Task-Parametrized Dynamics: Representation of Time and Decisions in Recurrent Neural Networks

How do recurrent neural networks (RNNs) internally represent elapsed time to initiate responses after learned delays? To address this question, we trained RNNs on delayed decision-making tasks of increasing complexity: binary decisions, context-dependent decisions, and perceptual integration. We analyzed RNN dynamics after training using eigenvalue spectra, connectivity structure, and population trajectories, and found that 1) distinct dynamical regimes emerge across networks trained on the same task whereby oscillatory dynamics support precise timing, and integration supports evidence accumulation, 2) a population-wide representation of time and decision variables emerges rather than dedicated sub-populations to tracking time and other task-specific variables; and 3) the neural trajectories align only with the output weights near decision points, as shown by trajectory readout correlations, revealing task-driven coordination of precisely timed task representation and readout. These results show that RNNs can use either integration or oscillations to represent time, and highlight how structured connectivity enables diverse solutions to temporal computation problems, consistent with biological principles of degeneracy and functional redundancy.