Estimating Spectrum-Free Information Bounds for Generative Surrogates Beyond Conditional Collapse

Abstract

Conditional generative surrogates in high-energy physics, such as models that predict reconstructed jets from partons, are often evaluated on $1\text{D}$ marginal divergences among other metrics. Taken alone these metrics can reward conditional collapse. On a CMS simulation benchmark, a sampler that ignores the conditioner beats a trained Mixture Density Network (MDN) on all four target marginals under both KL and Wasserstein-1, and cannot be stably separated from a Conditional Flow Matching (CFM) model on two of the four. We instead score the models with the Continuous Ranked Probability Skill Score (CRPSS) from forecast verification, taking the exact marginal as the reference. We show how global skill depends on the evaluation spectrum, and we also report it within bins of a conditioning variable, where that dependence largely goes away. We then introduce a data-driven $k$-Nearest-Neighbor ($k$-NN) extrapolation that estimates the best CRPS the conditioning information allows. Both models agree with this estimate on all four targets, which suggests that current architectures have reached the information available in the conditioner, at least as far as these per-target scores can tell.