This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing ``messages'' based only on the representation of the source of each edge. In GNN-FiLM, the representation of the target node of an edge is additionally used to compute a transformation that can be applied to all incoming messages, allowing feature-wise modulation of the passed information.

 Results of experiments comparing different GNN architectures on three tasks from the literature are presented, based on re-implementations of baseline methods. Hyperparameters for all methods were found using extensive search, yielding somewhat surprising results: differences between baseline models are smaller than reported in the literature. Nonetheless, GNN-FiLM outperforms baseline methods on a regression task on molecular graphs and performs competitively on other tasks.
 Learning from graph-structured data has seen explosive growth over the last few years, as graphs are a convenient formalism to model the broad class of data that has objects (treated as vertices) with some known relationships (treated as edges). Example usages include reasoning about physical and biological systems, knowledge bases, computer programs, and relational reasoning in computer vision tasks. This graph construction is a highly complex form of feature engineering, mapping the knowledge of a domain expert into a graph structure which can be consumed and exploited by high-capacity neural network models. Many neural graph learning methods can be summarised as neural message passing (Gilmer et al., 2017) : nodes are initialised with some representation and then exchange information by transforming their current state (in practice with a single linear layer) and sending it as a message to all neighbours in the graph. At each node, messages are aggregated in some way and then used to update the associated node representation. In this setting, the message is entirely determined by the source node (and potentially the edge type) and the target node is not taken into consideration. A (partial) exception to this is the family of Graph Attention Networks (Veličković et al., 2018) , where the agreement between source and target representation of an edge is used to determine the weight of the message in an attention architecture. However, this weight is applied to all dimensions of the message at the same time. A simple consequence of this observation may be to simply compute messages from the pair of source and target node state. However, the linear layer commonly used to compute messages would only allow additive interactions between the representations of source and target nodes. More complex transformation functions are often impractical, as computation in GNN implementations is dominated by the message transformation function. However, this need for non-trivial interaction between different information sources is a common problem in neural network design. A recent trend has been the use of hypernetworks (Ha et al., 2017) , neural networks that compute the weights of other networks. In this setting, interaction between two signal sources is achieved by using one of them as the input to a hypernetwork and the other as input to the computed network. While an intellectually pleasing approach, it is often impractical because the prediction of weights of non-trivial neural networks is computationally expensive. Approaches to mitigate this exist (e.g., Wu et al. (2019) handle this in natural language processing), but are often domain-specific. A more general mitigation method is to restrict the structure of the computed network. Recently, "feature-wise linear modulations" (FiLM) were introduced in the visual question answering domain (Perez et al., 2017) . Here, the hypernetwork is fed with an encoding of a question and produces an element-wise affine function that is applied to the features extracted from a picture. This can be adapted to the graph message passing domain by using the representation of the target node to compute the affine function. This compromise between expressiveness and computational feasibility has been very effective in some domains and the results presented in this article indicate that it is also a good fit for the graph domain. This article explores the use of hypernetworks in learning on graphs. Sect. 2 first reviews existing GNN models from the related work to identify commonalities and differences. This involves generalising a number of existing formalisms to new formulations that are able to handle graphs with different types of edges, which are often used to model different relationship between vertices. Then, two new formalisms are introduced: Relational Graph Dynamic Convolutional Networks (RGDCN), which dynamically compute the neural message passing function as a linear layer, and Graph Neural Networks with Feature-wise Linear Modulation (GNN-FiLM), which combine learned message passing functions with dynamically computed element-wise affine transformations. In Sect. 3, a range of baselines are compared in extensive experiments on three tasks from the literature, spanning classification, regression and ranking tasks on small and large graphs. Experiments were performed on re-implementations of existing model architectures in the same framework and hyperparameter setting searches were performed with the same computational budgets across all architectures. The results show that differences between baselines are smaller than the literature suggests and that the new FiLM model performs well on a number of interesting tasks. After a review of existing graph neural network architectures, the idea of using hypernetworkinspired models in the graph setting was explored. This led to two models, Graph Dynamic Convolutional Networks and GNNs with feature-wise linear modulation, were presented. While GDCNs seem to be impractical to train, experiments show that GNN-FiLM is competitive with or improving on baseline models on three tasks from the literature. The extensive experiments also show that a number of results from the literature could benefit from more substantial hyperparameter search and are often missing comparisons to a number of obvious baselines: • The results in Tab. 1 indicate that GATs have no advantage over GGNNs or R-GCNs on the PPI task, which does not match the findings by Veličković et al. (2018) . • The results in Tab. 3 indicate that R-GCNs are outperforming GGNNs substantially on the VarMisuse task, contradicting the findings of Allamanis et al. (2018) . • The GNN-MLP models are obvious extensions that are often alluded to, but are not part of the usually considered set of baseline models. Nonetheless, experiments across all three tasks have shown that these methods outperform better-published techniques such as GGNNs, R-GCNs and GATs, without a substantial runtime penalty. These results indicate that there is substantial value in independent reproducibility efforts and comparisons that include "obvious" baselines, matching the experiences from other areas of machine learning as well as earlier work by Shchur et al. (2018) on reproducing experimental results for GNNs on citation network tasks.
new GNN formalism + extensive experiments; showing differences between GGNN/GCN/GAT are smaller than thought The paper proposes a new Graph Neural Network architecture that uses Feature-wise Linear Modulation to condition the source-to-target node message-passing based on the target node representation.