用函数空间代替向量空间，让知识图谱嵌入更灵活、可计算。
Embedding Knowledge Graph in Function Spaces
- 在有限维函数空间中计算嵌入，而非传统向量空间
- 支持组合、导数、原函数等数学操作，表达能力更强
- 代码开源，适合研究表示学习与形式化推理的学者
我们提出一种新型嵌入方法，不再依赖传统的有限维向量空间，而是将嵌入运算置于有限维函数空间中，显著区别于标准的知识图谱嵌入技术。最初使用多项式函数计算嵌入，随后引入具有不同层数复杂度的神经网络以实现更复杂的表示。我们论证，采用函数进行嵌入计算能提升表达能力，带来更多自由度，并支持实体表示的组合、导数和原函数等操作。此外，我们详细描述了方法构建步骤，并提供代码以保证可复现性，促进该领域进一步探索与应用。
原文摘要 · Abstract (English)
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding techniques. Initially employing polynomial functions to compute embeddings, we progress to more intricate representations using neural networks with varying layer complexities. We argue that employing functions for embedding computation enhances expressiveness and allows for more degrees of freedom, enabling operations such as composition, derivatives and primitive of entities representation. Additionally, we meticulously outline the step-by-step construction of our approach and provide code for reproducibility, thereby facilitating further exploration and application in the field.
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