Predictive Zonotope Reduction: Precise Runtime Monitoring under Uncertainty
arXiv:2609.03699
2026
Geometry
1 ideas extracted · analyzed Sep 4, 2026
What the math gives to ML
The paper treats uncertainty-representation compression as a sequential decision problem rather than applying one fixed reduction rule everywhere. Its transferable asset is the zonotope representation, whose generator-wise absolute sums provide cheap coordinatewise hull bounds, combined with finite-horizon lookahead over candidate reductions. This can support certified neural-network inference by dynamically compressing activation uncertainty after affine or nonlinear layers while minimizing predicted downstream over-approximation error. The practical first target is a robust MLP, where several inexpensive generator-pruning rules are selected per layer and input instead of using one global reducer.
Ideas from this paper
Unverified
2026
Propagate uncertain inputs or parameter perturbations through a neural network with zonotopes, and choose the reduction rule after each layer using short lookahead that predicts downstream certified-bound error. Candidate reducers can include largest-generator retention, box conversion, and norm-based merging; unlike a fixed policy, the chosen rule depends on the current generator geometry and remaining network depth. The goal is tighter robustness bounds at the same generator budget, or the…
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