A mathematical certification for positivity conditions in Neural Networks with applications to partial monotonicity and Trustworthy AI

ANNs are often excluded from critical applications like credit scoring because their "black-box" nature makes it difficult to verify they follow required rules—such as ensuring that increasing one input (e.g., income) always increases the output (e.g., loan approval). This paper addresses that barrier by introducing LipVor, an algorithm that can mathematically certify whether a trained neural network follows partial monotonicity constraints.

The new certification method works without requiring special network architectures or restrictions during training, meaning organizations could use standard, unconstrained neural networks in regulated domains rather than having to redesign models specifically to meet trustworthiness requirements. This potentially makes powerful AI tools accessible to critical applications where they were previously unusable.

The algorithm certifies trustworthiness through a finite number of test evaluations combined with mathematical properties of the network, rather than examining the entire network structure. By testing specific points and using the network's Lipschitz properties (how much outputs can change relative to inputs), the method constructs "safe neighborhoods" where the network is guaranteed to behave as required.

This approach could extend beyond monotonicity to verify other important properties like convexity, suggesting the framework has broader applications for certifying different types of trustworthy AI behavior in high-stakes domains such as finance, healthcare, and criminal justice.