Efficient spike-coding with multiplicative adaptation in a spike response model

Neural adaptation underlies the ability of neurons to maximize encoded informa-tion over a wide dynamic range of input stimuli. Recent spiking neuron mod-els like the adaptive Spike Response Model implement adaptation as additive fixed-size fast spike-triggered threshold dynamics and slow spike-triggered cur-rents. Such adaptation accurately models neural spiking behavior over a limited dynamic input range. To extend efficient coding over large changes in dynamic in-put range, we propose a multiplicative adaptive Spike Response Model where the spike-triggered adaptation dynamics are scaled multiplicatively by the adaptation state at the time of spiking. We show that, unlike the additive adaptation model, the firing rate in our multiplicative adaptation model saturates to a realistic max-imum spike-rate regardless of input magnitude. Additionally, when simulating variance switching experiments, the model quantitatively fits experimental data over a wide dynamic range. Dynamic threshold models of adaptation furthermore suggest a straightforward interpretation of neural activity in terms of dynamic dif-ferential signal encoding with shifted and weighted exponential kernels. We show that when thus encoding rectified filtered stimulus signals, the multiplicative adap-tive Spike Response Model achieves a high coding efficiency and maintains this efficiency over changes in the dynamic signal range of several orders of magni-tude, without changing model parameters.