Many machine learning applications involve learning a latent representation of data, which is often high-dimensional and difficult to directly interpret. In this work, we propose "Moment Pooling", a natural extension of Deep Sets networks which drastically decrease latent space dimensionality of these networks while maintaining or even improving performance. Moment Pooling generalizes the summation in Deep Sets to arbitrary multivariate moments, which enables the model to achieve a much higher effective latent dimensionality for a fixed latent dimension. We demonstrate Moment Pooling on the collider physics task of quark/gluon jet classification by extending Energy Flow Networks (EFNs) to Moment EFNs. We find that Moment EFNs with latent dimensions as small as 1 perform similarly to ordinary EFNs with higher latent dimension. This small latent dimension allows for the internal representation to be directly visualized and interpreted, which in turn enables the learned internal jet representation to be extracted in closed form.

翻译：许多机器学习应用涉及学习数据的高维潜在表示，这些表示往往难以直接解释。本文提出"矩池化"（Moment Pooling）方法，这是Deep Sets网络的自然扩展，能够在维持甚至提升性能的同时显著降低此类网络的潜在空间维度。矩池化将Deep Sets中的求和运算泛化为任意多元矩，使得模型在固定潜在维度下可实现更高的有效潜在维度。我们通过将能量流网络（EFNs）扩展为矩EFNs，在夸克/胶子喷注分类对撞机物理任务中验证了矩池化的有效性。研究发现，潜在维度低至1的矩EFNs与具有更高潜在维度的普通EFNs表现相近。这种极低的潜在维度使得内部表示可直接可视化与解释，进而能够以闭合形式提取学习到的内部喷注表示。