Recent advances in knowledge graph embedding (KGE) rely on
Euclidean/hyperbolic orthogonal relation transformations to model intrinsic
logical patterns and topological structures. However, existing approaches are
confined to rigid relational orthogonalization with restricted dimension and
homogeneous geometry, leading to deficient modeling capability. In this work,
we move beyond these approaches in terms of both dimension and geometry by
introducing a powerful framework named GoldE, which features a universal
orthogonal parameterization based on a generalized form of Householder
reflection. Such parameterization can naturally achieve dimensional extension
and geometric unification with theoretical guarantees, enabling our framework
to simultaneously capture crucial logical patterns and inherent topological
heterogeneity of knowledge graphs. Empirically, GoldE achieves state-of-the-art
performance on three standard benchmarks. Codes are available at
this https URL

最近的知识图谱嵌入（KGE）研究依赖于欧几里得 / 双曲正交关系变换以建模内在的逻辑模式和拓扑结构。然而，现有方法局限于维度有限和同质几何的刚性关系正交化，导致建模能力不足。本文介绍了一种名为 GoldE 的强大框架，它基于广义 Householder 反射形式的通用正交参数化，从维度和几何方面突破了这些方法的限制。这种参数化可以自然地实现维度扩展和几何统一，并具备理论保证，使我们的框架能够同时捕捉到知识图谱的重要逻辑模式和固有拓扑异质性。在实证方面，GoldE 在三个标准基准上实现了最先进的性能。代码可在提供的网址中获得。

通用正交参数化的知识图谱嵌入泛化

Generalizing Knowledge Graph Embedding with Universal Orthogonal  Parameterization

The last decade has witnessed an experimental revolution in data science and
machine learning, epitomised by deep learning methods. Indeed, many
high-dimensional learning tasks previously thought to be beyond reach -- such
as computer vision, playing Go, or protein folding -- are in fact feasible with
appropriate computational scale. Remarkably, the essence of deep learning is
built from two simple algorithmic principles: first, the notion of
representation or feature learning, whereby adapted, often hierarchical,
features capture the appropriate notion of regularity for each task, and
second, learning by local gradient-descent type methods, typically implemented
as backpropagation.
While learning generic functions in high dimensions is a cursed estimation
problem, most tasks of interest are not generic, and come with essential
pre-defined regularities arising from the underlying low-dimensionality and
structure of the physical world. This text is concerned with exposing these
regularities through unified geometric principles that can be applied
throughout a wide spectrum of applications.
Such a 'geometric unification' endeavour, in the spirit of Felix Klein's
Erlangen Program, serves a dual purpose: on one hand, it provides a common
mathematical framework to study the most successful neural network
architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand,
it gives a constructive procedure to incorporate prior physical knowledge into
neural architectures and provide principled way to build future architectures
yet to be invented.

通过统一的几何原理，深度学习可以更好地揭示基本规律，提供数学框架来研究卷积神经网络、循环神经网络、图神经网络和变压器网络等神经网络，且可以将物理学知识结合到神经网络结构中，从而提供了未来神经网络结构的原则性方法。