  Deep Learning predictions with measurable confidence are increasingly
desirable for real-world problems, especially in high-risk settings. The
Conformal Prediction (CP) framework is a versatile solution that guarantees a
maximum error rate given minimal constraints. In this paper, we propose a novel
conformal loss function that approximates the traditionally two-step CP
approach in a single step. By evaluating and penalising deviations from the
stringent expected CP output distribution, a Deep Learning model may learn the
direct relationship between the input data and the conformal p-values. We carry
out a comprehensive empirical evaluation to show our novel loss function's
competitiveness for seven binary and multi-class prediction tasks on five
benchmark datasets. On the same datasets, our approach achieves significant
training time reductions up to 86% compared to Aggregated Conformal Prediction
(ACP), while maintaining comparable approximate validity and predictive
efficiency.
