Linearisation, splitting property and homotopy algebras

What the math gives to ML

The paper gives a constructive algebraic criterion for when a nonlinear formal map or vector field can be removed by a near-identity change of coordinates: linearisation is equivalent to the existence of a splitting map into coderivations satisfying an explicit intertwining identity. This suggests a principled local-conjugacy module for latent dynamical models, in which a nonlinear world-model transition is represented in coordinates where its learned dynamics are approximately linear. The transferable asset is the recursive near-identity coordinate transform and its certificate-like equivariance constraint, which can be converted into a polynomial jet regularizer and tested on rollout stability and linear extrapolation.