2.3.1. Latency Encoding

A straightforward means to forming a temporal representation of an input feature is to signal its intensity based on the latency of a spike. Specifically, if we consider an encoding LIF neuron that is injected with a fixed input current, then the time taken for it to respond with a spike can be determined as a function of the current's intensity: by interpreting the feature's value as a current, it is therefore possible for it to be mapped to a unique firing time. For an encoding LIF neuron i with a fixed firing threshold that only receives a constant current I_i, its first response time is given by (Gerstner and Kistler, 2002):

where we use the same parameter selections for τ_m and ϑ as used in section 2.1, and the resistance is set to R = 4MΩ. In terms of relating feature values to current intensities, we take one of two different approaches. In the first approach we arbitrarily associate each feature value with a unique intensity value, which is ideally suited to the case where features are limited to a small number of discrete values. In the second approach, and in the case where features take real values, we devise a more direct association; specifically, each value x_i belonging to a feature vector x is normalized to fall within the unit range before being scaled by a factor I_max, providing the current intensity I_i. The specific choice of I_max used depends on the studied dataset. Regardless of the approach we take, and in order to maintain a tight distribution of early spike arrivals, we disregard spikes with timings >9 ms by setting them to infinity.