Rigorous large-data limits for t-SNE at realistic perplexities

Prove rigorous convergence of minimizers of the discrete t-SNE energy as the sample size tends to infinity under realistic perplexity growth regimes.

Background

The paper discusses continuum approximations to t-SNE obtained by replacing empirical sums with integrals and implicitly defined bandwidths with explicit limiting functions. These derivations interchange several limits without establishing convergence for the original stochastic finite-sample energy.

The authors identify rigorous convergence of minimizers for the original t-SNE energy, as the number of data points grows and for practically realistic perplexities, as a challenging unresolved problem.

References

We consider the problem of rigorously proving limits of minimizers of the t-SNE energy as $n \to \infty$ and for realistic perplexities to be a challenging, open problem, which we do not seek to address in this work.

— On the Abundance of Critical Points of the t-SNE Energy  (2609.04379 - Haridas et al., 3 Sep 2026) in Section 2, subsection “Continuum Model”