COMPUTING WITH THE LEAKY INTEGRATE-AND-FIRE NEURON - LOGARITHMIC COMPUTATION AND MULTIPLICATION

The leaky integrate-and-fire (LIF) model of neuronal spiking (Stein 19 67) provides an analytically tractable formalism of neuronal firing ra te in terms of a neuron's membrane time constant, threshold, and refra ctory period. LIF neurons have mainly been used to model physiological ly realistic spike trains, but little application of the LIF model app ears to have been made in explicitly computational contexts. In this a rticle, we show that the transfer function of a LIF neuron provides, o ver a wide-parameter range, a compressive nonlinearity sufficiently cl ose to that of the logarithm so that LIF neurons can be used to multip ly neural signals by mere addition of their outputs yielding the logar ithm of the product. A simulation of the LIF multiplier shows that und er a wide choice of parameters, a LIF neuron can log-multiply its inpu ts to within a 5% relative error.