Bit Flip Attacks (BFAs) are a well-established class of adversarial attacks, originally developed for Convolutional Neural Networks within the computer vision domain. Most recently, these attacks have been extended to target Graph Neural Networks (GNNs), revealing significant vulnerabilities. This new development naturally raises questions about the best strategies to defend GNNs against BFAs, a challenge for which no solutions currently exist. Given the applications of GNNs in critical fields, any defense mechanism must not only maintain network performance, but also verifiably restore the network to its pre-attack state. Verifiably restoring the network to its pre-attack state also eliminates the need for costly evaluations on test data to ensure network quality. We offer first insights into the effectiveness of existing honeypot- and hashing-based defenses against BFAs adapted from the computer vision domain to GNNs, and characterize the shortcomings of these approaches. To overcome their limitations, we propose Crossfire, a hybrid approach that exploits weight sparsity and combines hashing and honeypots with bit-level correction of out-of-distribution weight elements to restore network integrity. Crossfire is retraining-free and does not require labeled data. Averaged over 2,160 experiments on six benchmark datasets, Crossfire offers a 21.8% higher probability than its competitors of reconstructing a GNN attacked by a BFA to its pre-attack state. These experiments cover up to 55 bit flips from various attacks. Moreover, it improves post repair prediction quality by 10.85%. Computational and storage overheads are negligible compared to the inherent complexity of even the simplest GNNs.

Graph Neural Networks (GNNs) have become essential for handling large-scale graph applications. However, the computational demands of GNNs necessitate the development of efficient methods to accelerate inference. Mixed precision quantization emerges as a promising solution to enhance the efficiency of GNN architectures without compromising prediction performance. Compared to conventional deep learning architectures, GNN layers contain a wider set of components that can be quantized, including message passing functions, aggregation functions, update functions, the inputs, learnable parameters, and outputs of these functions. In this paper, we introduce a theorem for efficient quantized message passing to aggregate integer messages. It guarantees numerical equality of the aggregated messages using integer values with respect to those obtained with full (FP32) precision. Based on this theorem, we introduce the Mixed Precision Quantization for GNN (MixQ-GNN) framework, which flexibly selects effective integer bit-widths for all components within GNN layers. Our approach systematically navigates the wide set of possible bit-width combinations, addressing the challenge of optimizing efficiency while aiming at maintaining comparable prediction performance. MixQ-GNN integrates with existing GNN quantization methods, utilizing their graph structure advantages to achieve higher prediction performance. On average, MixQ-GNN achieved reductions in bit operations of 5.5x for node classification and 5.1x for graph classification compared to architectures represented in FP32 precision.

The lottery ticket hypothesis (LTH) is well-studied for convolutional neural networks but has been validated only empirically for graph neural networks (GNNs), for which theoretical findings are largely lacking. In this paper, we identify the expressivity of sparse subnetworks, i.e. their ability to distinguish non-isomorphic graphs, as crucial for finding winning tickets that preserve the predictive performance. We establish conditions under which the expressivity of a sparsely initialized GNN matches that of the full network, particularly when compared to the Weisfeiler-Leman test, and in that context put forward and prove a Strong Expressive Lottery Ticket Hypothesis. We subsequently show that an increased expressivity in the initialization potentially accelerates model convergence and improves generalization. Our findings establish novel theoretical foundations for both LTH and GNN research, highlighting the importance of maintaining expressivity in sparsely initialized GNNs. We illustrate our results using examples from drug discovery.

This paper proposes the Compressed Binary Matrix (CBM) format, a novel, computation-friendly compression scheme for binary matrices. CBM not only reduces the memory footprint of the matrix but also enables faster matrix multiplication between binary and dense, real-valued matrices. The CBM format can be applied to accelerate various graph-related tasks, where the (binary) adjacency matrix of the graph is repeatedly multiplied by another matrix, such as during inference and training of various types of Graph Neural Networks (GNNs). The format is evaluated on a shared-memory architecture in both serial and parallel settings. Experimental results show that CBM can reduce the memory footprint of real-world graphs up to$11 \times$, and that the parallel matrix multiplication using CBM is more than$5 \times$faster than state-of-the-art sparse-dense matrix multiplication kernels. Furthermore, when applied to the inference stage of Graph Convolutional Networks (GCNs), the CBM format achieves speedups close to$2.5 \times$compared to inference using other parallel matrix multiplication kernels.

Prior attacks on graph neural networks have focused on graph poisoning and evasion, neglecting the network's weights and biases. For convolutional neural networks, however, the risk arising from bit flip attacks is well recognized. We show that the direct application of a traditional bit flip attack to graph neural networks is of limited effectivity. Hence, we discuss the Injectivity Bit Flip Attack, the first bit flip attack designed specifically for graph neural networks. Our attack targets the learnable neighborhood aggregation functions in quantized message passing neural networks, degrading their ability to distinguish graph structures and impairing the expressivity of the Weisfeiler-Leman test. We find that exploiting mathematical properties specific to certain graph neural networks significantly increases their vulnerability to bit flip attacks. The Injectivity Bit Flip Attack can degrade the maximal expressive Graph Isomorphism Networks trained on graph property prediction datasets to random output by flipping only a small fraction of the network's bits, demonstrating its higher destructive power compared to traditional bit flip attacks transferred from convolutional neural networks. Our attack is transparent, motivated by theoretical insights and confirmed by extensive empirical results.