In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the cross-entropy loss, outperforms regression with a mean squared error loss in its ability to learn high-entropy feature representations. Based on the analysis, we propose an ordinal entropy loss to encourage higher-entropy feature spaces while maintaining ordinal relationships to improve the performance of regression tasks. Experiments on synthetic and real-world regression tasks demonstrate the importance and benefits of increasing entropy for regression.

翻译：在计算机视觉中，人们常观察到将回归问题表述为分类任务往往能取得更好的性能。我们研究了这一有趣现象，并通过推导证明，使用交叉熵损失的分类方法在学习高熵特征表示方面优于使用均方误差损失的回归方法。基于这一分析，我们提出了一种序数熵损失，旨在鼓励更高熵的特征空间，同时保持序数关系，以提升回归任务的性能。在合成数据和真实世界回归任务上的实验表明，增加熵对回归任务的重要性和益处。