Memory, Prediction and Computation in the Kuramoto model

Nonlinear dynamical systems, such as recurrent neural networks, have proved a powerful model for temporal data, exhibiting remarkable predictive capacity even for chaotic time series. However such performance relies on finding the right parameter regimes, a challenging process for large dynamical systems required to model complex data. Here we investigate the computational capability of interacting phase oscillators, described by the Kuramoto model and coupled to synthetic input data with tunable correlation times. Our approach enables systematic exploration of qualitatively distinct parameter regimes, separated by phase transitions, as well as how they interact with the structure in the data. We use information-theoretic measures to quantify the memory and predictive capacities of many-oscillator systems and analyze their computational efficiency through the lens of the information bottleneck principle. Our work offers an insight into the emergence of computation from the collective behaviors of large dynamical systems.