English

Large data limits and scaling laws for tSNE

Statistics Theory 2024-10-18 v1 Machine Learning Analysis of PDEs Machine Learning Statistics Theory

Abstract

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 nn \to \infty. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.

Cite

@article{arxiv.2410.13063,
  title  = {Large data limits and scaling laws for tSNE},
  author = {Ryan Murray and Adam Pickarski},
  journal= {arXiv preprint arXiv:2410.13063},
  year   = {2024}
}
R2 v1 2026-06-28T19:25:02.141Z