Balanced input allows optimal encoding in a stochastic binary neural network model: an analytical study

Abstract

Recent neurophysiological experiments have demonstrated a remarkable effect of attention on the underlying neural activity that suggests for the first time that information encoding is indeed actively influenced by attention. Single cell recordings show that attention reduces both the neural variability and correlations in the attended condition with respect to the non-attended one. This reduction of variability and redundancy enhances the information associated with the detection and further processing of the attended stimulus. Beyond the attentional paradigm, the local activity in a neural circuit can be modulated in a number of ways, leading to the general question of understanding how the activity of such circuits is sensitive to these relatively small modulations. Here, using an analytically tractable neural network model, we demonstrate how this enhancement of information emerges when excitatory and inhibitory synaptic currents are balanced. In particular, we show that the network encoding sensitivity--as measured by the Fisher information--is maximized at the exact balance. Furthermore, we find a similar result for a more realistic spiking neural network model. As the regime of balanced inputs has been experimentally observed, these results suggest that this regime is functionally important from an information encoding standpoint.

Figure 1. Architecture of the stochastic binary neurons network with Glauber dynamics.

(See text for details).

Figure 2. Stochastic binary neurons network behavior as a function of the inhibition level

. Current balance (top), Fano factor reduction (middle) (for a bias ) and Fisher information scaled down by (for a bias ) (bottom). (Left) Case of selective populations, for which input balance occurs at (dashed line). (Right) Case of selective populations, for which input balance occurs at (dashed line). All results are analytical.

Figure 3. Spiking neurons network behavior as a function of the inhibition level

. (A) Mean synaptic current and (B) estimated Fisher information for the population receiving an extra bias . This quantity measures the network activity sensitivity to the bias and is calculated at bias Hz (black, blue and green curves, respectively). The Fisher information peaks around the excitatory and inhibitory synaptic currents balance. Due to noise in the data, it is almost impossible to distinguish the different curves.

Figure 4. Fisher information behavior for the spiking neurons network as a function of the inhibition level

. (A) Mean spike count , (B) its derivative with respect to the bias, , (C) the spike count variance and (D) the estimated Fisher information (red) and its analytical fit (dashed black). The analytical fit works very well, showing that the Fisher information peaks around input balance because also peaks there. In turn, this quantity peaks because the mean spike count has, with respect to , a maximum (absolute) slope around balance.