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 with progressively increasing temporal demands, including binary decisions, context-dependent decisions, and perceptual integration. We analyzed trained networks using connectivity statistics, eigenvalue spectra, readout alignment, and low-dimensional population trajectories. Across tasks, networks converged to qualitatively distinct but behaviourally comparable dynamical solutions, including oscillatory and non-oscillatory (ramping/decaying) regimes, consistent with solution degeneracy. Population activity was well approximated by a low-dimensional subspace and distributed across recurrent units rather than localized to individual neurons. Readout alignment was strongly epoch-dependent: as required by the near-zero target output during that epoch, activity evolved largely in the readout-null subspace prior to response generation, and became increasingly aligned with the output dimension near decision time. In sign-symmetric tasks, trained networks preserved exact sign-flip equivariance inherited from architecture and training symmetry. Together, these results show that temporal and decision-related computations can emerge through multiple dynamical regimes, while maintaining structured low-dimensional representations and comparable behavioural performance, mirroring biological principles of degeneracy and functional redundancy.