Spiking Neural Networks with Elephant Reinforcement

What the math gives to ML

The paper introduces a finite spiking network whose firing threshold is driven by a signed, cumulative reinforcement state rather than by a fixed or exponentially decaying adaptation variable. The transferable asset is the separation between membrane potential, reinforcement memory, and update count, together with a positive-part threshold that selectively suppresses activity after positive reinforcement while allowing negative reinforcement to reduce the threshold. This can become a drop-in adaptive-threshold mechanism for surrogate-gradient SNNs, especially when sustained input causes pathological high firing rates or unstable recurrent activity. The paper's Wasserstein contraction and mean-field results motivate testing whether the same memory produces more stable population dynamics, although the extracted material does not provide enough theorem detail to transplant the formal bound directly.