# Large data limits and scaling laws for tSNE

arXiv: https://arxiv.org/abs/2410.13063 · HTML: https://mlsanity.com/paper/2410.13063/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [Clustering with t-SNE, provably](https://mlsanity.com/paper/1706.02582/) (2017)
- [An Analysis of the t-SNE Algorithm for Data Visualization](https://mlsanity.com/paper/1803.01768/) (2018)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [t-SNE, Forceful Colorings and Mean Field Limits](https://mlsanity.com/paper/2102.13009/) (2021)
- [On Probabilistic Embeddings in Optimal Dimension Reduction](https://mlsanity.com/paper/2408.02433/) (2024)

## Built on by (most cited first, 4 of 4)

- [Attraction-Repulsion Swarming: A Generalized Framework of t-SNE via Force Normalization and Tunable Interactions](https://mlsanity.com/paper/2411.10617/) (2024)
- [On the continuum limit of t-SNE for data visualization](https://mlsanity.com/paper/2604.12041/) (2026)
- [Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels](https://mlsanity.com/paper/2505.24311/) (2025)
- [On the Abundance of Critical Points of the t-SNE Energy](https://mlsanity.com/paper/2609.04379/) (2026)

## Abstract (arXiv)

This work considers large-data asymptotics for t-distributed stochastic neighbor embedding (tSNE), a widely-used non-linear dimension reduction algorithm. We identify an appropriate continuum limit of the tSNE objective function, which can be viewed as a combination of a kernel-based repulsion and an asymptotically-vanishing Laplacian-type regularizer. As a consequence, we show that embeddings of the original tSNE algorithm cannot have any consistent limit as n → ∞. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.