用李群表示理论构建可扩展的稀疏向量集，支持无分类层训练和动态扩类。
Series of quasi-uniform scatterings with fast search, root systems and neural network classifications
- 基于李群不可约表示构造高维空间中均匀分布的向量集合。
- 可在不重新训练网络的情况下动态扩展类别数，支持大规模分类任务。
- 对齐结构简化最近邻搜索，适合需要灵活扩类的神经网络场景。
本文提出一种在给定维度的空间中构建可扩展大型向量集合的方法。这些集合可用于神经网络潜在空间配置与训练。对于类别数量大或未知的分类问题，该方法可构建无需分类层的分类器，并在不从头训练网络的前提下扩展类别数。该构造可在最小可能维度下生成间距良好的大型向量集合。若类别数已知或可预测，可选择足够大小的向量集合；若需大幅扩充类别，可在同一潜在空间扩展集合，或将其嵌入更高维但保持相同间距的集合中。此外，所构造向量集合的规则对称结构能显著简化潜在空间中最近簇中心或嵌入的搜索问题。其构造基础为半单李群不可约表示的组合与几何性质。
原文摘要 · Abstract (English)
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification problem with large or unknown number of classes this allows to construct classifiers without classification layer and extend the number of classes without retraining of network from the very beginning. The construction allows to create large well-spaced vector collections in spaces of minimal possible dimension. If the number of classes is known or approximately predictable, one can choose sufficient enough vector collection size. If one needs to significantly extend the number of classes, one can extend the collection in the same latent space, or to incorporate the collection into collection of higher dimensions with same spacing between vectors. Also, regular symmetric structure of constructed vector collections can significantly simplify problems of search for nearest cluster centers or embeddings in the latent space. Construction of vector collections is based on combinatorics and geometry of semi-simple Lie groups irreducible representations with highest weight.
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