Near-critical slow dynamics enable flexible temporal computations and generalization

Abstract

Although neural activity often evolves along low-dimensional manifolds, such descriptions do not explain the dynamical mechanisms that generate, constrain, and stabilize computation. Identifying these mechanisms is essential for predicting responses to perturbations, understanding generalization to untrained signals, and explaining how similar computations arise from distinct circuit implementations. Here we use recurrent neural networks trained on an interval timing task as a model system to uncover the dynamical mechanisms of neural computation. We show that, despite converging to highly diverse attractor architectures, trained networks share a conserved transient dynamics. During learning, networks self-organize near dynamical bifurcations, forming structured ghost sets of slow points characterized by graded spectra of near-zero eigenvalues. These slow sets form a dynamical scaffold that constrains trajectory evolution. Inputs transiently reconfigure the vector field and reposition activity within this scaffold, while the underlying slow set governs subsequent dynamics. As a result, temporal computation is implemented through structured transient evolution rather than convergence to fixed points or persistent activity states. The extent of the slow sets predicts generalization to unseen temporal intervals, and networks lacking such organization fail to extrapolate reliably. To test sufficiency, we construct a minimal dynamical system endowed with analogous slow set geometry that reproduces interval timing without learning, providing a benchmark for identifying the essential dynamical ingredients of temporal computation. Together, these results identify structured slow transients as a candidate dynamical mechanism for temporal computation, provide a mechanistic interpretation of slow low-dimensional manifolds as emergent consequences of underlying state-space structure, and suggest that computational capacity in near-critical systems arises from the organization of transient flow rather than attractor states alone.