Towards Interpretable Sparse Graph Representation Learning with Laplacian Pooling

Abstract

Recent work in graph neural networks (GNNs) has lead to improvements in molecular activity and property prediction tasks. However, GNNs lack interpretability as they fail to capture the relative importance of various molecular substructures due to the absence of efficient intermediate pooling steps for sparse graphs. To address this issue, we propose LaPool (Laplacian Pooling), a novel, data-driven, and interpretable graph pooling method that takes into account the node features and graph structure to improve molecular understanding. Inspired by theories in graph signal processing, LaPool performs a feature-driven hierarchical segmentation of molecules by selecting a set of centroid nodes from a graph as cluster representatives. It then learns a sparse assignment of remaining nodes into these clusters using an attention mechanism. We benchmark our model by showing that it outperforms recent graph pooling layers on molecular graph understanding and prediction tasks. We then demonstrate improved interpretability by identifying important molecular substructures and generating novel and valid molecules, with important applications in drug discovery and pharmacology.Preprint. Under review.

Learnable Structural Semantic Readout for Graph Classification

“…5 The detailed architectures are described in Table II. We remark that any other hierarchical graph pooling techniques [19], [29], which are not included in our experiments, are also compatible with our readout layer; this means that their final classification performance can be further improved with the help of SSRead.…”

Understanding Pooling in Graph Neural Networks

“…The literature about learning on point clouds also introduced pooling techniques to generalize the typical pooling layers for grids, with most approaches based on voxelization techniques [48,45,43,31]. Many pooling operators have also been proposed based on graph spectral theory [7,36,23], or different clustering, sparsification, and decomposition techniques [35,3,42,53].…”

“…Consider a graph space defined on compact node and edge attribute sets X, E, and let K(G) represent the number of nodes of G = POOL(G), where K(G) ≤ K for all G and for some finite K ∈ N. By representing the output of the selection function as a matrix S ∈ R N ×K , we can then interpret SEL as permutation-equivariant node embedding operation x i → S i,: , from the space of node attributes to the space of supernodes assignments R K where we assumed, without loss of generality, that S i,k = 0 for all k > K(G) (this is necessary to ensure that any number of nodes K(G) can be computed by Table 1: Pooling methods in the SRC framework. GNN indicates a stack of one or more messagepassing layers, MLP is a multi-layer perceptron, L is the normalized graph Laplacian, β is a regularization vector (see [42]), D is the degree matrix, u max is the eigenvector of the Laplacian associated with the largest eigenvalue, i is a vector of indices, A i,i selects the rows and columns of A according to i.…”

“…Generally, non-trainable methods are useful when there is strong prior information about the desired behavior of pooling (e.g., preserving connectivity [16] or filtering out some particular graph frequencies [42]). These prior assumptions are usually grounded on graph-theoretical properties and are useful when few data are available, since they do not increase the overall number of parameters and introduce no additional optimization objectives when training the GNN.…”

“…In many cases, K(G) is a function of N (e.g. the ratio N/2), but K(G) could also depend on the input graph in a more complex way (e.g., [42,28]).…”