A frozen rate operator from the complete larval connectome: degree and weight govern the gross response, exact wiring governs input routing and mushroom-body modes

Abstract

Connectome-constrained models now reproduce neural activity in several systems, yet each inherits a circuit's degree and weight statistics along with its exact wiring, leaving open which dynamical properties the wiring fixes beyond those statistics. We separate the two by running the complete larval Drosophila connectome, 2'825 neurons in its strongly connected core, as a frozen leaky-tanh rate operator with no single-neuron parameter fitted, and comparing it against a degree-and-weight-matched rewiring ensemble and further controls. All properties are the operator's, attributable to wiring and weights alone, not a measurement of larval activity. The gross dynamical signature is largely fixed by coarse statistics: the operator is non-normal and near-linear, with gain and effective dimensionality within a few percent of the ensemble. Two spatially resolved properties break this pattern. First, under sparse afferent drive the operator confines activity to a fifth of the core, against two thirds for the ensemble and all of it for a random graph, a confinement that survives a cell-class-preserving null. Second, the mushroom body concentrates the leading driving modes far beyond the ensemble, surviving size-matched, singular-subspace, and family-wise controls, while its leverage elsewhere stays diffuse. Both depend on the exact placement of synapses. A connectome's gross operator behavior is therefore largely a property of its degree and weight statistics, while the routing of input and the identity of the dominant driving modes are written into its exact wiring. We propose this decomposition as a general tool: it measures whether the exact wiring of any structured network carries information beyond its degree and weight statistics, a question any use of biological connectivity as an architectural prior eventually faces.