2026-09-03
Propagation-grown networks beat cortex on wiring and communication. As echo-state reservoirs, human connectomes keep memory more stably via a distributed rich club.
Cortical wiring is usually told as an optimal bargain: short links save metabolism, a few long shortcuts keep communication cheap. That cost-efficiency story has run network neuroscience since Cajal. Communication efficiency, though, depends on the assumed dynamics. Shortest-path routing needs every region to know the global topology, which looks less and less plausible. Broadcasting (propagation) and random-walk diffusion are the usual alternatives.
If regions only optimize their own local payoff under a different dynamics, is the human cortex still optimal? Does better communication imply better computation? Groups at Cambridge MRC-CBU and Hamburg couple a game-theoretic generative model to reservoir computing to ask both. The paper is now in Science Advances.
Connectomes from 100 unrelated HCP subjects, Schaefer-100 cortex, 20% density, undirected binary graphs. The generator starts from a ring. At each step 10 nodes are drawn; each compares keeping its current edges with rewiring inside that clique, and picks the locally better option, ignoring everyone else. Payoff is Euclidean wiring cost plus one of three communication capacities: routing on shortest paths, propagation along all paths with long routes decaying, or diffusion via random-walk effective distance. A trade-off parameter alpha is set so density matches the empirical networks. One hundred synthetic graphs per condition. Nulls: degree-preserving randomization, latticization, long-range rewiring, and Erdos-Renyi. Statistics default to p<0.01.
Computation uses the adjacency matrix as an echo-state reservoir. Only the readout is trained. The task is memory capacity: a random input sequence, recall at increasing lags. Lesions remove the top 20 degree hubs in order.
Generated networks under all three dynamics match empirical endpoint similarity at 0.5 to 0.6 versus about 0.2 for nulls; link-prediction accuracy about 80% versus 65%, F1 about 0.5-0.6 versus 0.2. Diffusion graphs look most brain-like in clustering (0.5 to 0.6) but almost lack long-range edges, so mean path length is worse than cortex. Routing graphs look random. Propagation graphs wire more cheaply, shorten paths, and sit near cortex on small-worldness and spectral complexity.
Memory capacity does not follow mean path length. Cortex ranks first, then propagation and the long-range-rewired null; diffusion loses to several nulls. Fully random graphs also lose to degree-preserving randomizations of cortex, so heterogeneous degree itself helps.
Plot memory against global propagation efficiency and cortex sits on the Pareto front in a stable high-performance, lower-efficiency band. Propagation and routing sit near an unstable kink: push communication further and memory falls. Lesioning the top 20 hubs leaves cortical function standing; knocking out oligarch hubs in propagation graphs collapses both memory and communication, then the network restabilizes once those hubs are gone. Readout weight versus nodal propagation strength is Spearman rho=0.42 in cortex and rho=0.14 (p=0.15) in propagation graphs, where the readout sits almost entirely on the oligarchy.
A per-edge cost-benefit audit says the oligarchy is mostly a cheap on-ramp built by peripheral nodes, spatially bunched around posterior cingulate and precuneus. That map tracks the sensorimotor-association axis and the unimodal-transmodal gradient.
The paper adds a third axis to the cost-efficiency story: computational reliability. For anyone building brain-inspired reservoirs the lesson is concrete. Shorter paths and cheaper wiring do not mean higher or more stable memory. Parking computation on a tight spatial clique of hubs looks efficient until lesions and run-to-run variance collect the bill.
This is a normative model. It argues why cortex might be organized this way; it does not claim development actually plays this game. The transfer to AI is a structural lesson, not a new training algorithm.
The authors restrict themselves to binary symmetric graphs; weights and direction would need continuous games, and empirical human connectomes used here are symmetric too. Computation is only memory capacity. Whether working memory, integration, or navigation still show the inverted-U is untested. The generator matches connection count, not topology, which is a feature and also limits how far it can reproduce cortex. The preprint abstract matches the journal abstract; the text reports correlations and p-values, not an absolute memory-capacity number. This write-up uses the bioRxiv full text; if Science Advances revised figure values, the journal wins.