By leveraging Tweedie's formula on higher order moments, we generalize

Antonymy has long received particular attention in lexical semantics. Previous studies have shown that antonym pairs frequently co-occur in text, across genres and parts of speech, more often than would be expected by chance. However, whether this co-occurrence pattern is distinctive of antonymy remains unclear, due to a lack of comparison with other semantic relations. This work fills the gap by comparing antonymy with three other relations across parts of speech using robust co-occurrence metrics. We find that antonymy is distinctive in three respects: antonym pairs co-occur with high strength, in a preferred linear order, and within short spans. All results are available online.

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.