Heterogeneous self-couplings enable scale-invariant memory and cognitive flexibility without criticality

The hierarchical organization of the brain underlies its ability to process information across multiple time scales and support flexible behavior through context-dependent computation. Here, we study a recurrent neural network model with heterogeneous self-interactions across nodes, capturing key features of neuronal circuits, including intrinsic diversity of dynamical time scales and multistable low-dimensional manifolds. We investigate the emergence of scale-invariant dynamics without assuming criticality, challenging the view that power-law statistics necessarily arise from self-organized critical states. We show that heterogeneous self-interactions alone are sufficient to generate scale-invariant memory in subcritical regimes, while enhancing the network's dynamical richness and computational capacity. Notably, this mechanism promotes the spontaneous emergence of hierarchical organization. We assess the functional implications of this framework using short-term memory tasks and the Wisconsin Card Sorting Test, which probes cognitive flexibility and adaptive rule switching. Compared to models with heterogeneous time constants, our approach achieves comparable performance with more parsimonious synaptic modifications, while preserving scale-invariant dynamics.