Continuous partitioning of neuronal variability

Neurons exhibit substantial trial-to-trial variability in response to repeated stimuli, posing a major challenge for understanding the information content of neural spike trains. In visual cortex, responses show greater-than-Poisson variability, whose origins and structure remain unclear. To address this puzzle, we introduce a continuous, doubly stochastic model of spike train variability that partitions neural responses into a smooth stimulus-driven component and a time-varying stochastic gain process. We applied this model to spike trains from four visual areas (LGN, V1, V2, and MT) and found that the gain process is well described by an exponentiated power law, with increasing amplitude and slower decay at higher levels of the visual hierarchy. The model also provides analytical expressions for the Fano factor of binned spike counts as a function of timescale, linking observed variability to underlying modulatory dynamics. Together, these results establish a principled framework for characterizing neural variability across cortical processing stages.