Training Mixed-Monotone Neural Networks for Verification Without Set Propagation
Read the original on arXiv Machine Learning →The paper introduces a new neural network architecture that represents mixed‑monotone functions as the difference of two monotone subnetworks, enabling tight output enclosures via only two forward passes of opposite corners of an input interval. The enclosure size is a closed‑form function of the network weights, allowing direct minimization during training. Experiments on regression and dynamical‑system benchmarks show that the trained networks achieve enclosure sizes within 0.5% of a proven lower bound while maintaining prediction accuracy, and the method is significantly faster and often tighter than existing techniques such as CROWN, α‑CROWN, and zonotope propagation.
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