keyword

monotonic neural networks

Monotonic neural networks are artificial neural network architectures designed to ensure that the predicted output consistently increases or decreases monotonically with respect to all or a specified subset of their input variables. This mathematical constraint can be achieved through various architectural mechanisms, such as constraining connection weights to non-negative values alongside monotonic activation functions, utilizing specialized network layers, or parameterizing the derivative via integration to ensure positive gradients. Because strictly monotonic univariate functions are guaranteed to be invertible, these networks are widely used to construct expressive, invertible transformations in normalizing flows and generative models, as well as to enforce domain knowledge, safety requirements, and algorithmic fairness in predictive applications.

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Normalizing Flows: An Introduction and Review of Current Methods

Ivan Kobyzev, Simon J.D. Prince, Marcus A. Brubaker

OrganizationsBorealis AIYork University

Why you should read this

Explains the mathematical foundations and architectural design principles of normalizing flows, offering a clear guide to how these models achieve exact probability density estimation and efficient sampling.

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.

Source

https://arxiv.org/pdf/1908.09257

Added

2026-09-24