On the Abundance of Critical Points of the t-SNE Energy

תקציר מקורי באנגליתarXiv:2609.04379v1 Announce Type: new Abstract: This paper considers the energy landscape of the t-SNE algorithm. While this algorithm has enjoyed broad adoption, the non-convexity of the associated energy has made it difficult to rigorously understand what the algorithm captures in many settings. In particular, a number of well-known numerical examples, several of which are reproduced in this article, suggest a complicated energy landscape with many local minimizers that do not respect the topology or clustering structure of the underlying data. This work seeks to provide first steps towards a rigorous explanation of these phenomena. Specifically, for a general family of energies, which include both the original t-SNE algorithm and recently identified large data limits, and for densities