Shared input and recurrency in neural networks for metabolically efficient information transmission

Shared input to a population of neurons induces noise correlations, which can decrease the information carried by a population activity. Inhibitory feedback in recurrent neural networks can reduce the noise correlations and thus increase the information carried by the population activity. However, the activity of inhibitory neurons is costly. This inhibitory feedback decreases the gain of the population. Thus, depolarization of its neurons requires stronger excitatory synaptic input, which is associated with higher ATP consumption. Given that the goal of neural populations is to transmit as much information as possible at minimal metabolic costs, it is unclear whether the increased information transmission reliability provided by inhibitory feedback compensates for the additional costs. We analyze this problem in a network of leaky integrate-and-fire neurons receiving correlated input. By maximizing mutual information with metabolic cost constraints, we show that there is an optimal strength of recurrent connections in the network, which maximizes the value of mutual information-per-cost. For higher values of input correlation, the mutual information-per-cost is higher for recurrent networks with inhibitory feedback compared to feedforward networks without any inhibitory neurons. Our results, therefore, show that the optimal synaptic strength of a recurrent network can be inferred from metabolically efficient coding arguments and that decorrelation of the input by inhibitory feedback compensates for the associated increased metabolic costs.Author summary: Information processing in neurons is mediated by electrical activity through ionic currents. To reach homeostasis, neurons must actively work to reverse these ionic currents. This process consumes energy in the form of ATP. Typically the more energy the neuron can use, the more information it can transmit. It is generally assumed that due to evolutionary pressures, neurons evolved to process and transmit information efficiently at high rates but also at low costs. Many studies have addressed this balance between transmitted information and metabolic costs for the activity of single neurons. However, information is often carried by the activity of a population of neurons instead of single neurons, and few studies investigated this balance in the context of recurrent neural networks, which can be found in the cortex. In such networks, the external input from thalamocortical synapses introduces pairwise correlations between the neurons, complicating the information transmission. These correlations can be reduced by inhibitory feedback through recurrent connections between inhibitory and excitatory neurons in the network. However, such activity increases the metabolic cost of the activity of the network. By analyzing the balance between decorrelation through inhibitory feedback and correlation through shared input from the thalamus, we find that both the shared input and inhibitory feedback can help increase the information-metabolic efficiency of the system.