Discrete stepping and nonlinear ramping dynamics underlie spiking responses of LIP neurons during decision-making

Neurons in macaque area LIP exhibit gradual ramping in their trial-averaged spike responses during sensory decision-making. However, recent work has sparked debate over whether single-trial LIP spike trains are better described by discrete \"stepping\" or continuous drift-diffusion (\"ramping\") dynamics. Here we address this controversy using powerful model-based analyses of LIP spike responses. We extended latent dynamical models of LIP spike trains to incorporate non-Poisson spiking, baseline firing rates, and various nonlinear relationships between the latent variable and firing rate. Moreover, we used advanced model-comparison methods, including cross-validation and a fully Bayesian information criterion, to evaluate and compare models. These analyses revealed that when non-Poisson spiking was incorporated into existing stepping and ramping models, a majority of neurons remained better described by stepping dynamics, even when conditioning on evidence level or choice. However, an extended ramping model with a non-zero baseline and a compressive output nonlinearity accounted for roughly as many neurons as the stepping model. The latent dynamics inferred under this model exhibited high diffusion variance for many neurons, making them qualitatively different than slowly-evolving continuous dynamics. These findings generalized to alternative tasks, suggesting that a robust fraction of LIP neurons are better described by each model class.