A Mathematical Certification for Positivity Conditions in Neural Networks With Applications to Partial Monotonicity and Trustworthy AI

Summary

This paper presents LipVor, an algorithm that certifies whether a closed-box model such as an artificial neural network is positive, based on a finite number of evaluations. Because partial monotonicity can be expressed as a positivity condition on partial derivatives, LipVor can certify partial monotonicity of a trained network without constrained architectures or piecewise linear activations. The authors suggest this could allow unconstrained networks in critical fields such as credit scoring.