Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks only, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of conditional molecule generation. Deep learning on graphs has very recently become a popular research topic, with useful applications across fields such as chemistry BID5 , medicine (Ktena et al.) , or computer vision (Simonovsky & Komodakis, 2017) . Past work has concentrated on learning graph embedding tasks so far, i.e. encoding an input graph into a vector representation. This is in stark contrast with fastpaced advances in generative models for images and text, which have seen massive rise in quality of generated samples. Hence, it is an intriguing question how one can transfer this progress to the domain of graphs, i.e. their decoding from a vector representation. Moreover, the desire for such a method has been mentioned in the past by BID7 .However , learning to generate graphs is a difficult problem for methods based on gradient optimization, as graphs are discrete structures. Incremental construction involves discrete decisions, which are not differentiable. Unlike sequence (text) generation, graphs can have arbitrary connectivity and there is no clear best way how to linearize their construction in a sequence of steps.In this work, we propose to sidestep these hurdles by having the decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. In a probabilistic graph, the existence of nodes and edges, as well as their attributes, are modeled as independent random variables. The method is formulated in the framework of variational autoencoders (VAE) by BID12 .We demonstrate our method , coined GraphVAE, in cheminformatics on the task of molecule generation. Molecular datasets are a challenging but convenient testbed for our generative model, as they easily allow for both qualitative and quantitative tests of decoded samples. While our method is applicable for generating smaller graphs only and its performance leaves space for improvement, we believe our work is an important initial step towards powerful and efficient graph decoders. In this work we addressed the problem of generating graphs from a continuous embedding in the context of variational autoencoders. We evaluated our method on two molecular datasets of different maximum graph size. While we achieved to learn embedding of reasonable quality on small molecules, our decoder had a hard time capturing complex chemical interactions for larger molecules. Nevertheless, we believe our method is an important initial step towards more powerful decoders and will spark interesting in the community.There are many avenues to follow for future work. Besides the obvious desire to improve the current method (for example, by incorporating a more powerful prior distribution or adding a recurrent mechanism for correcting mistakes), we would like to extend it beyond a proof of concept by applying it to real problems in chemistry, such as optimization of certain properties or predicting chemical reactions. An advantage of a graph-based decoder compared to SMILES-based decoder is the possibility to predict detailed attributes of atoms and bonds in addition to the base structure, which might be useful in these tasks. Our autoencoder can also be used to pre-train graph encoders for fine-tuning on small datasets BID6 .
We demonstate an autoencoder for graphs. Learning to generate graphs using deep learning methods in "one shot", directly outputting node and edge existence probabilities, and node attribute vectors. A variational auto encoder to generate graphs