Metastable Neural Assemblies on a Wiring-Weight Continuum

Abstract

Neural population activity typically evolves on low-dimensional manifolds and can be described as trajectories through quasi-stable assembly states. Here we develop a unified definition of clustered neural networks with local excitatory-inhibitory balance in which enhanced within-cluster effective coupling is implemented through connection probability (structural clustering), synaptic efficacy (weight clustering), or any mixture of both. We introduce a single mixing parameter{kappa} [isin] [0, 1] that redistributes a defined cluster contrast between connection probabilities and synaptic efficacies while preserving the mean input of the underlying balanced random network. Mean-field theory and binary-network simulations show that metastable dynamics are supported across the full{kappa} continuum. Varying{kappa} changes higher-order input structure, reshaping multistable regimes, correlation structure, and the balance between single- and multi-cluster episodes. Because real nervous systems jointly organize topology and synaptic strength, our approach provides a biologically interpretable parametrization of clustered assembly models and a basis for future models combining structural and functional plasticity. We further demonstrate metastable switching in spiking leaky integrate-and-fire networks and in a BrainScaleS-2 neuromorphic implementation for the cases of structural, weight, and combined clustering. The{kappa} -framework offers a controlled translation axis for neuromorphic and other constrained substrates, exposing trade-offs between routed synapse count, fan-in, synaptic weight resolution, and calibration when implementing attractor-based computational primitives.