准均匀散射序列与快速搜索、根系和神经网络分类
Series of quasi-uniform scatterings with fast search, root systems and neural network classifications
AI总结：
本文提出了一种基于半单李群不可约表示构造大规模可扩展向量集合的方法，用于神经网络潜在空间配置和分类任务。
摘要：
本文描述了一种构建预定义空间中给定维度下大规模可扩展向量集合的方法。这些集合对于神经网络潜在空间配置和训练非常有用。在具有大量或未知类别的分类问题中，这种方法允许在不使用分类层的情况下构建分类器，并且可以在不重新训练网络的情况下扩展类别数量。该构造允许在最小可能的维度空间中创建大规模且分布良好的向量集合。如果类别数已知或可以大致预测，可以选择足够大的向量集合大小。如果需要显著扩展类别数量，可以在相同的潜在空间中扩展集合，或将其纳入更高维度的集合中，保持向量之间的相同间距。构造的向量集合的规则对称结构可以显著简化在潜在空间中搜索最近聚类中心或嵌入的问题。向量集合的构造基于半单李群不可约表示的组合学和几何学中的最高权。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
