Quantifying Minute-by-Minute Modeling of Cognitive Fatigue in a Stroop Task: Slower Exponential Decay and the Effect of a Brief Rest

Sustained attention usually deteriorates during hour-scale tasks. However, it remains unclear whether this attention decline is the same at a minute-by-minute scale, and also if there would be a benefit of having very short rests. This study specifically seeks to answer which simple fatigue process best identifies performance over a 60-minute Stroop-type task, and whether having a brief mid-task rest significantly improves the performance of a task. This study hypothesized that a slower exponential decline of attention would fit better than a standard or faster decline, and also that adding a one-minute passive rest with a small post-break boost would improve task performance without affecting the fit before the break. This study implemented four fatigue regimes (standard, slower, faster, and recovery) as one-minute-step exponential models with Gaussian observation noise. Grid search was conducted to set parameters by minimizing mean squared error against the benchmark, while estimating uncertainty for error metrics with bootstrap confidence intervals and the one for correlation with Fisher-z intervals. For each regime, this study ran R=10,000 simulations (seed=2025). Run-mean trajectories were reported with 95% pointwise bands, while conducting sensitivity analyses varying the fatigue rate, noise level, recovery magnitude, and break timing. Results in this study supported the hypothesis that the slower model provided the best overall performance (e.g. r=0.89, mean squared error = 0.0035), followed by the recovery model (r=0.86, mean squared error =0.0043), and the faster model (r=0.71, mean squared error = 0.0117). These findings were supported by the sensitivity analysis that deviating fatigue rate from its fitted value degraded the fit of the model, while higher noise widened bands without increasing means. In addition, more end-of-task performance was preserved by earlier breaks.