One of the main barriers to adoption of Machine Learning (ML) is that ML models can fail unexpectedly. In this work, we aim to provide practitioners a guide to better understand why ML models fail and equip them with techniques they can use to reason about failure. Specifically, we discuss failure as either being caused by lack of reliability or lack of robustness. Differentiating the causes of failure in this way allows us to formally define why models fail from first principles and tie these definitions to engineering concepts and real-world deployment settings. Throughout the document we provide 1) a summary of important theoretic concepts in reliability and robustness, 2) a sampling current techniques that practitioners can utilize to reason about ML model reliability and robustness, and 3) examples that show how these concepts and techniques can apply to real-world settings.

Uncertainty quantification of neural networks is critical to measuring the reliability and robustness of deep learning systems. However, this often involves costly or inaccurate sampling methods and approximations. This paper presents a sample-free moment propagation technique that propagates mean vectors and covariance matrices across a network to accurately characterize the input-output distributions of neural networks. A key enabler of our technique is an analytic solution for the covariance of random variables passed through nonlinear activation functions, such as Heaviside, ReLU, and GELU. The wide applicability and merits of the proposed technique are shown in experiments analyzing the input-output distributions of trained neural networks and training Bayesian neural networks.