Series of quasi-uniform scatterings with fast search, root systems and neural network classifications

TL;DR

This paper introduces a method to construct large, extendable, well-spaced vector collections in high-dimensional spaces, facilitating neural network classification without retraining and simplifying nearest neighbor searches.

Contribution

It presents a novel geometric and combinatorial approach to create scalable vector collections for neural networks, enabling flexible classification and efficient search.

Findings

Constructed vector collections are large, well-spaced, and extendable.

Method allows classification without retraining when adding new classes.

Regular symmetric structures simplify nearest neighbor search.

Abstract

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.