Anytime-Valid Confidence Sequences for Consistent Uncertainty Estimation
  in Early-Exit Neural Networks
Metod Jazbec Patrick Forré Stephan Mandt Dan Zhang Eric Nalisnick
Early-exit neural networks (EENNs) facilitate adaptive inference by producing
predictions at multiple stages of the forward pass. In safety-critical
applications, these predictions are only meaningful when complemented with
reliable uncertainty estimates. Yet, due to their sequential structure, an
EENN's uncertainty estimates should also be consistent: labels that are deemed
improbable at one exit should not reappear within the confidence interval / set
of later exits. We show that standard uncertainty quantification techniques,
like Bayesian methods or conformal prediction, can lead to inconsistency across
exits. We address this problem by applying anytime-valid confidence sequences
(AVCSs) to the exits of EENNs. By design, AVCSs maintain consistency across
exits. We examine the theoretical and practical challenges of applying AVCSs to
EENNs and empirically validate our approach on both regression and
classification tasks.