Probabilistic Neuronal Dynamics: Expanding LIF Temporal Dynamics for Probabilistic Spike Generation

The temporal modeling capability of a spiking neuron depends on both how its dynamics weight historical inputs and how the resulting membrane state is converted into binary spikes. In a primitive reset-free leaky integrate-and-fire (LIF) neuron, these two stages are respectively constrained by a single geometric temporal response and a deterministic threshold that maps membrane values on the same side of the threshold to the same instantaneous event. These coupled restrictions motivate a neuronal mechanism that enriches the temporal response space before firing while allowing the magnitude of the resulting membrane trajectory to modulate spike generation without abandoning binary communication. We propose Probabilistic Neuronal Dynamics (PND), which expands this response space through multiple learnable temporal modes. A learned readout combines these modes into a scalar membrane trajectory, allowing the neuron to shape its response across delays beyond a single geometric decay. An exponential event model maps the readout to a firing probability, so membrane magnitude controls firing tendency while each emitted spike remains hard and binary. We characterize the response space through basis-rank analysis and non-geometric mode composition. Learned-mode measurements reveal diverse response shapes with low redundancy, and a capacity sweep links state expansion to improved task performance before saturation. Component comparisons identify the task-level role of expanded dynamics and examine probabilistic firing with its associated gradient rule. Repeated inference shows stable aggregate predictions under stochastic sampling. Across temporal modeling benchmarks, PND achieves competitive performance while retaining parallelizable pre-spike computation and sparse binary communication.