Summation and multiplication: two distinct operation domains of leaky integrate-and-fire neurons

Abstract

The spiking frequency of a leaky integrate-and-fire (LIF) neuron can be proportional to the sum or the product of a number n≥2 of input frequencies. In the paper, the parameter domains (discharge time constants and synaptic weights) for these two operation modes are defined theoretically and studied by simulations. Summation is based on the frequency division principle and requires discharge time constant as long as possible. In this mode, the LIF neuron is subject to phase locking effects and is insensitive to the irregularity of the input spike trains. Multiplication is based on coincidence detection and requires shorter time constants. Simulations show that the quality of the mulutiplication function decreases for large irregularities of the input spike trains, that there is an optimum value of the synaptic weights and that there is a consequent input-output frequency level drop. In the brain, the frequency level decrease observed from retina to higher cortical areas might indicate the presence of multiplication-type layers. Physiologically, distant synapses are probably mainly involved in summation while proximal synapses are used for multiplicatton. It is proposed that learning involves synaptic relocation as well as weights modification.