Overcoming the Curse of Dimensionality: Structural Connectivity Reconstruction via Pairwise Information Flow in Nonlinear Networks

Inferring structural connectivity from observed dynamics remains a fundamental open problem in complex systems, particularly for nonlinear networks where direct measurements are unavailable, and existing methodological approaches each incur characteristic limitations. Model-based methods require prior knowledge of the mechanistic form of the underlying dynamics, while model-free approaches often lack quantitative correspondence to network structural connectivity, and suffer from the curse of dimensionality as the size and complexity of the system increases. Here we show that pairwise time-delayed information flow is sufficient to recover, without high-dimensional conditioning, structural connectivity in general nonlinear networks. We introduce a pairwise delayed information flow (PDIF) as an information-theoretic framework and derive a theoretical quadratic relationship between PDIF and coupling strength, establishing a direct correspondence between information flow and network architecture. We further show that indirect interaction contributions are suppressed at leading order, enabling accurate reconstruction solely from pairwise measurements. Combining binary state representations, pairwise inference, and time-delayed statistics, PDIF overcomes the dimensionality barrier while remaining model-agnostic and scalable. Validated across nonlinear dynamical systems, neuronal network models, and large-scale electrophysiological recordings, PDIF achieves high reconstruction accuracy and robustness to noise, outperforming existing methods. These results establish a principled, efficient and model-agnostic framework for connectivity reconstruction, and reveal a general mechanism by which pairwise observable statistics encode network structure in nonlinear systems.