The Drift-Diffusion Model (DDM) is widely accepted for two-alternative forced-choice decision paradigms thanks to its simple formalism and close fit to behavioral and neurophysiological data. However, this formalism presents strong limitations in capturing inter-trial dynamics at the single-trial level and endogenous influences. We propose a novel model, the non-linear Drift-Diffusion Model (nl-DDM), that addresses these issues by allowing the existence of several trajectories to the decision boundary. We show that the non-linear model performs better than the drift-diffusion model for an equivalent complexity. To give better intuition on the meaning of nl-DDM parameters, we compare the DDM and the nl-DDM through correlation analysis. This paper provides evidence of the functioning of our model as an extension of the DDM. Moreover, we show that the nl-DDM captures time effects better than the DDM. Our model paves the way toward more accurately analyzing across-trial variability for perceptual decisions and accounts for peri-stimulus influences.

The Drift-Diffusion Model (DDM) is widely accepted for two-alternative forced-choice decision paradigms thanks to its simple formalism, straightforward interpretation, and close fit to behavioral and neurophysiological data. However, this formalism presents strong limitations to capture inter-trial dependency and dynamics at the single-trial level. We propose a novel model, the non-linear Drift-Diffusion Model (nl-DDM), that addresses these issues by allowing the existence of several trajectories to the decision boundary. We show that the fitting accuracy of our model is comparable to the accuracy of the DDM, with the non-linear model performing better than the drift-diffusion model for an equivalent complexity. To give better intuition on the meaning of nl-DDM parameters, we compare the DDM and the nl-DDM through correlation analysis. This paper provides evidence of the functioning of our model as an extension of the DDM. Our model paves the way toward more accurately analyzing single-trial dynamics for perceptual decisions and accounts for pre- and post-stimulus influences.