# Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels

arXiv: https://arxiv.org/abs/2505.24311 · HTML: https://mlsanity.com/paper/2505.24311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 5 of 5)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [An Analysis of the t-SNE Algorithm for Data Visualization](https://mlsanity.com/paper/1803.01768/) (2018)
- [Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations](https://mlsanity.com/paper/1902.05804/) (2019)
- [Large data limits and scaling laws for tSNE](https://mlsanity.com/paper/2410.13063/) (2024)

## Abstract (arXiv)

We extend the results by Auffinger and Fletcher in 2023 on the large-sample limit of t-SNE to a broader class of input and output kernels. We prove that under natural assumptions on the input distribution and the decay of the output kernel, if perplexity scales linearly with data size, the empirical measures and values of minimizers converge to an equilibrium distribution. We conclude with numerical examples comparing different kernels.