Finite integration time can shift optimal sensitivity away from criticality

Sensitivity to small changes in the environment is crucial for many real-world tasks, enabling living and artificial systems to make correct behavioral decisions. It has been shown that such sensitivity is maximized when a system operates near the critical point of a phase transition. However, proximity to criticality introduces large fluctuations and diverging timescales. Hence, to leverage the maximal sensitivity, it would require impractically long integration periods. Here, we analytically and computationally demonstrate how the optimal tuning of a recurrent neural network is determined given a finite integration time. Rather than maximizing the theoretically available sensitivity, we find networks attain different sensitivities depending on the available time. Consequently, the optimal dynamic regime can shift away from criticality when integration times are finite, highlighting the necessity of incorporating finite-time considerations into studies of information processing.