Delay-Dependent Gating in Modular RNNs

Coordinating information across neural systems requires integrating signals that propagate with heterogeneous delays; however, few models examine how stochastic transmission delays shape internal dynamics. We introduce a minimal modular recurrent neural network (RNN) composed of three interacting modules connected through delay buffers simulating variable conduction times. A scalar gate modulates inter-module influence. Across three delay regimes-short (HC), intermediate (IC), and long (LC)-we show that (1) task performance follows an inverted-U pattern, (2) the gate reflects temporal coordination demands rather than task rules, and (3) its functional role shifts from harmful (HC) to neutral (IC) to compensatory (LC). These results provide a mechanistic account of how temporal constraints shape cognitive control.