高阶关联广泛存在于各种复杂系统中，而超图是一种能有效刻画对象间高阶关联的数据结构。近年来，以超图神经网络为代表的超图表示学习方法被广泛用于高阶关联语义计算，并因其强大的关联表征能力获得了学术界和工业界的广泛关注。在实际应用中，不同场景中的高阶关联往往呈现出不同特性，典型特性包括对偶、极性、多类型等，这些特性中蕴含的多元相互作用和丰富的语义信息对超图表示学习方法提出了新的挑战。面向实际应用场景中数据的多样性以及关联的复杂性，现有超图表示学习方法主要面临着四方面挑战：关联语义耦合导致的信息损失、关联语义冲突导致的表征一致性差、关联语义异构导致的协同计算困难和面向多场景的高阶关联建模适应性弱。针对上述挑战，本文开展了以下研究： 第一，针对关联语义耦合导致的信息损失问题，本文提出了一种对偶超图表示学习方法。本文引入了对偶通道超图建模策略和对偶消息传递机制，显式建模了对象间的对偶高阶关联，缓解了信息损失的问题，实现了对偶高阶关联语义计算。实验结果表明了该方法能够充分捕获和表征数据中的对偶高阶关联。 第二，针对关联语义冲突导致的表征一致性差问题，本文提出了一种符号超图表示学习方法。本文设计了符号引导的超图卷积机制，并基于双极性策略和符号融合模块实现了冲突语义的对立统一表征。实验结果表明了该方法可以准确刻画极性高阶关联的语义信息，显著提升下游任务性能。 第三，针对关联语义异构导致的协同计算困难问题，本文提出了一种多路超图表示学习方法。本文设计了关联类型感知的高阶消息传递和基于注意力的多关联融合机制，实现了多路协同语义计算。该方法进一步基于自监督对比学习方法鼓励模型在学习过程中保留关联的独特语义，提升了节点表示的可分性。实验结果表明了该方法可以有效挖掘多类型高阶关联中丰富的结构和语义信息。 最后，针对多场景中的超图结构建模适应性弱的问题，本文提出了贝叶斯超图鲁棒建模方法。本文将超图结构建模任务视为一个数据驱动的序列决策问题，并构建超图代理模型拟合潜在的目标函数，通过迭代搜索高潜力的候选超图结构逐步生成质量良好的超图结构。实验结果表明了该方法能够面向不同场景实现超图结构的鲁棒建模，显著提升超图表示学习的性能。

High-order correlations widely exist in various complex systems, and the hypergraph is a powerful data structure that can effectively capture high-order correlations among objects. In recent years, hypergraph representation learning methods, in particular hypergraph neural networks, have been widely used in high-order correlation semantic computation, and have attracted extensive attention from both the academic and industrial communities due to their powerful representation capabilities for high-order correlations. In practice, high-order correlations in different scenarios often exhibit various characteristics, such as duality, polarity, and multiple types. The complex interactions and rich semantic information embedded in these characteristics pose new challenges to hypergraph representation learning methods. When confronted with the diversity of data and the complexity of correlations in the wild, existing hypergraph representation learning methods face four critical challenges: 1) information loss caused by correlation semantic coupling, 2) poor representation consistency incurred by correlation semantic conflicts, 3) difficulties in collaborative computation caused by heterogeneous correlation semantics, and 4) weak adaptability in modeling high-order correlations for multiple scenarios. This thesis makes the following efforts to address these challenges.First, to address the information loss caused by correlation semantic coupling, a dual hypergraph representation learning method is proposed. This method adopts a dual-channel hypergraph modeling strategy and a dual message passing mechanism to explicitly model dual high-order correlations among objects, so as to mitigate information loss and realize dual high-order correlation semantic computation. Experimental results demonstrate that this method can effectively capture and represent the dual high-order correlations in the data.Second, to address the representation inconsistency issues caused by semantic conflicts of correlations, a signed hypergraph representation learning method is proposed. This method employs a sign-guided hypergraph convolution mechanism enhanced by a bipolar strategy as well as a sign fusion module, and achieves a unified representation of conflicting semantics. Experimental results demonstrate that this method can accurately characterize the semantic information of high-order correlations with polarity, significantly improving the performance of downstream tasks.Third, to tackle the challenges posed by the heterogeneity of correlation semantics in collaborative computation, a multiplex hypergraph representation learning approach is proposed. This approach adopts a type-aware high-order message passing mechanism, together with an attention-based multi-correlation fusion module to achieve multiplex collaborative semantic computation. It also introduces a self-supervised contrastive learning module to retain unique correlation semantics throughout the learning process, thereby enhancing the node representations with accurate semantic information. Experimental results show that this method can effectively mine the rich structural properties and semantic information within multi-type high-order correlations.Finally, to address the issue of weak adaptability in hypergraph structure modeling across multiple scenarios, a Bayesian hypergraph robust modeling method is proposed. This method treats the task of hypergraph structure modeling as a data-driven sequential decision-making problem. It uses a hypergraph surrogate model to fit the underlying target function and establish a corresponding posterior probability distribution. Through iteratively searching for high-potential candidate hypergraph structures, the Bayesian hypergraph robust modeling method can finally generate high-quality hypergraph structures. Experimental results demonstrate that this method can achieve robust hypergraph structure modeling for diverse scenarios.