D Rotermund | PubMed Health

PubMed2003

Optimal neural rate coding leads to bimodal firing rate distributions.

Many experimental studies concerning the neuronal code are based on graded responses of neurons, given by the emitted number of spikes measured in a certain time window. Correspondingly, a large body of neural network theory deals with analogue neuron models and discusses their potential use for computation or function approximation. All physical signals, however, are of limited precision, and neuronal firing rates in cortex are relatively low. Here, we investigate the relevance of analogue signal processing with spikes in terms of optimal stimulus reconstruction and information theory. In particular, we derive optimal tuning functions taking the biological constraint of limited firing rates into account. It turns out that depending on the available decoding time T, optimal encoding undergoes a phase transition from discrete binary coding for small T towards analogue or quasi-analogue encoding for large T. The corresponding firing rate distributions are bimodal for all relevant T, in particular in the case of population coding.

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PubMed2002

Optimal short-term population coding: when Fisher information fails.

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal 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 to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (f(min)T, f(max)T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.

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