Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

翻译：针对新物理过程的异常检测方法通常受限于低维空间，这是因为高维概率密度的学习存在困难。尤其在基本粒子层级，在流行的密度估计方法中融入置换不变性和可变长度输入等理想特性变得尤为困难。本研究提出一种基于扩散模型的粒子物理数据置换不变密度估计器，专门设计用于处理可变长度输入。通过将学习的密度作为置换不变异常检测评分，我们有效识别了在仅背景假设下似然较低的喷注，从而验证了该方法的效果。为验证密度估计方法的有效性，我们研究了学习密度的比值，并将其与监督分类算法获得的结果进行了比较。