标题： 从语义到层级：用于时序知识图谱推理的混合欧几里得-切向-双曲空间模型 显示英文标题

标题： From Semantics to Hierarchy: A Hybrid Euclidean-Tangent-Hyperbolic Space Model for Temporal Knowledge Graph Reasoning

摘要： 时序知识图谱（TKG）推理根据历史数据预测未来的事件，但由于涉及复杂的语义和层次信息，这是一项具有挑战性的任务。 现有的欧几里得模型擅长捕捉语义，但在处理层次结构方面存在困难。 相反，双曲模型能够很好地管理层次特征，但由于浅层模型参数的限制以及依赖L2范数的深层模型缺乏适当的归一化，它们无法表示复杂的语义。 当前的解决方案，如曲率变换，不足以解决这些问题。 在这项工作中，我们提出了一种新颖的混合几何空间方法，该方法利用了欧几里得模型和双曲模型的优点。 我们的方法从单空间参数建模过渡到多空间参数建模，有效地捕捉了语义和层次信息。 最初，通过欧几里得空间中的事实共现和自回归方法结合归一化来捕获复杂的语义。 然后，使用缩放机制将嵌入转换为切线空间，在保留语义信息的同时，通过查询-候选分离建模方法重新学习层次结构，随后将其转换为双曲空间。 最后，通过可学习的查询特定混合系数结合双曲和欧几里得评分函数，实现了用于层次和语义学习的混合归纳偏差，利用来自双曲和欧几里得空间的嵌入。 在四个TKG基准数据集上的实验结果表明，与先前的单空间模型相比，我们的方法在YAGO上的平均互信息排名减少了高达15.0%的误差。 此外，丰富的可视化分析验证了我们方法的有效性，展示了对于具有不同语义和层次复杂度的数据集的适应能力。 显示英文摘要

摘要： Temporal knowledge graph (TKG) reasoning predicts future events based on historical data, but it's challenging due to the complex semantic and hierarchical information involved. Existing Euclidean models excel at capturing semantics but struggle with hierarchy. Conversely, hyperbolic models manage hierarchical features well but fail to represent complex semantics due to limitations in shallow models' parameters and the absence of proper normalization in deep models relying on the L2 norm. Current solutions, as curvature transformations, are insufficient to address these issues. In this work, a novel hybrid geometric space approach that leverages the strengths of both Euclidean and hyperbolic models is proposed. Our approach transitions from single-space to multi-space parameter modeling, effectively capturing both semantic and hierarchical information. Initially, complex semantics are captured through a fact co-occurrence and autoregressive method with normalizations in Euclidean space. The embeddings are then transformed into Tangent space using a scaling mechanism, preserving semantic information while relearning hierarchical structures through a query-candidate separated modeling approach, which are subsequently transformed into Hyperbolic space. Finally, a hybrid inductive bias for hierarchical and semantic learning is achieved by combining hyperbolic and Euclidean scoring functions through a learnable query-specific mixing coefficient, utilizing embeddings from hyperbolic and Euclidean spaces. Experimental results on four TKG benchmarks demonstrate that our method reduces error relatively by up to 15.0% in mean reciprocal rank on YAGO compared to previous single-space models. Additionally, enriched visualization analysis validates the effectiveness of our approach, showing adaptive capabilities for datasets with varying levels of semantic and hierarchical complexity.