The Zonotopic Mixture Filter

What the math gives to ML

The paper provides a constructive way to combine probabilistic mode weights with guaranteed set-membership enclosures. Its key transferable mechanism is admissible zonotopic mixture reduction: components may be merged only when the enclosing zonotope contains the union of all merged sets, while their probability masses are summed exactly. This can become a certified uncertainty-propagation layer for neural networks, representing multimodal input, parameter, or latent-state uncertainty without collapsing it into a single Gaussian or interval. The resulting model predicts both a reachable set and a guaranteed coverage mass, enabling falsifiable robustness and calibration tests.