Sensitivity of Spiking Neural Networks Due to Input Perturbation

Background: To investigate the behavior of spiking neural networks (SNNs), the sensitivity of input perturbation serves as an effective metric for assessing the influence on the network output. However, existing methods fall short in evaluating the sensitivity of SNNs featuring biologically plausible leaky integrate-and-fire (LIF) neurons due to the intricate neuronal dynamics during the feedforward process. Methods: This paper first defines the sensitivity of a temporal-coded spiking neuron (SN) as the deviation between the perturbed and unperturbed output under a given input perturbation with respect to overall inputs. Then, the sensitivity algorithm of an entire SNN is derived iteratively from the sensitivity of each individual neuron. Instead of using the actual firing time, the desired firing time is employed to derive a more precise analytical expression of the sensitivity. Moreover, the expectation of the membrane potential difference is utilized to quantify the magnitude of the input deviation. Results/Conclusions: The theoretical results achieved with the proposed algorithm are in reasonable agreement with the simulation results obtained with extensive input data. The sensitivity also varies monotonically with changes in other parameters, except for the number of time steps, providing valuable insights for choosing appropriate values to construct the network. Nevertheless, the sensitivity exhibits a piecewise decreasing tendency with respect to the number of time steps, with the length and starting point of each piece contingent upon the specific parameter values of the neuron.