  Conformal prediction is a distribution-free technique for establishing valid
prediction intervals. Although conventionally people conduct conformal
prediction in the output space, this is not the only possibility. In this
paper, we propose feature conformal prediction, which extends the scope of
conformal prediction to semantic feature spaces by leveraging the inductive
bias of deep representation learning. From a theoretical perspective, we
demonstrate that feature conformal prediction provably outperforms regular
conformal prediction under mild assumptions. Our approach could be combined
with not only vanilla conformal prediction, but also other adaptive conformal
prediction methods. Apart from experiments on existing predictive inference
benchmarks, we also demonstrate the state-of-the-art performance of the
proposed methods on large-scale tasks such as ImageNet classification and
Cityscapes image segmentation.The code is available at
\url{https://github.com/AlvinWen428/FeatureCP}.
