On Deep Neural Network Calibration by Regularization and its Impact on Refinement

Abstract: Deep neural networks have been shown to be highly miscalibrated. often they tend to be overconfident in their predictions. It poses a significant challenge for safety-critical systems to utilise deep neural networks (DNNs), reliably. Many recently proposed approaches to mitigate this have demonstrated substantial progress in improving DNN calibration. However, they hardly touch upon refinement, which historically has been an essential aspect of calibration. Refinement indicates separability of a network's correct and incorrect predictions. This paper presents a theoretically and empirically supported exposition reviewing refinement of a calibrated model. Firstly, we show the breakdown of expected calibration error (ECE), into predicted confidence and refinement under the assumption of over-confident predictions. Secondly, linking with this result, we highlight that regularization based calibration only focuses on naively reducing a model's confidence. This logically has a severe downside to a model's refinement as correct and incorrect predictions become tightly coupled. Lastly, connecting refinement with ECE also provides support to existing refinement based approaches which improve calibration but do not explain the reasoning behind it. We support our claims through rigorous empirical evaluations of many state of the art calibration approaches on widely used datasets and neural networks. We find that many calibration approaches with the likes of label smoothing, mixup etc. lower the usefulness of a DNN by degrading its refinement. Even under natural data shift, this calibration-refinement trade-off holds for the majority of calibration methods.