The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.
Symbolic discovery of governing equations from data is limited not only by algorithm design and data volume, but by the geometry of the attractor: what the long-run dynamics allow to be recovered. Using a within-system design on Lorenz-84, where one forcing parameter drives fixed…
Oscillatory neural networks (ONNs) have emerged as a promising neuromorphic architecture, leveraging coupled dynamical systems to perform computation and represent information through phase relationships. Their interactions can be designed to support intrinsic energy-minimizing d…
Intelligence appears under different names in different fields: as data compression in statistics and machine learning, as universal computation in dynamical systems, and as adaptive behavior in agents. Each field carries its own objective, and the two most influential drives oft…
Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such l…
Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such an understanding could help to strip down overladen FM architecture…
Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inv…