Structural Compression as an Early Warning Signal Beyond Critical Slowing Down

Early warning signals (EWS) for critical transitions are traditionally based on dynamical indicators such as rising variance and autocorrelation, commonly associated with the phenomenon of critical slowing down (CSD). However, these indicators are mechanism-dependent and may fail in multivariate systems where structural changes precede observable dynamical signatures. This work introduces structural compression as an alternative early warning signal, operationalized via the spectral effective rank of rolling covariance matrices. The proposed metric captures the reduction of effective degrees of freedom in complex systems, reflecting an increasing coupling and loss of independent modes prior to regime shifts. Using a controlled multivariate Ornstein–Uhlenbeck (OU) framework, we demonstrate that structural compression provides a significantly earlier and more robust signal of impending transitions compared to classical variance-based indicators. The approach is particularly suited for high-dimensional systems where collapse is driven by endogenous structural reorganization rather than exogenous shocks. Boundary conditions and limitations are explicitly discussed, including cases where structural compression is not expected to provide reliable signals (e.g., oscillatory instabilities, isotropic noise regimes). The results suggest that incorporating structural metrics can substantially improve early warning detection in complex adaptive systems across domains such as ecology, finance, and socio-technical systems. This preprint aims to contribute to the ongoing development of next-generation early warning frameworks beyond critical slowing down. early warning signals, critical transitions, structural compression, spectral entropy, effective rank, covariance structure, complex systems, multivariate dynamics, critical slowing down, Ornstein–Uhlenbeck process