Unbounded Activations for Constrained Monotonic Neural Networks

Davide Sartor, Alberto Sinigaglia, Gian Antonio Susto

Keywords: Monotonic, Neural Networks

TL;DR: This paper proves that constrained MLPs are universal approximators for a broad class of activations, This includes most modern activations, even convex ones like ReLU. A novel parametrization is introduced, reducing sensibility to initialization.

Abstract:

Monotonic multi-layer perceptrons (MLPs) are crucial in applications requiring interpretable and trustworthy machine learning models, particularly in domains where decisions must adhere to specific input-output relationships. Traditional approaches that build monotonic MLPs with universal approximation guarantees often rely on constrained weights and bounded activation functions, which suffer from optimization issues.
In this work, we prove that non-negative constrained weights MLPs with activations that saturate on alternating sides are universal approximators for the class of monotonic functions. Thanks to this new result, we show that non-positive constrained weights MLPs with convex monotone activations, contrary to their non-negative constrained counterpart, are universal approximators.
Despite such guarantees, we also show that such classes of MLPs are hard to optimize. Therefore, we propose a novel parametrization that eliminates the need for weight constraints, allowing the network to dynamically adjust activations based on weight signs, thus enhancing optimization stability and performance.
Experiments demonstrate that our approach maintains theoretical guarantees and significantly outperforms existing monotonic architectures in approximation accuracy.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 10083