Optimization Principles for the Neural Code

Animals receive information from the world in the form of continuous functions of time. At a very early stage in processing, however, these continuous signals are converted into discrete sequences of identical "spikes". All information that the brain receives about the outside world is encoded in the arrival times of these spikes. The goal of this thesis is to determine if there is a universal principle at work in this neural code. We are motivated by several recent experiments on a wide range of sensory systems which share four main features: High information rates, moderate signal to noise ratio, efficient use of the spike train entropy to encode the signal, and the ability to extract nearly all the information encoded in the spike train with a linear response function triggered by the spikes. We propose that these features can be understood in terms of codes "designed" to maximize information flow. To test this idea, we use the fact that any point process encoding of an analog signal embedded in noise can be written in the language of a threshold crossing model to develop a systematic expansion for the transmitted information about the Poisson limit--the limit where there are no correlations between the spikes. All codes take the same simple form in the Poisson limit, and all of the seemingly unrelated features of the data arise naturally when we optimize a simple linear filtered threshold crossing model. We make a new prediction: Finding the optimum requires adaptation to the statistical structure of the signal and noise, not just to DC offsets. The only disagreement we find is that real neurons outperform our model in the task it was optimized for--they transmit much more information. We then place an upper bound on the amount of information available from the leading term in the Poisson expansion for any possible encoding, and find that real neurons do exceedingly well even by this standard. We conclude that several important features of the neural code can be understood in terms of simple, physically motivated variational principles.