# Impact of Parameter Variability on Transfer Function

In aVLSI neuromorphic engineering neuronal parameters vary slightly between neurons, due to mismatch in the transistors they are built from. Similar variability is likely to be present in networks of biological neurons. The impact of such parameter variability on the transfer function of some models, like e.g. the LIF neuron, is analytically tractable under some assumptions on the synaptic dynamics and input ISI distribution.

For more complex models, like the DPI- or double exponential neurons in our new chip generation simulations can be used to achieve the same. In the figure below we see the mean and standard deviation of the transfer functions of a DPI and an Axon Hillock neuron.

Figure 1: Transfer Function of mismatched DPI and AxonHillock circuits

With such measurements we can determine how strongly a model reacts to parameter variability and thus its robustness towards transistor mismatch. In this particular comparison the DPI neuron is much more robust against parameter variability, except for variations in the threshold parameter, which has a particularly strong impact around the 20Hz input mark. Thanks to this kind of analysis we know which parameters we ought to try to optimize in during chip layout to achieve less neuron-level variability and we can compare the suitability of different models for our technology.