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We first extend the classic Tweedie’s formula to a wider range of distributions, then derive a novel identity that links the Stein score under a generalized Gaussian (energy model) noise to the gradient of a matched Energy Score (a scoring rule), connecting two seemingly disparate approaches to generative modeling. Among other things, this enables energy-score-based denoising models to be plugged into standard diffusion pipelines, but with heavy‑tailed noise.

We propose a novel methodology - Causal Disentanglement with Exteme Values (CDEV) - to identify representations learned by GANs. When trained on raw whale communication, it finds - for the first time - specific acoustic attributes that might serve as carriers of meaning.

Modeling the translation and review processes as zero-inflated fat-tailed distributions, we show how to extract useful information on translators’ reliability with as little as one review per translation.