Abstract
This paper proposed a new method to determine the neuronal tuning curves for maximum information efficiency by computing the optimum firing rate distribution. Firstly, we proposed a general definition for the information efficiency, which is relevant to mutual information and neuronal energy consumption. The energy consumption is composed of two parts: neuronal basic energy consumption and neuronal spike emission energy consumption. A parameter to model the relative importance of energy consumption is introduced in the definition of the information efficiency. Then, we designed a combination of exponential functions to describe the optimum firing rate distribution based on the analysis of the dependency of the mutual information and the energy consumption on the shape of the functions of the firing rate distributions. Furthermore, we developed a rapid algorithm to search the parameter values of the optimum firing rate distribution function. Finally, we found with the rapid algorithm that a combination of two different exponential functions with two free parameters can describe the optimum firing rate distribution accurately. We also found that if the energy consumption is relatively unimportant (important) compared to the mutual information or the neuronal basic energy consumption is relatively large (small), the curve of the optimum firing rate distribution will be relatively flat (steep), and the corresponding optimum tuning curve exhibits a form of sigmoid if the stimuli distribution is normal.
Highlights
INTRODUCTIONNeuronal systems are assumed to be optimized for information encoding after millions of years of natural selection, in the sense that the capacity of the neural systems (or channels in the language of information society) for information transmission is occupied as much as possible, leaving as little as possible the “power” of the channels being unutilized
Neuronal systems are assumed to be optimized for information encoding after millions of years of natural selection, in the sense that the capacity of the neural systems for information transmission is occupied as much as possible, leaving as little as possible the “power” of the channels being unutilized
As one can calculate the tuning curve numerically if optimum firing rate distribution for information efficiency and the stimuli distribution are given, we focused on exploring the optimum firing rate distribution for the information efficiency in this paper
Summary
Neuronal systems are assumed to be optimized for information encoding after millions of years of natural selection, in the sense that the capacity of the neural systems (or channels in the language of information society) for information transmission is occupied as much as possible, leaving as little as possible the “power” of the channels being unutilized. To obtain tuning curves in this way, the following three elements need to be considered: the calculation of energy consumption (Levy and Baxter, 1996; Wang and Zhang, 2007; Torreal dea Francisco et al, 2009; Berger and Levy, 2010; Sengupta and Stemmler, 2014; Sengupta et al, 2014), the definition of the information efficiency (Levy and Baxter, 1996; Moujahid et al, 2011; Kostal and Lansky, 2013; Sengupta et al, 2014), and the probability distribution of inputs (Dayan and Abbott, 2001; Nikitin et al, 2009). The optimum spike count response distribution (the probability distribution of the numbers of the spikes emitted by the neuron for different inputs, which is explained in details in Section The model for information-efficiency in neuronal encoding system) is analyzed in terms of full entropy and energy consumption, and a combination of exponential-based functions is designed for it.
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