The Neural Race Model

Perceptual decisions unfold in time: noisy evidence is integrated until a commitment threshold is reached, jointly producing a choice and a reaction time. Classical race models capture this mechanism through simple parametric drift and diffusion, but cannot represent how rich, high-dimensional stimuli shape accumulation on individual trials. We introduce the $\textbf{Neural Race Model}$ (NRM), a stimulus-conditional neural stochastic differential equation in which one accumulator per alternative races towards a learnable, stimulus-dependent threshold. Drift, diffusion, and threshold are parameterised by neural networks conditioned on a stimulus embedding, allowing both accumulation dynamics and decision urgency to vary across trials. The model is trained end-to-end on the joint reaction-time-and-choice likelihood via a smooth surrogate for the discontinuous first-passage event, combined with Monte Carlo trajectory averaging and gradient propagation through the stochastic adjoint. The surrogate recovers the classical hard threshold in the appropriate limit and is removed at test time. Each component admits a natural correspondence with elements of the primate decision-making circuit, preserving the mechanistic interpretability of classical models. We evaluate the NRM on multiple perceptual decision-making benchmarks against classical sequential-sampling and image-computable reaction-time models. Across tasks and metrics, the NRM tracks the human noise ceiling more closely than all baselines, demonstrating that stimulus-conditional stochastic accumulation and end-to-end differentiability can be achieved within a single, principled framework. Code will be publicly released.