EPS Dashboard

Authors: Shaul Tolkovsky, Ori Meidler, Or Zuk

Summary

The authors propose a new way to measure whether a high-dimensional distribution is fragmented into separated clusters ("mode separation") versus just spread out. They construct a diffusion process whose stationary distribution matches the data, then analyze its autocovariance: SSA (a scalar summarizing barrier strength) and DA (directions ordered by metastability, not variance). They derive theory under a Gaussian null and apply the method using pretrained score-based generative models to scale to high dimensions.

Main takeaways:

Mode separation (how sharply a distribution splits into barrier-separated clusters) is geometrically distinct from dispersion, but existing tools like entropy and PCA don't capture it
They use a reversible diffusion process with the target density as its equilibrium and extract two readouts from its autocovariance matrix
SSA (Sum of Squared Autocorrelations) is a scalar that rises with barrier strength; DA (Dominant Autocorrelation directions) finds metastable directions instead of high-variance ones like PCA
The method works with samples and a score function, so it scales via pretrained diffusion models
Applications include Gaussian mixtures (SSA tracks mutual information), SDXL image generation (reveals structure entropy/PCA miss), and molecular dynamics (recovers known slow degrees of freedom)

Relevance

Not directly related to my persona/marker work—this is about clustering and geometric structure in general distributions. Could be tangentially useful if I ever wanted to characterize how personas are separated in activation space, but it's not a natural fit for behavioral conditioning experiments.

Abstract

arXiv:2605.08777v1 Announce Type: new Abstract: Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet existing tools fall short: differential entropy rises with spread regardless of fragmentation, PCA orders directions by variance regardless of barriers, and mutual information requires a mixture decomposition one usually does not have. We measure mode separation through a single stochastic process intrinsic to the density: a unique reversible diffusion with $f$ as its stationary distribution and constant scalar diffusion coefficient. We extract two readouts from its autocovariance matrix: SSA (Sum of Squared Autocorrelations), a scalar barrier-sensitive measure; and DA (Dominant Autocorrelation directions), linear projections ordered by metastability rather than variance. Under an isotropic-Gaussian null, we derive a closed-form spectrum for the empirical autocovariance that generalizes Marchenko--Pastur, with an analytic upper edge that selects the lag at which DA is read off. Both readouts use only samples and a score function, scaling to high dimensions through pretrained score-based generative models via Tweedie's identity. We apply our framework to three settings: (i) synthetic Gaussian mixtures, where SSA tracks mutual information; (ii) SDXL text-to-image generations, where SSA and DA capture structure that entropy and PCA miss; and (iii) molecular dynamics of alanine dipeptide, where DA recovers the known slow backbone dihedrals from static samples alone.