H$^2$EDL: Hyper Evidential Deep Learning for Hierarchical Classification

H$^2$EDL：用于层级分类的超证据深度学习

Abstract: Fine-grained recognition often involves hierarchical label spaces, where a model may be confident about a coarse semantic concept while remaining uncertain among its descendant classes. Such structured ambiguity requires uncertainty representations that capture both fine-grained classes and intermediate concepts.

摘要： 细粒度识别通常涉及层级化的标签空间，模型可能对粗粒度的语义概念有把握，但在其子类之间却存在不确定性。这种结构化的模糊性需要能够同时捕捉细粒度类别和中间概念的不确定性表示。

However, existing tools each capture only half of it: flat evidential classifiers quantify total ignorance with a single vacuity on the leaf frame, and hierarchical classifiers propagate point probabilities with no notion of evidence. Hyper-opinions would unify the two, but their general form is exponential in the label count, and existing hyper-evidential networks either require composite labels to be supplied in the training data or read them off an unstructured weight pattern, with no principled notion of which composites deserve mass.

然而，现有的工具往往只能解决其中一半的问题：扁平化的证据分类器仅通过叶子节点上的单一空值来量化总体的无知，而层级分类器则在传播点概率时缺乏证据的概念。超观点（Hyper-opinions）理论上可以统一两者，但其通用形式在标签数量上呈指数级增长；现有的超证据网络要么要求在训练数据中提供复合标签，要么从非结构化的权重模式中读取，缺乏关于哪些复合标签应分配权重的原则性定义。

We observe that the taxonomy itself is the missing hyperdomain. Its subtrees and leaf singletons form a linear-size focal family, and one local Dirichlet opinion per branching node induces every composite mass in closed form. The resulting model, H$^2$EDL, can be interpreted in two complementary ways using the same set of parameters.

我们观察到，分类体系本身就是缺失的超域（hyperdomain）。其子树和叶子节点构成了线性规模的焦点族，且每个分支节点的一个局部狄利克雷观点（Dirichlet opinion）可以以闭式形式导出所有复合权重。由此产生的模型 H$^2$EDL，可以使用同一组参数以两种互补的方式进行解释。

From a prediction perspective, it functions as a hierarchical classifier that preserves consistency across different levels of the label tree. From a probabilistic perspective, it defines a valid tree-structured hyper-opinion, where the mass assigned to each node represents the belief that reaches that node but does not provide sufficient confidence to further specialize into its descendants.

从预测的角度来看，它作为一个层级分类器，能够保持标签树不同层级间的一致性。从概率的角度来看，它定义了一个有效的树状结构超观点，其中分配给每个节点的权重代表了到达该节点的信念，但这些信念不足以提供进一步细化到其子节点的充分置信度。

On FGVC-Aircraft and DERM12345, H$^2$EDL reduces calibration error by approximately half compared with cross-entropy baselines, with the improvement becoming more pronounced at deeper hierarchy levels and under larger training budgets.

在 FGVC-Aircraft 和 DERM12345 数据集上，与交叉熵基准相比，H$^2$EDL 将校准误差降低了约一半，且这种改进在更深的层级和更大的训练预算下表现得更为显著。