On the Abundance of Critical Points of the t-SNE Energy
2026-09-07 12:00Science🔥 40.2 heat score
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On September 7, 2026, arXiv cs.LG published the paper “On the Abundance of Critical Points of the t-SNE Energy”, which systematically analyzed the distribution of critical points in the energy function of the t-SNE algorithm during the process of mapping high-dimensional data into low-dimensional space. The study indicated that the t-SNE optimization process involves numerous local minima and saddle points, and their number varies significantly depending on the data dimensionality and parameter settings. This finding reveals the complexity of topological structures in high-dimensional data reduction, provides a theoretical basis for understanding t-SNE’s behavior in clustering and nonlinear mapping, and suggests that global optimization strategies should be combined in practical applications to avoid the risk of falling into local optima.
This paper studies the energy landscape of the t-SNE algorithm. To address the difficulty of rigorously understanding the content captured by this algorithm due to its non-convex energy structure, the authors constructed an infinite number of critical points for the general energy family including the original t-SNE and recent large-sample limits. These critical configurations, based on discrete symmetries in both the feature space and the target embedding space and maintaining under gradient dynamics, exhibit characteristics commonly seen in experience, such as topological disruption and false clustering. The method is illustrated through numerical and analytical examples.