Time to jump: Exploring the distribution of noise in evidence accumulation as a function of time pressure

The diffusion model conceptualizes binary decisions as emerging from continuous evidence accumulation with Gaussian noise. The Lévy-flight model (LFM) extends this by allowing accumulation noise to follow a heavier-tailed distribution, enabling sudden, large jumps in evidence accumulation. The heavy-tailedness is governed by the stability parameter α, with smaller α-values indicating more frequent and larger jumps. We demonstrate through simulation that the LFM can generate near-symmetrical response time (RT) distributions typical under strict deadlines. In Study 1, we explored the influence of intense time pressure on α in a letter-number discrimination task, expecting higher time pressure to entail smaller α-values. Participants (N = 341) were assigned to an accuracy (unlimited RT), implicit deadline (feedback discouraging RTs over 500 ms), or explicit deadline condition (timeout at 500 ms). Given the LFM's intractable likelihood, we used BayesFlow, a framework for simulation-based inference with deep learning. Model comparisons consistently favored the LFM over diffusion model variants-even in the accuracy condition. Importantly, α-values decreased with increasing time pressure and were especially low in the explicit deadline condition, where RT distributions also approached symmetry. Estimating both the LFM and a structurally matched diffusion model, with and without timeout modeling, further showed that accounting for timeout-related RT truncation led to substantially lower diffusion model drift rates, whereas LFM drift rates changed only modestly. Study 2 (N = 160) replicated α's sensitivity to time pressure in a brightness discrimination task. Overall, α responded systematically to temporal constraints across both tasks and timeout modeling specifications.