When Do Local Score Models Extrapolate Across Size? A Diagnostic Theory and Benchmark (opens in new tab)

Scientific generative modeling often requires size transfer, where models trained on small systems are evaluated on larger ones. While translation-invariant architectures enable this evaluation, we show that architectural locality alone does not guarantee stable size extrapolation. Instead, stable extrapolation is governed by the quasi-locality of the Gaussian-smoothed score. Through Tweedie's formula, far-away perturbations can influence local ...