Graph Neural Networks Use Graphs When They Shouldn't

Predictions over graphs play a crucial role in various domains, including social networks, molecular biology, medicine, and more. Graph Neural Networks (GNNs) have emerged as the dominant approach for learning on graph data. Instances of graph labeling problems consist of the graph-structure (i.e., the adjacency matrix), along with node-specific feature vectors. In some cases, this graph-structure is non-informative for the predictive task. For instance, molecular properties such as molar mass depend solely on the constituent atoms (node features), and not on the molecular structure. While GNNs have the ability to ignore the graph-structure in such cases, it is not clear that they will. In this work, we show that GNNs actually tend to overfit the graph-structure in the sense that they use it even when a better solution can be obtained by ignoring it. We examine this phenomenon with respect to different graph distributions and find that regular graphs are more robust to this overfitting. We then provide a theoretical explanation for this phenomenon, via analyzing the implicit bias of gradient-descent-based learning of GNNs in this setting. Finally, based on our empirical and theoretical findings, we propose a graph-editing method to mitigate the tendency of GNNs to overfit graph-structures that should be ignored. We show that this method indeed improves the accuracy of GNNs across multiple benchmarks

Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.Comment: 20 pages; 7 figure

Spectral Adversarial Training for Robust Graph Neural Network

Recent studies demonstrate that Graph Neural Networks (GNNs) are vulnerable to slight but adversarially designed perturbations, known as adversarial examples. To address this issue, robust training methods against adversarial examples have received considerable attention in the literature. \emph{Adversarial Training (AT)} is a successful approach to learning a robust model using adversarially perturbed training samples. Existing AT methods on GNNs typically construct adversarial perturbations in terms of graph structures or node features. However, they are less effective and fraught with challenges on graph data due to the discreteness of graph structure and the relationships between connected examples. In this work, we seek to address these challenges and propose Spectral Adversarial Training (SAT), a simple yet effective adversarial training approach for GNNs. SAT first adopts a low-rank approximation of the graph structure based on spectral decomposition, and then constructs adversarial perturbations in the spectral domain rather than directly manipulating the original graph structure. To investigate its effectiveness, we employ SAT on three widely used GNNs. Experimental results on four public graph datasets demonstrate that SAT significantly improves the robustness of GNNs against adversarial attacks without sacrificing classification accuracy and training efficiency.Comment: Accepted by TKDE. Code availiable at https://github.com/EdisonLeeeee/SA

GCondNet: A Novel Method for Improving Neural Networks on Small High-Dimensional Tabular Data

Neural network models often struggle with high-dimensional but small sample-size tabular datasets. One reason is that current weight initialisation methods assume independence between weights, which can be problematic when there are insufficient samples to estimate the model's parameters accurately. In such small data scenarios, leveraging additional structures can improve the model's training stability and performance. To address this, we propose GCondNet, a general approach to enhance neural networks by leveraging implicit structures present in tabular data. We create a graph between samples for each data dimension, and utilise Graph Neural Networks (GNNs) for extracting this implicit structure, and for conditioning the parameters of the first layer of an underlying predictor MLP network. By creating many small graphs, GCondNet exploits the data's high-dimensionality, and thus improves the performance of an underlying predictor network. We demonstrate the effectiveness of our method on nine real-world datasets, where GCondNet outperforms 14 standard and state-of-the-art methods. The results show that GCondNet is robust and can be applied to any small sample-size and high-dimensional tabular learning task.Comment: Early version presented at the 17th Machine Learning in Computational Biology (MLCB) meeting, 202

Robust Graph Representation Learning via Predictive Coding

Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural ability of generative models to learn robust representations thanks to their peculiar credit assignment rule, that allows neural activities to converge to a solution before updating the synaptic weights. Graph neural networks are also message-passing models, which have recently shown outstanding results in diverse types of tasks in machine learning, providing interdisciplinary state-of-the-art performance on structured data. However, they are vulnerable to imperceptible adversarial attacks, and unfit for out-of-distribution generalization. In this work, we address this by building models that have the same structure of popular graph neural network architectures, but rely on the message-passing rule of predictive coding. Through an extensive set of experiments, we show that the proposed models are (i) comparable to standard ones in terms of performance in both inductive and transductive tasks, (ii) better calibrated, and (iii) robust against multiple kinds of adversarial attacks.Comment: 27 Pages, 31 Figure

Dynamic Inference on Graphs using Structured Transition Models

Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical towards the successful execution of such tasks. Graph neural networks (GNNs) provide a principled way of learning the dynamics of interactive systems but can suffer from scaling issues as the number of interactions increases. Furthermore, the problem of using learned GNN-based models for optimal control is insufficiently explored. In this work, we present a method for efficiently learning the dynamics of interacting systems by simultaneously learning a dynamic graph structure and a stable and locally linear forward model of the system. The dynamic graph structure encodes evolving contact modes along a trajectory by making probabilistic predictions over the edges of the graph. Additionally, we introduce a temporal dependence in the learned graph structure which allows us to incorporate contact measurement updates during execution thus enabling more accurate forward predictions. The learned stable and locally linear dynamics enable the use of optimal control algorithms such as iLQR for long-horizon planning and control for complex interactive tasks. Through experiments in simulation and in the real world, we evaluate the performance of our method by using the learned interaction dynamics for control and demonstrate generalization to more objects and interactions not seen during training. We introduce a control scheme that takes advantage of contact measurement updates and hence is robust to prediction inaccuracies during execution