Poster Presentation

Contributed Talk Session: Wednesday, August 5, 10:15 – 11:15 am, Skirball Theater
Poster D in Poster Session D: Wednesday, August 5, 2:00 – 3:45 pm, Kimmel Center, Shorin & Rosenthal Rooms

A Nonlocal Variational Framework for Optimal Neural Representations

Gengshuo John Tian¹, Brent Doiron²; ¹Flatiron Institute, ²University of Pittsburgh

Presenter: Gengshuo John Tian

Despite decades of study it still remains unclear how neural populations should organize their representation of sensory, motor, and cognitive variables so as to optimize discriminability. There are two important limitations in previous works. First, Fisher information (FI) is commonly used to measure the quality of population codes (Seung and Sompolinsky, 1993), yet FI is fundamentally a local measure that is incapable of capturing global structures of the representation, as is needed in coarse discrimination (Berens et al., 2011). Second, simplified forms of tuning functions (such as Gaussian bumps) are usually imposed for analytic tractability, but in real neural data, tuning curves are diverse and in most cases defy being described by an overly simplistic structure. Here, we tackle these issues by focusing on the representation of a one-dimensional periodic variable θ and analytically minimizing the average binary classification error between all θ pairs without any restriction on the shape of the tuning curves for various noise models. Our cost function accounts for both fine and coarse discrimination and the feasible set is an infinite-dimensional function space, making our formulation a nonlocal variational problem. We obtained the solution by viewing the space of neural response distributions as a Riemannian manifold in the sense of information geometry (Amari, 2016) and using a result from knot energy theory (Abrams et al., 2003). The optimality of the derived representation is demonstrated with simulations. We deduce two predictions from the model, one concerning the range of tuning curve shapes and the other relating neurons' variability to their tuning sharpness. Both of these predictions are verified in a head-direction cell dataset (Duszkiewicz et al., 2024). Our results point to a new framework for studying the global structure of neural representations.

Topic Area: Methods, Tools, Theory & Neural Coding