# Regensburg 2002 – wissenschaftliches Programm

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# SYPH: Physik im Hirn - Physical Approaches to Brain Function

## SYPH 2: Physik im Hirn - Physical Approaches to Brain Function

### SYPH 2.3: Poster

### Donnerstag, 14. März 2002, 15:30–18:00, Poster D

**Optimal neuronal population coding and Fisher information** — •Matthias Bethge, David Rotermund, and Klaus Pawelzik — University of Bremen, Institute of Theoretical Physics,

Kufsteiner Str., D-28334 Bremen

Efficient coding has been proposed as a first principle explaining
neuronal response properties in the central nervous system (Barlow).
Optimal codes, however, depend on the natural limitation of the
particular physical system. Here we investigate how optimal neural
encoding strategies are influenced by the finite number of neurons
*N* (place constraint), the limited decoding time window length *T*
(time constraint), the maximum neuronal firing rate *f*_{max}
(power constraint) and the maximal average rate ⟨ *f*
⟩_{max} (energy constraint). While Fisher information
provides a general lower bound for the mean squared error of
unbiased signal reconstruction, its use for determining optimal
encoding strategies is limited. Analyzing simple examples, we
illustrate some typical pitfalls and thereby show that Fisher
information mainly provides a valid measure for the precision of
a code in the low-noise limit given by large observation time
windows. In particular, we show that Fisher
information is not suitable to derive characteristic signatures of
optimal population codes. Alternatively, we analyze the minimum
mean squared error, whereby it turns out that labeled line coding
constitutes the major contribution to population codes for
small *T* and large *N*, while intensity coding, quantified by
Fisher information, can be neglected. Furthermore, it turns out
that the accuracy of unimodal coding schemes depends only weakly
on the tuning width as long as energy consumption can be
neglected.