CONE: Convex-Optimized-Synaptic Efficacies for Temporally Precise Spike Mapping

Spiking neural networks are well suited to perform time-dependent pattern recognition problems by encoding the temporal dimension in precise spike times. With an appropriate set of weights, a spiking neuron can emit precisely timed action potentials in response to spatiotemporal input spikes. However, deriving supervised learning rules for spike mapping is nontrivial due to the increased complexity. Existing methods rely on heuristic approaches that do not guarantee a convex objective function and, therefore, may not converge to a global minimum. In this paper, we present a novel technique to obtain the weights of spiking neurons by formulating the problem in a convex optimization framework, rendering it be compatible with the established methods. We introduce techniques to influence the weight distribution and membrane trajectory, and then study how these factors affect robustness in the presence of noise. In addition, we show how the existence of a solution can be determined and assess memory capacity limits of a neuron model using synthetic examples. The practical utility of our technique is further assessed by its application to gait-event detection using the experimental data.