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. While adaptation is an intrinsic feature of neuronal models like the Hodgkin-Huxley model, the challenge is to in- tegrate adaptation in models of neural computation. Recent computational models like the Adaptive Spike Response Model implement adaptation as spike-based addition of fixed-size fast spike-triggered threshold dynamics and slow spike- triggered currents. Such adaptation has been shown to accurately model neural spiking behavior over a limited dynamic range. Taking a cue from kinetic models of adaptation, we propose a multiplicative Adaptive Spike Response Model where the spike-triggered adaptation dynamics are scaled multiplicatively by the adap- tation state at the time of spiking. We show that unlike the additive adaptation model, the firing rate in the multiplicative adaptation model saturates to a maxi- mum spike-rate. When simulating variance switching experiments, the model also quantitatively fits the experimental data over a wide dynamic range. Furthermore, dynamic threshold models of adaptation suggest a straightforward interpretation of neural activity in terms of dynamic signal encoding with shifted and weighted exponential kernels. We show that when thus encoding rectified filtered stimulus signals, the multiplicative Adaptive Spike Response Model achieves a high coding efficiency and maintains this efficiency over changes in the dynamic signal range of several orders of magnitude, without changing model parameters.