Codes and Goals of Neuronal Representations

This thesis combines arguments of efficient coding with models and constraints of population coding and population dynamics in order to derive optimal population codes. Starting from the standard model of population coding for the study of optimal tuning widths, diverging conclusions in the literature are resolved by the introduction of a new independent parameter, namely the dynamic range of a tuning function. The difficulties of applying this standard model to neuronal representations of, say natural images, motivates a more exhaustive search for characteristic features of population codes that are most relevant for coding efficiency. Minimizing the dynamic ranges of the tuning functions turns out to be most important for the maximization of Fisher information. At the same time, however, the optimization of population codes without strong a priori constraints on the shape of tuning functions uncovers severe limitations of Fisher information as a measure for coding efficiency. Direct numerical evaluations of the minimum mean square error are used (for the first time in the literature) to compare the efficiency of characteristic examples of population codes, confirming the advantage of a small dynamic range. The results on optimal population coding in the first part of this thesis are summarized in the proposal of the Bernoulli coding hypothesis. In short, it states that rate coding at physiologically plausible time scales suggests the use of binary coding rather than analog coding.The Bernoulli coding hypothesis is challenged by criteria other than coding efficiency as well. Additionally to the study of the influence of computational constraints on the neuronal readout, the question of the robustness of a code and the possibility of faithful signal transmission in spite of the neuronal dynamics are investigated in the second part of the thesis. In particular the latter provides an additional, independent argument for the Bernoulli coding hypothesis.