Taylor-Informed Indirect Adaptive Predictive Control Using Jacobian-Frozen Affine Predictors
arXiv:2609.03348
2026
Dynamics
2 ideas extracted · analyzed Sep 4, 2026
What the math gives to ML
The paper offers a constructive local-prediction mechanism: identify a Taylor-structured polynomial approximation of a sampled nonlinear flow, then freeze its Jacobian at the current operating point to obtain a computationally cheap affine multi-step predictor. Its transferable asset is the separation between nonlinear model fitting and locally linear prediction, whose spectral properties can be checked at every step. A promising neural-network use is to apply Jacobian-frozen rollouts to recurrent world models or neural state-space models, with an explicit contraction test or penalty. A second transfer is a small, symmetry-informed polynomial adapter updated online by recursive least squares rather than fine-tuning all network weights.
Ideas from this paper
Unverified
2026
Replace an expensive nonlinear rollout of a recurrent or neural state-space model by a locally affine rollout whose Jacobian is evaluated once at the current state and then frozen over a short horizon. Use the resulting transition matrix as an explicit stability monitor and optionally penalize or clip its spectral radius, reducing exploding long-horizon predictions without forcing the entire nonlinear network to be globally contractive.
Useful7/10
Difficulty5/10
Novelty5/10
Unverified
2026
Attach a small, online-adapted Taylor-polynomial residual model to a neural dynamics model instead of adapting all network weights. Construct the dictionary from the local Taylor structure, remove monomials forbidden by known joint-odd symmetry, and update its coefficients with recursive least squares. This yields fast adaptation with an interpretable parameter count and a direct test of whether the assumed symmetry is valid.
Useful6/10
Difficulty4/10
Novelty6/10