TOWARDS NONLINEAR TIMESERIES PREDICTION FROM NEURAL DATA: DISENTANGLING LINEAR AND NONLINEAR DYNAMICS

Understanding how neural systems integrate information requires tools that go beyond linear descriptions. Predicting neural activity across time and brain regions is a central challenge, particularly given that neural dynamics are inherently multivariate and shaped by nonlinear mechanisms. To address this, we develop a framework for time-series prediction designed to distinguish between linear and genuinely nonlinear interactions.
We investigate predictive relationships by systematically comparing the capacity of different modeling approaches. By contrasting linear approximations with more complex nonlinear representations, we aim to isolate dynamics that escape traditional methods. This allows us to quantify the specific contribution of nonlinear mechanisms to signal predictability without assuming a specific underlying model structure.
The framework is applied to both synthetic and electrophysiological data to evaluate its robustness in diverse scenarios. This approach yields a quantitative measure of “functional nonlinearity,” aiming to characterize how brain interactions shift across different states and spatial scales. Overall, this work demonstrates that isolating nonlinear predictions is achievable, offering a tool to assess the complexity of neural networks beyond linear approximations.