Characterizing control between interacting subsystems with deep Jacobian estimation

A team from MIT and Harvard (Eisen et al., NeurIPS 2025) introduced JacobianODE, a data-driven, nonlinear control-theoretic framework that estimates the Jacobian of dynamical systems from time-series observations. Traditional methods for characterizing subsystem interactions rely on linear approximations, missing the rich contextual modulation present in biological systems like brain networks or gene regulatory circuits. JacobianODE overcomes this by leveraging neural networks to directly learn the Jacobian, even for high-dimensional chaotic systems, outperforming prior approaches on challenging benchmarks.

In a key demonstration, the team applied JacobianODE to a multi-area recurrent neural network trained on a working memory selection task. They found that the ‘sensory’ area progressively gains stronger control over the ‘cognitive’ area as learning proceeds—a finding only possible with nonlinear analysis. Moreover, JacobianODE enabled precise manipulation of the RNN’s behavior by controlling its dynamics through the estimated Jacobian. This work provides a foundational tool for understanding how biological subsystems interact and exert control, with potential implications for neuroscience, gene regulation, and AI interpretability.