This paper presents an approach to learning nD features equivariant under
orthogonal transformations for point cloud analysis, utilizing hyperspheres and
regular n-simplexes. Our main contributions are theoretical and tackle major
issues in geometric deep learning such as equivariance and invariance under
geometric transformations. Namely, we enrich the recently developed theory of
steerable 3D spherical neurons -- SO(3)-equivariant filter banks based on
neurons with spherical decision surfaces -- by extending said neurons to nD,
which we call deep equivariant hyperspheres, and enabling their stacking in
multiple layers. Using the ModelNet40 benchmark, we experimentally verify our
theoretical contributions and show a potential practical configuration of the
proposed equivariant hyperspheres.

提出了一种基于超球体和正则 n - 单纯形的学习 nD 特征使点云分析在正交转换下等变的方法。实验结果验证了该方法的理论贡献，并展示了深度等变超球体的实际应用潜力。

深度等变超球

Deep Equivariant Hyperspheres

Event-centric structured prediction involves predicting structured outputs of
events. In most NLP cases, event structures are complex with manifold
dependency, and it is challenging to effectively represent these complicated
structured events. To address these issues, we propose Structured Prediction
with Energy-based Event-Centric Hyperspheres (SPEECH). SPEECH models complex
dependency among event structured components with energy-based modeling, and
represents event classes with simple but effective hyperspheres. Experiments on
two unified-annotated event datasets indicate that SPEECH is predominant in
event detection and event-relation extraction tasks.

本文提出了一种基于能量的事件中心超球 (Structured Prediction with Energy-based Event-Centric Hyperspheres，SPEECH) 的结构预测方法，采用简单而有效的超球表示事件分类并能处理事件结构复杂的依赖关系，实验表明该方法在事件检测和事件关系提取任务中具有优势。