# Exploring possible vector systems for faster training of neural networks with preconfigured latent spaces

arXiv: https://arxiv.org/abs/2512.07509 · HTML: https://mlsanity.com/paper/2512.07509/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 9 of 9)

- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Multimodal Deep Learning](https://mlsanity.com/paper/2301.04856/) (2023)
- [CLIP-ReID: Exploiting Vision-Language Model for Image Re-Identification without Concrete Text Labels](https://mlsanity.com/paper/2211.13977/) (2022)
- [Harnessing the Universal Geometry of Embeddings](https://mlsanity.com/paper/2505.12540/) (2025)
- [Latent space configuration for improved generalization in supervised autoencoder neural networks](https://mlsanity.com/paper/2402.08441/) (2024)
- [Using predefined vector systems as latent space configuration for neural network supervised training on data with arbitrarily large number of classes](https://mlsanity.com/paper/2510.04090/) (2025)
- [Series of quasi-uniform scatterings with fast search, root systems and neural network classifications](https://mlsanity.com/paper/2512.04865/) (2025)

## Built on by (most cited first, 1 of 1)

- [Using predefined vector systems to speed up neural network multimillion class classification](https://mlsanity.com/paper/2604.00779/) (2026)

## Abstract (arXiv)

The overall neural network (NN) performance is closely related to the properties of its embedding distribution in latent space (LS). It has recently been shown that predefined vector systems, specifically An root system vectors, can be used as targets for latent space configurations (LSC) to ensure the desired LS structure. One of the main LSC advantage is the possibility of training classifier NNs without classification layers, which facilitates training NNs on datasets with extremely large numbers of classes. This paper provides a more general overview of possible vector systems for NN training along with their properties and methods for vector system construction. These systems are used to configure LS of encoders and visual transformers to significantly speed up ImageNet-1K and 50k-600k classes LSC training. It is also shown that using the minimum number of LS dimensions for a specific number of classes results in faster convergence. The latter has potential advantages for reducing the size of vector databases used to store NN embeddings.