SIGMa-DS: System identification from the geometric manifold of dynamical synchronization

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Machine learning

Background:

• Reservoir computers (RCs) are effective for modeling temporal data.
• Current limitations prevent direct analysis of internal RC models, hindering understanding and testing predictions.

Purpose of the Study:

• To develop a method for extracting and perturbing internal models learned by RCs.
• To enable causal hypothesis testing in predictive dynamical models.

Main Methods:

• Formulating reservoir computing using differential geometry (SIGMa-DS).
• Developing a theory of dynamical generalized synchronization (DGS).
• Leveraging nonlinear manifold geometry of RC dynamics.

Main Results:

• Successfully extracted and perturbed internal models within RCs using DGS.
• Quantitatively explored the nonlinear geometry of synchronization manifolds.
• Demonstrated a method applicable to experimental systems without needing reservoir dynamics equations.

Conclusions:

• SIGMa-DS provides a robust geometric framework for understanding RCs.
• Enables causal hypothesis testing and enhances the utility of RCs as predictive models.
• Generalizes to experimental systems, advancing predictive modeling.