Solving polynomial inequalities over spaces of convex sets and applications

What the math gives to ML

The paper develops a constructive least-solution calculus for recursive inequalities whose unknowns are convex sets, with expressions built from union, Minkowski addition, nonnegative dilation, convex combinations, and strict convex joins. Its transferable asset is the ability to eliminate mutually recursive set variables while preserving the smallest reachable over-approximation and keeping the result inside a computable representation family. This suggests a certified set-valued propagation engine for recurrent, implicit, or iterated neural modules, where hidden-state reachable sets are solved symbolically rather than expanded for a fixed number of iterations. A practical first version should use polytopes or unions of polytopes and compare recursive elimination against ordinary layer-by-layer interval or zonotope propagation.