Equivariant neural networks, whose hidden features transform according to representations of a group $G$ acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and equivariant representation learning to the field of unsupervised deep learning. We propose a general learning strategy based on an encoder-decoder framework in which the latent representation is separated in an invariant term and an equivariant group action component. The key idea is that the network learns to encode and decode data to and from a group-invariant representation by additionally learning to predict the appropriate group action to align input and output pose to solve the reconstruction task. We derive the necessary conditions on the equivariant encoder, and we present a construction valid for any $G$, both discrete and continuous. We describe explicitly our construction for rotations, translations and permutations. We test the validity and the robustness of our approach in a variety of experiments with diverse data types employing different network architectures.

Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level unsupervised learning (e.g. node clustering). Despite its wide range of possible applications, graph-level unsupervised learning has not received much attention yet. This might be mainly attributed to the high representation complexity of graphs, which can be represented by $n!$ equivalent adjacency matrices, where $n$ is the number of nodes.In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data. Our proposed model indirectly learns to match the node ordering of input and output graph, without imposing a particular node ordering or performing expensive graph matching. We demonstrate the effectiveness of our proposed model for graph reconstruction, generation and interpolation and evaluate the expressive power of extracted representations for downstream graph-level classification and regression.

SUMMARY: Optimizing small molecules in a drug discovery project is a notoriously difficult task as multiple molecular properties have to be considered and balanced at the same time. In this work, we present our novel interactive in silico compound optimization platform termed grünifai to support the ideation of the next generation of compounds under the constraints of a multiparameter objective. grünifai integrates adjustable in silico models, a continuous representation of the chemical space, a scalable particle swarm optimization algorithm and the possibility to actively steer the compound optimization through providing feedback on generated intermediate structures. AVAILABILITY AND IMPLEMENTATION: Source code and documentation are freely available under an MIT license and are openly available on GitHub (https://github.com/jrwnter/gruenifai). The backend, including the optimization method and distribution on multiple GPU nodes is written in Python 3. The frontend is written in ReactJS.

UNLABELLED: An open-access World Wide Web application has been developed which enables the cross-linking of anatomical data on the phenotypic manifestations of human and mouse malformation syndromes to data on gene function and/or expression patterns in the mouse GXD database. Ultimately, the system has been designed to assist biologists in the process of discovering hitherto unidentified malformation genes. More specifically, it facilitates search from the phenotypic level. AVAILABILITY: The application and further information is available at http://genetics.ich.ucl.ac.uk/linksearchtool.

A central problem in current biology is elucidating the molecular networks that drive developmental change and physiological function. Such knowledge is needed partly to understand these networks, partly to be able to manipulate them, and partly to understand and help treat those human congenital abnormalities that arise as a result of mutation. Thus far, bioinformatics technology has been of limited use in this enterprise, mainly because its core focus has been on sequence technology and data archiving. For bioinformatics to be of use in this next tier of investigations, genetic and protein data need to be both archived and searchable by tissue since this is the level at which these networks operate. The resulting databases in turn require ontologies of developmental anatomy that can provide the formal infrastructure for handling gene expression, microarray and other tissue-based data. Here, the progress in making such ontologies, particularly for the developing mouse, is reported and the uses to which they are and will be put, together with the resources and tools currently available for investigating molecular networks and the genetic basis of congenital abnormalities, are considered.