# Using predefined vector systems to speed up neural network multimillion class classification

arXiv: https://arxiv.org/abs/2604.00779 · HTML: https://mlsanity.com/paper/2604.00779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 14 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Practical and Optimal LSH for Angular Distance](https://mlsanity.com/paper/1509.02897/) (2015)
- [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)
- [Exploring possible vector systems for faster training of neural networks with preconfigured latent spaces](https://mlsanity.com/paper/2512.07509/) (2025)

## Abstract (arXiv)

Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can be significantly reduced. This is achieved by associating label prediction with the O(1) complexity closest cluster center search in a vector system used as target for latent space configuration (LSC). The proposed method only requires finding indexes of several largest and lowest values in the embedding vector making it extremely computationally efficient. We show that the proposed method does not change NN training accuracy computational results. We also measure the time required by different computational stages of NN inference and label prediction on multiple datasets. The experiments show that the proposed method allows to achieve up to 11.6 times overall acceleration over conventional methods. Furthermore, the proposed method has unique properties which allow to predict the existence of new classes.