In computational neuroscience, a key question is how information is represented in the activity of neurons (spike trains). Many questions about the nature of this 'neural code' remain open, for instance: How is the brain capable of forming stable representations from noisy, variable input? And what is the role of trial-to-trial variability? In this talk, I will present a model that can represent various forms of input in a self-consistent way.

The Generalized Linear Model (GLM) is a powerful tool in assessing neural spike responses. While the GLM is a descriptive model of how neurons respond to their input, we show here how it can be interpreted to unify encoding (how a neuron represents its input in its output spike train) and decoding (how the input can be reconstructed from the output spike train) properties. We analytically derive a model that is very similar to a GLM and that can be interpreted as a recurrent network of neurons that tracks a continuously varying input. In this model, every neuron only fires a spike if this reduces the mean-squared error between the received input and a prediction of the input based on the output spike trains of the network, implementing a form of Lewicki's `matching pursuit'. 

This model adds a functional interpretation to the originally purely descriptive GLM. The framework predicts that the feature a neuron represents determines an the neuron's spike-generating dynamics and connectivity to other neurons should strongly depend on each other. Moreover, representations in this network are very robust to noise, but that the network spike response can show strong trial-to-trial variability due to the degeneracy of the code, adding a new functional interpretation to the often observed trial-to-trial variability.