Neural circuits operate on multiple timescales simultaneously. Sensory neurons respond in milliseconds. Integration neurons accumulate evidence over seconds. Working memory persists for minutes. The standard explanation is that these timescales are tuned — intrinsic membrane properties, specific channel conductances, carefully calibrated time constants. The diversity is assumed to be a designed feature.
Zenari et al. show it's a structural inevitability. Using heterogeneous dynamical mean-field theory on random recurrent networks, they demonstrate that the diversity of timescales emerges from network topology alone. The mechanism: partial symmetry in synaptic weights combined with degree heterogeneity creates an emergent self-coupling whose strength scales with a neuron's connectivity. Hub neurons — the highly connected ones — develop stronger self-coupling, which produces slower dynamics. They become integrators not because their membranes are different but because their position in the network forces them to be.
The non-Markovian memory is the key detail. In a network with homogeneous connectivity, the mean-field dynamics are memoryless — the current state determines the future. Introduce degree heterogeneity and the dynamics become history-dependent. The past affects the present through the topology itself, not through any explicit memory mechanism. The network remembers because it is heterogeneous.
Validated on actual mouse connectome data: the model predicts observed single-neuron timescale distributions and their positive correlation with incoming connectivity. Hub neurons filter broadband input into slow frequencies, enabling temporal multiplexing — different timescales processed in parallel by different structural positions.
The through-claim: temporal structure in a network is not a separate design parameter. It is inherited from spatial structure. Build a heterogeneous network and temporal diversity follows as a mathematical consequence. You cannot have a scale-free topology without also having a spectrum of timescales, because the degree distribution IS the timescale distribution, mediated by emergent self-coupling. The clock is not installed in the neurons. The clock is the wiring.