Neural networks can integrate sensory information and generate continuously varying outputs, even though individual neurons communicate only with spikes---all-or-none events. Here we show how this can be done efficiently if spikes communicate "prediction errors" between neurons. This framework gives us a method to implement any linear dynamical system optimally in a recurrent network of integrate and fire neurons. We will concentrate on two illustractive examples: a "diffusion model" for decision making and a simplified arm controller.

This a naturally accounts for two puzzling aspects of cortex. First, it provides a rationale for the tight balance and correlations between excitation and inhibition. Second, it predicts asynchronous and irregular firing as a consequence of predictive population coding, even without any external source of noise. These networks are far more accurate and robust than comparable rate models. This suggests the reliability of cortical representations could have been strongly under-estimated. Moreover, this model has implications implications for sensory and motor tuning curves. We will concentrate on two illustractive examples: a "diffusion model" for decision making and a simplified arm controller.