Application of uncertainty propagation in deep neural networks: Innovations in metrology and the introduction of QuadLU activation function

This paper extends the foundational work that integrates the principles of GUM with simple neural network structures, namely multilayer perceptrons (MLP). Our research primarily focuses on applying the law of propagation of uncertainty for deep neural networks (DNNs) to different architectures and validating the results. In this context, we introduce QuadLU, a novel, differentiable, parametrized activation function, which simplifies the computation of both function and derivative values. Our findings have been practically realized in the form of simple reference implementations. These implementations are used as testbeds to validate the quality of uncertainty propagation, employing the Monte Carlo method. To promote wider research and application, we ensure that our software adheres to the FAIR principles - Findable, Accessible, Interoperable, and Reusable.