It is well known that vision classification models suffer from poor calibration in the face of data distribution shifts. In this paper, we take a geometric approach to this problem. We propose Geometric Sensitivity Decomposition (GSD) which decomposes the norm of a sample feature embedding and the angular similarity to a target classifier into an instance-dependent and an instance-independent com-ponent. The instance-dependent component captures the sensitive information about changes in the input while the instance-independent component represents the insensitive information serving solely to minimize the loss on the training dataset. Inspired by the decomposition, we analytically derive a simple extension to current softmax-linear models, which learns to disentangle the two components during training.

It is well known that vision classification models suffer from poor calibration in the face of data distribution shifts. In this paper, we take a geometric approach to this problem. We propose Geometric Sensitivity Decomposition (GSD) which decomposes the norm of a sample feature embedding and the angular similarity to a target classifier into an instance-dependent and an instance-independent com-ponent. The instance-dependent component captures the sensitive information about changes in the input while the instance-independent component represents the insensitive information serving solely to minimize the loss on the training dataset. Inspired by the decomposition, we analytically derive a simple extension to current softmax-linear models, which learns to disentangle the two components during training.

In machine learning, it is observed that probabilistic predictions sometimes disagree with averaged actual outcomes on certain subsets of data. This is also known as miscalibration that is responsible for unreliability and unfairness of practical machine learning systems. In this paper, we put forward an evaluation metric for calibration, coined field-level calibration error, that measures bias in predictions over the input fields that the decision maker concerns. We show that existing calibration methods perform poorly under our new metric. Specifically, after learning a calibration mapping over the validation dataset, existing methods have limited improvements in our error metric and completely fail to improve other non-calibration metrics such as the AUC score. We propose Neural Calibration, a new calibration method, which learns to calibrate by making full use of all input information over the validation set. We test our method on five large-scale real-world datasets. The results show that Neural Calibration significantly improves against uncalibrated predictions in all well-known metrics such as the negative log-likelihood, the Brier score, the AUC score, as well as our proposed field-level calibration error.