We review the concepts of interpretability and explainability as they apply to machine learning in physics. We define interpretability as concerning the structural transparency of a model (the ability to understand or approximate its inner workings) and explainability as concerning the scientific content of a model (the ability to map it onto domain knowledge). We discuss the trade-offs each entails (interpretability vs. expressivity; explainability vs. adaptability), the contexts in which each is needed, and the intrinsic and post-hoc tools available for achieving them. Throughout, we emphasize that machine-learned models are subject to the same scientific questions as classical models, differing only in scale, and that interpretability and explainability are best understood as deliberate modeling choices rather than inherent properties. We also emphasize the importance of task specification and intervention plans as a core aspect of model design.
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.