  Conformal prediction has emerged as a rigorous means of providing deep
learning models with reliable uncertainty estimates and safety guarantees. Yet,
its performance is known to degrade under distribution shift and long-tailed
class distributions, which are often present in real world applications. Here,
we characterize the performance of several post-hoc and training-based
conformal prediction methods under these settings, providing the first
empirical evaluation on large-scale datasets and models. We show that across
numerous conformal methods and neural network families, performance greatly
degrades under distribution shifts violating safety guarantees. Similarly, we
show that in long-tailed settings the guarantees are frequently violated on
many classes. Understanding the limitations of these methods is necessary for
deployment in real world and safety-critical applications.
