Spanning the arc between optimality theories and data
Ideas about optimization are at the core of how we approach biological complexity. Quantitative predictions about biological systems have been successfully derived from first principles in the context of efficient coding, metabolic and transport networks, evolution, reinforcement learning, and decision making, by postulating that a system has evolved to optimize some utility function under biophysical constraints. Yet as normative theories become increasingly high-dimensional and optimal solutions stop being unique, it gets progressively hard to judge whether theoretical predictions are consistent with, or "close to", data. I will illustrate these issues using efficient coding applied to simple neuronal models as well as to a complex and realistic biochemical reaction network. As a solution, we developed a statistical framework which smoothly interpolates between ab initio optimality predictions and Bayesian parameter inference from data, while also permitting statistically rigorous tests of optimality hypotheses.
Rational thoughts in neural codes
First, we describe a new method for inferring the mental model of an animal performing a natural task. We use probabilistic methods to compute the most likely mental model based on an animal’s sensory observations and actions. This also reveals dynamic beliefs that would be optimal according to the animal’s internal model, and thus provides a practical notion of “rational thoughts.” Second, we construct a neural coding framework by which these rational thoughts, their computational dynamics, and actions can be identified within the manifold of neural activity. We illustrate the value of this approach by training an artificial neural network to perform a generalization of a widely used foraging task. We analyze the network’s behaviour to find rational thoughts, and successfully recover the neural properties that implemented those thoughts, providing a way of interpreting the complex neural dynamics of the artificial brain. Joint work with Zhengwei Wu, Minhae Kwon, Saurabh Daptardar, and Paul Schrater.