Abstract
Biological networks tend to leverage selective sparsity as an economic strategy to optimize function while minimizing wiring costs. In contrast, achieving synchronization in engineered systems such as semiconductor laser arrays is traditionally expected to require resource-intensive coupling to overcome intrinsic frequency disorders. We demonstrate that selectively coupled sparse networks can outperform fully connected architectures, achieving near-complete synchronization with a significantly reduced coupling budget. Using an evolutionary algorithm, we identify a “pairing opposites” principle: optimal structures specifically prioritize connections between oscillators with the largest opposite frequency detuning. This topology neutralizes dynamical interference induced by redundant links, leading to stable synchronization. We formalize this mechanism through a thermodynamic potential framework, mapping time-delayed phase dynamics to an energy landscape where optimal sparsity prunes additional states to stabilize global phase-locking. Furthermore, we show that the optimal connectivity scales inversely with system size. This principle provides a resource-efficient blueprint for synchronizing and stabilizing diverse complex networks, from photonic arrays to neuromorphic hardware.