Graph neural networks to learn joint representations of disjoint molecular graphs Chen Shao12 Chen Zhou1 and Pascal Friederich13

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Graph neural networks to learn joint representations of

disjoint molecular graphs

Chen Shao1,2, Chen Zhou1, and Pascal Friederich1,3,*

1Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Am

Fasanengarten 5, 76131 Karlsruhe, Germany

2Present address: Institute for Applied Informatics and Formal Description

Systems, Karlsruhe Institute of Technology, Kaiserstr. 89, 76133 Karlsruhe

Germany

3Institute of Nanotechnology, Karlsruhe Institute of Technology,

Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

*Contact: pascal.friederich@kit.edu

Abstract

Graph neural networks are widely used to learn global representations of graphs, which

are then used for regression or classiﬁcation tasks. Typically, the graphs in such data sets are

connected, i.e. each training sample consists of a single internally connected graph associated

with a global label. However, there is a wide variety of yet unconsidered but application-

relevant tasks, where labels are assigned to sets of disjoint graphs, which requires the generation

of global representations of disjoint graphs. In this paper, we present a new data set with

chemical reactions, which is illustrating this task. Each sample consists of a pair of disjoint

molecular graphs and a joint label representing a scalar measure associated with the chemical

reaction of the molecules. We show the initial results of graph neural networks that are able

to solve the task within a combinatorial subset of the data set, but do not generalize well to

the full data set and unseen (sub)graphs.

1 Introduction

In the last few years, graph neural networks (GNNs) attracted growing attention in chemical

sciences, where they play an important role in solving challenges in molecular property prediction

and design. Currently, GNNs are widely used for regression and classiﬁcation tasks, e.g. to predict

molecular solubility or toxicity. However, most currently considered tasks of GNNs are limited

to single input molecular graphs, i.e. they use internally connected input molecular graphs to

learn node and edge representations, convert them to global graph representations, from which the

global label is then predicted. However, there is a wide range of real-world tasks where global labels

are assigned to sets of input graphs, rather than single input graphs. Examples for such tasks is

the prediction of solubility (not for a single solvent but for arbitrary combinations of solvents and

solutes), reactivity prediction, where two or more molecular graphs react and the task is to identify

the reaction center or a global property such as the reaction energy or reaction barrier, catalytic

activity, e.g. of catalytic surfaces and given reactants, and many more. Common in all those

tasks is that the joint label depends not on one but on multiple disjoint input graphs.

arXiv:2210.09517v2 [cs.CE] 30 Oct 2022

Figure 1: New task for graph learning: Learning joint representations to predict global labels from

sets of disjoint input graphs.

Many GNNs for tasks in chemistry depend not only on the connectivity of the nodes in the

input graph but also on their geometric arrangement. The labels in the task we are presenting

here are typically invariant to the relative geometric arrangement of the diﬀerent molecular graphs.

However, the internal geometry of each of the input graphs might still add useful information about

the ﬁnal label, even though the geometry follows from the connectivity and the node features, and

thus might as well be learned, given enough data. The development of GNN architectures for the

task of learning global representations of disjoint graphs is therefore a highly relevant research

area, and we hope that this work stimulates further development in that direction.

2 Related Works

The prediction of molecular properties is a cornerstone in chemistry, e.g. in drug discovery, where

accurate predictions are needed to identify drug candidates in an eﬃcient and computationally

inexpensive way. Molecular graphs allow us to learn informative representations of molecules, by

learning from the chemical structure of a molecule directly and enhancing that information with

physics-informed features of atoms and bonds, potentially including the 3D geometry information

of the molecular structure. The basic principle of GNNs is as follows: Atoms that are connected

by bonds are close in the graph, which means that they have the greatest inﬂuence on each other.

Through graph convolutions or message passing, such pairwise inﬂuence decays with the distance

between the atoms. This enables GNNs to learn informative atom representations which can then

be combined to global vector representations of entire molecules.

GNNs have found tremendous success in processing molecules and molecule properties, which

has become one of their main applications1. Seminal work by Duvenaud et al. showed how

GNNs can be seen as a generalized and learnable alternative to until then prevalent ﬁngerprint

representations of molecules.2Gilmer et al. suggested a more generalized framework which they

called message passing neural networks (MPNNs) and showed that MPNNs can accurately predict

quantum mechanical properties, calculated by density functional theory (DFT), which allows the

wider and more successful application of GNN to quantum chemistry.3Nowadays, many GNN

architectures are available in the hope of being able to replace expensive quantum mechanical

calculations with fast data-driven predictions.4 5 6 7.

Each molecule and associated molecular property can be uniquely determined by its 3D rep-

resentation. After seminal and very promising work in that direction,3, Schütt et al.8lever-

aged continuous-ﬁlter convolutions to learn local atomic environments in an architecture consist-

ing of atom-wise blocks and interaction blocks. This idea is further optimized in DimeNet and

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GraphneuralnetworkstolearnjointrepresentationsofdisjointmoleculargraphsChenShao1,2,ChenZhou1,andPascalFriederich1,3,*1InstituteofTheoreticalInformatics,KarlsruheInstituteofTechnology,AmFasanengarten5,76131Karlsruhe,Germany2Presentaddress:InstituteforAppliedInformaticsandFormalDescriptionSystems,Karl...

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Graph neural networks to learn joint representations of disjoint molecular graphs Chen Shao12 Chen Zhou1 and Pascal Friederich13

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