  The key factor in implementing machine learning algorithms in decision-making
situations is not only the accuracy of the model but also its confidence level.
The confidence level of a model in a classification problem is often given by
the output vector of a softmax function for convenience. However, these values
are known to deviate significantly from the actual expected model confidence.
This problem is called model calibration and has been studied extensively. One
of the simplest techniques to tackle this task is focal loss, a generalization
of cross-entropy by introducing one positive parameter. Although many related
studies exist because of the simplicity of the idea and its formalization, the
theoretical analysis of its behavior is still insufficient. In this study, our
objective is to understand the behavior of focal loss by reinterpreting this
function geometrically. Our analysis suggests that focal loss reduces the
curvature of the loss surface in training the model. This indicates that
curvature may be one of the essential factors in achieving model calibration.
We design numerical experiments to support this conjecture to reveal the
behavior of focal loss and the relationship between calibration performance and
curvature.
