INTERPRETABLE GEOMETRIC DEEP LEARNING VIA LEARNABLE RANDOMNESS INJECTION

Abstract

Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learning (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models are often complicated and hardly interpretable, which poses concerns to scientists who are to deploy these models in scientific analysis and experiments. This work proposes a general mechanism, learnable randomness injection (LRI), which allows building inherently interpretable models based on general GDL backbones. LRI-induced models, once trained, can detect the points in the point cloud data that carry information indicative of the prediction label. We also propose four datasets from real scientific applications that cover the domains of high-energy physics and biochemistry to evaluate the LRI mechanism. Compared with previous post-hoc interpretation methods, the points detected by LRI align much better and stabler with the ground-truth patterns that have actual scientific meanings. LRI is grounded by the information bottleneck principle, and thus LRI-induced models are also more robust to distribution shifts between training and test scenarios.

1. INTRODUCTION

The measurement of many scientific research objects can be represented as a point cloud, i.e., a set of featured points in some geometric space. For example, in high energy physics (HEP), particles generated from collision experiments leave spacial signals on the detectors they pass through (Guest et al., 2018) ; In biology, a protein is often measured and represented as a collection of amino acids with spacial locations (Wang et al., 2004; 2005) . Geometric quantities of such point cloud data often encode important properties of the research object, analyzing which researchers may expect to achieve new scientific discoveries (Tusnady & Simon, 1998; Aad et al., 2012) . Recently, machine learning techniques have been employed to accelerate the procedure of scientific discovery (Butler et al., 2018; Carleo et al., 2019) . For geometric data as above, geometric deep learning (GDL) (Bronstein et al., 2017; 2021) has shown great promise and has been applied to the fields such as HEP (Shlomi et al., 2020; Qu & Gouskos, 2020) , biochemistry (Gainza et al., 2020; Townshend et al., 2021) and so on. However, geometric data in practice is often irregular and highdimensional. Think about a collision event in HEP that generates hundreds to thousands of particles, or a protein that consists of tens to hundreds of amino acids. Although each particle or each amino acid is located in a low-dimensional space, the whole set of points eventually is extremely irregular and high-dimensional. So, current research on GDL primarily focuses on designing neural network (NN) architectures for GDL models to deal with the above data challenge. GDL models have to preserve some symmetries of the system and incorporate the inductive biases reflected by geometric principles to guarantee their prediction quality (Cohen & Welling, 2016; Bogatskiy et al., 2020) , and therefore often involve dedicated-designed complex NN architectures. Albeit with outstanding prediction performance, the complication behind GDL models makes them hardly interpretable. However, in many scientific applications, interpretable models are in need (Roscher et al., 2020) : For example, in drug discovery, compared with just predicting the binding affinity of a protein-ligand pair, it is more useful to know which groups of amino acids determine the affinity and where can be the binding site, as the obtained knowledge may guide future research directions (Gao et al., 2018; Karimi et al., 2019; 2020) . Moreover, scientists tend to only trust inter-1

availability

Our code and datasets are available at https://github.com/Graph-COM/LRI.

