用双曲空间建模表格数据的规则结构,提升分类准确率。
Manifold Constrained Tabular Deep Neural Networks

- 将特征映射到双曲空间,模拟树状决策逻辑。
- 在30个数据集上平均排名最优,超越主流梯度提升机和深度网络。
- 适合需要可解释规则推理的工业级表格分类任务。
表格分类常由局部、条件触发的规则驱动,而非平滑全局模式。但传统表格深度神经网络基于欧几里得表示,偏好平滑变化与语义局部性,导致难以有效表达离散的规则划分结构。为此,我们提出HDE-Net,一种在双曲空间中进行层级决策建模的流形约束神经网络。首先将异构特征抽象为统一的隐式决策节点(LDNs),并嵌入庞加莱球,形成连续表示,类似树状推理结构。针对数值特征,引入软决策路由机制,以可微方式近似基于区间的局部规则,使其LDN语义更接近类别特征。此外,熵感知容量分配算法动态调整每个数值特征的LDN数量,平衡表达能力与复杂度。在TALENT-tiny-core分类基准(30个数据集)上,HDE-Net取得最佳平均排名,性能优于工业级GBDT及近期表格深度网络,同时保持高效率。
原文摘要 · Abstract (English)
Tabular classification is often governed by local, condition-triggered rules rather than smooth global patterns. However, tabular deep neural networks (DNNs) are typically built upon Euclidean representations that favor smooth variations and semantic locality. This potential geometric mismatch can make it challenging for tabular DNNs to efficiently represent the discrete, rule-partitioned structures often underlying tabular classification. To address this issue, we propose HDE-Net, a manifold-constrained DNN that enables hierarchical decision modeling in hyperbolic space. We first abstract heterogeneous features into unified Latent Decision Nodes (LDNs) and embed them in the Poincaré ball, forming a continuous representation that resembles tree-structured reasoning. For numerical features, we introduce a Soft Decision Routing mechanism that approximates range-based local rules in a differentiable manner, bringing their LDN semantics closer to those of categorical features. An entropy-aware capacity allocation algorithm further adapts the number of LDNs per numerical feature to balance expressiveness and complexity. On the TALENT-tiny-core classification benchmark (30 datasets), HDE-Net achieves the \textit{best average rank}, outperforming both industrial GBDTs and recent tabular DNNs while maintaining high efficiency.
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