Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues with these methods related to finding low-dimensional representation of the data, the so-called curse of dimensionality. Geometric deep learning methods for data learning often include set of assumptions on the geometry of the feature space. Some of these assumptions include pre-selected metrics on the feature space, usage of the underlying graph structure, which encodes the data points proximity. However, the later assumption of using a graph as the underlying discrete structure, encodes only the binary pairwise relations between data points, restricting ourselves from capturing more complex higher-order relationships, which are often often present in various systems. These assumptions together with data being discrete and finite can cause some generalisations, which are likely to create wrong interpretations of the data and models outputs. Hence overall this can cause wrong outputs of the embedding models themselves, while these models being quite and trained on large corpora of data, such as BERT, Yi and other similar models.The objective of our research is twofold, first, it is to develop the alternative framework to characterize the embedding methods dissecting their possible inconsistencies using combinatorial approach of higher-order structures which encode the embedded data. Second objective is to explore the assumption of the underlying structure of embeddings to be graphs, substituting it with the hypergraph and using the hypergraph theory to analyze this structure. We also demonstrate the embedding characterization on the usecase of the arXiv data.

本研究解决了当前几何学习方法在低维表示中的维度诅咒问题，通过组合方法更好地表征嵌入模型。提出替代性框架，利用超图理论分析嵌入结构，以克服传统图结构仅捕捉二元关系的局限性。研究发现提升了对复杂系统中高阶关系的理解及模型输出的准确性。

解析嵌入方法：从数据中学习高阶结构