On the Existence of Geometrically Attracting Measures for Iterated Function Systems with Varying Sets of Transformations

What the math gives to ML

The paper develops geometric-attraction criteria for iterated function systems whose transformation families and selection probabilities change with time. Its transferable mechanism is a quantitative contraction condition on products of time-dependent random-map gains, guaranteeing that state distributions forget their initialization at a geometric rate in bounded-Lipschitz distance. A direct neural-network use is a stochastic recurrent or state-space architecture with time-varying candidate layers, where the candidate Jacobian gains and routing probabilities are constrained so that their cumulative expected gain decays geometrically. The central falsifiable prediction is that the initialization-distance decay rate is controlled by the accumulated logarithmic contraction exponent.