Implementing and integrating spiking neurons for neuromorphic hardware realization conforming to spiking neural networks holds great promise in enabling efficient learning and decision‐making. The spiking neurons, however, may lack the spiking dynamics to encode the dynamical information in complex real‐world problems. Herein, using filamentary memristors from solution‐processed hexagonal boron nitride, this study assembles leaky integrate‐and‐fire spiking neurons and, particularly, harnesses the common switching stochasticity feature in the memristors to allow key neural dynamics, including Poisson‐like spiking and adaptation. The neurons, with the dynamics fitted via hardware‐algorithm codesign, suggest a potential in realizing spike‐based neuromorphic hardware capable of handling complex problems. Simulation of an autoencoder for anomaly detection of time‐series real analog and digital data from physical systems is demonstrated, underscoring its promising prospect in applications, especially, at the edges with limited computation resources, for instance, auto‐pilot, manufacturing, wearables, and Internet of things.