Entropy rigidity of $u$-Gibbs measures

What the math gives to ML

The paper’s transferable asset is a constructive cohomological view of multiplicative Jacobian growth: spatially varying expansion can be decomposed into a constant exponential rate plus a telescoping potential difference. In a neural dynamical system, this is more flexible than forcing the Jacobian determinant to be one or pointwise constant, because the potential absorbs state-dependent fluctuations without changing long-run orbit-average expansion. The resulting regularizer can make recurrent, neural-ODE, or invertible-network rollouts more stable while preserving a prescribed Lyapunov-like growth rate. The most direct experiment is to train a small invertible recurrent map with this residual-coboundary penalty and compare long-horizon stability and optimization against a pointwise log-determinant penalty.