making mapping the detailed dynamics and connectivity of neural circuits a reality. This new data inspires us to think of novel theories and allows us to confront new and old theoretical ideas about the behavior of neural circuits in unprecedented detail.
As of August 16, 2013