KFC-SNN: A Kalman-Filtered Complex-Valued Spiking Neural Network for Robust Temporal Learning

Spiking neural networks (SNNs) offer a promising approach to energy-efficient temporal processing through intrinsic memory and sparse event communication. However, disturbances can disrupt membrane dynamics and spike generation, undermining computational reliability. Biologically inspired gating mechanisms use temporal state information to improve robustness, motivating a complementary estimation-based account of how current inputs should be combined with neuronal history. Guided by the prediction-and-correction principle of Kalman filtering, we introduce a Kalman-Filtered Complex-Valued (KFC) SNN that combines Kalman-inspired predictive fusion dynamics (KF) with complex-valued spike representations (CS). The KF neuron forms a prediction from the preceding membrane state and treats the current input as an observation. The prediction and observation are adaptively weighted following the Kalman filtering principle to regulate the membrane potential, thereby reducing the influence of input disturbances. The CS mechanism introduces imaginary spikes that regulate real-valued firing through activity-dependent inhibition, while providing an additional output stream that carries temporal information. We further develop a general framework for membrane-potential regulation that describes a class of input-state integration mechanisms through a common convex optimization formulation, with KF as a quadratic instance. Experiments on SHD, SSC, and ESC-50 demonstrate improved classification accuracy and robustness to stochastic input corruptions over the evaluated spiking baselines, including gains of 5.7 percentage points in clean accuracy on ESC-50 and 13.5 percentage points under Gaussian noise on SHD.