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：新物理过程的异常检测方法由于难以学习高维概率密度，通常局限于低维空间。尤其在组分层面，在主流密度估计方法中纳入置换不变性和可变长度输入等理想特性变得十分困难。本研究提出一种基于扩散模型的置换不变密度估计器，专门用于处理粒子物理数据中的可变长度输入。通过将学习到的密度作为置换不变异常检测评分，我们有效识别了在本底假设下似然度较低的喷注，从而验证了该方法的有效性。为评估密度估计方法，我们研究了学习密度的比值，并与监督分类算法得到的结果进行了比较。