关系压缩：约束表示中关系保真度的框架
Relational Compression: A Framework for Relational Fidelity in Constrained Representations
浏览论文内容
中文总结 AI 辅助
针对关系信息压缩问题，提出关系压缩框架，统一图摘要、谱稀疏化等方法，以有限码字碰撞实现关系保真，并通过实验验证其有效性。
中文摘要 AI 辅助
当感兴趣的信息存在于元素之间的关系而非元素本身时，压缩表示应保留什么？我们在经典的源-描述-重建意义上构建关系压缩，但将关系结构本身作为保真度承载内容。每个实例指定源关系、保留的描述、重建或评估的关系、保真度准则以及约束资源。我们利用这一接口将图摘要、谱稀疏化、相似性保持表示和关系蒸馏中的选定方法置于统一框架内，同时明确它们不同的重建和资源假设。我们开发了有限码字碰撞作为具体实现。同码字概率产生一种关系几何，将配对特定对齐和分离与聚合Rényi-2占用率及分类赋值的球面几何联系起来，并与平方欧氏质心重建、归一化图关联和切割建立精确的目标对应关系。图和图像研究展示了有限码字族内的互补路径：图和教师定义的关系需求直接作用于相等性或碰撞，而重建则通过联合解码器起作用。这些结果共同说明，如何在统一的约束表示框架内制定和测试不同的关系需求。
英文摘要
What should a compressed representation preserve when the information of interest lies in relationships among elements rather than in the elements themselves? We formulate relational compression in the classical source-description-reconstruction sense, but with relational structure itself as the fidelity-bearing content. Each instance specifies the source relation, retained description, reconstructed or evaluated relation, fidelity criterion, and constrained resource. We use this interface to situate selected methods from graph summarization, spectral sparsification, similarity-preserving representation, and relational distillation within a common formulation while keeping their different reconstruction and resource assumptions explicit. We develop finite-codeword collision as one concrete realization. Same-codeword probability yields a relational geometry linking pair-specific alignment and separation to aggregate Rényi-2 occupancy and the spherical geometry of categorical assignments, with exact objective correspondences to squared-Euclidean centroid reconstruction and normalized graph association and cut. Graph and image studies illustrate complementary routes within the finite-codeword family: graph- and teacher-defined relational requirements act directly on equality or collision, while reconstruction acts through a joint decoder. Together, these results illustrate how distinct relational requirements can be formulated and tested within a common constrained-representation framework.
