一种层次损失及其在非层次分类时的问题
A hierarchical loss and its problems when classifying non-hierarchically
AI总结：
本文提出一种基于超度量树的层次损失，用于按语义层次惩罚分类错误，但实验发现随机梯度下降最小化交叉熵时该损失同样下降，表明其不宜作为训练目标，更适合作为分类器性能度量。
摘要：
无法区分牧羊犬和摩天大楼，应当比无法区分牧羊犬和贵宾犬更严重并受到更大惩罚；毕竟，牧羊犬和贵宾犬都属于犬类。然而，在通过神经网络进行文本或视觉分类/识别时，现有的失败度量（所谓的“损失”或“胜出”）很少利用先验信息，例如牧羊犬与贵宾犬的相似度高于与摩天大楼的相似度。我们定义了一种度量，除其他作用外，它能够对无法区分牧羊犬和摩天大楼施加比无法区分牧羊犬和贵宾犬更大的惩罚。与先前采用的方法不同，该度量基于与任意给定的树状组织相关联的超度量树，该树状组织将分类器的类别组织成语义上有意义的层次结构。超度量树是一种具有所谓超度量距离度量的树，使得所有叶节点到根节点的距离相同。遗憾的是，大量数值实验表明，通过随机起点进行随机梯度下降训练神经网络的标准做法，在最小化标准交叉熵损失时，往往几乎与直接最小化层次损失时一样地降低层次损失。因此，这种层次损失作为普通的、随机初始化的随机梯度下降要最小化的目标并不可靠；层次损失的主要价值可能仅在于作为分类器成功程度的一种有意义的度量。
英文摘要：
Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics of failure (so-called "loss" or "win") used in textual or visual classification/recognition via neural networks seldom leverage a-priori information, such as a sheepdog being more similar to a poodle than to a skyscraper. We define a metric that, inter alia, can penalize failure to distinguish between a sheepdog and a skyscraper more than failure to distinguish between a sheepdog and a poodle. Unlike previously employed possibilities, this metric is based on an ultrametric tree associated with any given tree organization into a semantically meaningful hierarchy of a classifier's classes. An ultrametric tree is a tree with a so-called ultrametric distance metric such that all leaves are at the same distance from the root. Unfortunately, extensive numerical experiments indicate that the standard practice of training neural networks via stochastic gradient descent with random starting points often drives down the hierarchical loss nearly as much when minimizing the standard cross-entropy loss as when trying to minimize the hierarchical loss directly. Thus, this hierarchical loss is unreliable as an objective for plain, randomly started stochastic gradient descent to minimize; the main value of the hierarchical loss may be merely as a meaningful metric of success of a classifier.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
