On the power of message passing for learning on graph-structured data

This thesis proposes novel approaches for machine learning on irregularly structured input data such as graphs, point clouds and manifolds. Specifically, we are breaking up with the regularity restriction of conventional deep learning techniques, and propose solutions in designing, implementing and scaling up deep end-to-end representation learning on graph-structured data, known as Graph Neural Networks (GNNs). GNNs capture local graph structure and feature information by following a neural message passing scheme, in which node representations are recursively updated in a trainable and purely local fashion. In this thesis, we demonstrate the generality of message passing through a unified framework suitable for a wide range of operators and learning tasks. Specifically, we analyze the limitations and inherent weaknesses of GNNs and propose efficient solutions to overcome them, both theoretically and in practice, e.g., by conditioning messages via continuous B-spline kernels, by utilizing hierarchical message passing, or by leveraging positional encodings. In addition, we ensure that our proposed methods scale naturally to large input domains. In particular, we propose novel methods to fully eliminate the exponentially increasing dependency of nodes over layers inherent to message passing GNNs. Lastly, we introduce PyTorch Geometric, a deep learning library for implementing and working with graph-based neural network building blocks, built upon PyTorch

SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.Comment: Presented at CVPR 201

Molecular mechanism of poly(ADP-ribosyl)ation by PARP1 and identification of lysine residues as ADP-ribose acceptor sites

Poly(ADP-ribose) polymerase 1 (PARP1) synthesizes poly(ADP-ribose) (PAR) using nicotinamide adenine dinucleotide (NAD) as a substrate. Despite intensive research on the cellular functions of PARP1, the molecular mechanism of PAR formation has not been comprehensively understood. In this study, we elucidate the molecular mechanisms of poly(ADP-ribosyl)ation and identify PAR acceptor sites. Generation of different chimera proteins revealed that the amino-terminal domains of PARP1, PARP2 and PARP3 cooperate tightly with their corresponding catalytic domains. The DNA-dependent interaction between the amino-terminal DNA-binding domain and the catalytic domain of PARP1 increased Vmax and decreased the Km for NAD. Furthermore, we show that glutamic acid residues in the auto-modification domain of PARP1 are not required for PAR formation. Instead, we identify individual lysine residues as acceptor sites for ADP-ribosylation. Together, our findings provide novel mechanistic insights into PAR synthesis with significant relevance for the different biological functions of PARP family member