Early-exit neural networks (EENNs) enable adaptive and efficient inference by providing predictions at multiple stages during the forward pass. In safety-critical applications, these predictions are meaningful only when accompanied by reliable uncertainty estimates. A popular method for quantifying the uncertainty of predictive models is the use of prediction sets. However, we demonstrate that standard techniques such as conformal prediction and Bayesian credible sets are not suitable for EENNs. They tend to generate non-nested sets across exits, meaning that labels deemed improbable at one exit may reappear in the prediction set of a subsequent exit. To address this issue, we investigate anytime-valid confidence sequences (AVCSs), an extension of traditional confidence intervals tailored for data-streaming scenarios. These sequences are inherently nested and thus well-suited for an EENN's sequential predictions. We explore the theoretical and practical challenges of using AVCSs in EENNs and show that they indeed yield nested sets across exits. Thus our work presents a promising approach towards fast, yet still safe, predictive modeling

翻译：早退神经网络（EENNs）通过在正向传播的多个阶段提供预测，实现了自适应且高效的推理。在安全关键型应用中，这些预测只有在配备可靠的不确定性估计时才有意义。量化预测模型不确定性的一种常用方法是使用预测集。然而，我们证明，诸如共形预测和贝叶斯可信集等标准技术并不适用于EENNs。它们倾向于在多个退出点之间生成非嵌套的集合，这意味着在某个退出点被认为不可能的标签可能会在后续退出点的预测集中重新出现。为解决这一问题，我们研究了任意时间有效置信序列（AVCSs），这是为数据流场景定制的传统置信区间的扩展。这些序列本质上是嵌套的，因此非常适合EENNs的顺序预测。我们探讨了在EENNs中使用AVCSs的理论与实践挑战，并证明它们确实能在不同退出点之间产生嵌套集合。因此，我们的工作为快速且仍安全的预测建模提供了一种有前景的方法。