Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on $\sim 60,000$ crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps and elastic moduli of crystals, achieving better than DFT accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically-intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli)

Deep representation learning for human motion prediction and classification

Generative models of 3D human motion are often restricted to a small number of activities and can therefore not generalize well to novel movements or applications. In this work we propose a deep learning framework for human motion capture data that learns a generic representation from a large corpus of motion capture data and generalizes well to new, unseen, motions. Using an encoding-decoding network that learns to predict future 3D poses from the most recent past, we extract a feature representation of human motion. Most work on deep learning for sequence prediction focuses on video and speech. Since skeletal data has a different structure, we present and evaluate different network architectures that make different assumptions about time dependencies and limb correlations. To quantify the learned features, we use the output of different layers for action classification and visualize the receptive fields of the network units. Our method outperforms the recent state of the art in skeletal motion prediction even though these use action specific training data. Our results show that deep feedforward networks, trained from a generic mocap database, can successfully be used for feature extraction from human motion data and that this representation can be used as a foundation for classification and prediction.Comment: This paper is published at the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 201

GADY: Unsupervised Anomaly Detection on Dynamic Graphs

Anomaly detection on dynamic graphs refers to detecting entities whose behaviors obviously deviate from the norms observed within graphs and their temporal information. This field has drawn increasing attention due to its application in finance, network security, social networks, and more. However, existing methods face two challenges: dynamic structure constructing challenge - difficulties in capturing graph structure with complex time information and negative sampling challenge - unable to construct excellent negative samples for unsupervised learning. To address these challenges, we propose Unsupervised Generative Anomaly Detection on Dynamic Graphs (GADY). To tackle the first challenge, we propose a continuous dynamic graph model to capture the fine-grained information, which breaks the limit of existing discrete methods. Specifically, we employ a message-passing framework combined with positional features to get edge embeddings, which are decoded to identify anomalies. For the second challenge, we pioneer the use of Generative Adversarial Networks to generate negative interactions. Moreover, we design a loss function to alter the training goal of the generator while ensuring the diversity and quality of generated samples. Extensive experiments demonstrate that our proposed GADY significantly outperforms the previous state-of-the-art method on three real-world datasets. Supplementary experiments further validate the effectiveness of our model design and the necessity of each module

WL meet VC

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the $1\text{-}\mathsf{WL}$. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the $1\text{-}\mathsf{WL}$ and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.Comment: arXiv admin note: text overlap with arXiv:2206.1116