Modelling non-Euclidean data is difficult since objects for comparison can be formed of different numbers of constituent parts with different numbers of relations between them, and traditional (Euclidean) methods are non-trivial to apply. Message passing enables such modelling by leveraging the structure of the relations within a (or between) given object(s) in order to represent and compare structure in a vectorized form of fixed dimensions.
In this work, we contribute novel message passing techniques that improve state of the art for non-Euclidean modelling in a set of specifically chosen domains. In particular, (1) we introduce an attention-based structure-aware global pooling operator for graph classification and demonstrate its effectiveness on a range of chemical property prediction benchmarks, we also show that our method outperforms state of the art graph classifiers in a graph isomorphism test, and demonstrate the interpretability of our method with respect to the learned attention coefficients. (2) We propose a style similarity measure for Boundary Representations (B-Reps) that leverages the style signals in the second order statistics of the activations in a pre-trained (unsupervised) 3D encoder, and learns their relative importance to an end-user through few-shot learning. Our approach differs from existing data-driven 3D style methods since it may be used in completely unsupervised settings. We show quantitatively that our proposed method with B-Reps is able to capture stronger style signals than alternative methods on meshes and point clouds despite its significantly greater computational efficiency. We also show it is able to generate meaningful style gradients with respect to the input shape. (3) We introduce a novel message passing-based model of computation and demonstrate its effectiveness in expressing the complex dependencies of biological systems necessary to model life-like systems and tracing cell lineage during cancerous tumour growth, and demonstrate the improvement over existing methods in terms of post-analysis
