Weisfeiler and Leman Go Gambling: Why Expressive Lottery Tickets Win

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.

Efficient Mixed Precision Quantization in Graph Neural Networks

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.

On the Relationship Between Robustness and Expressivity of Graph Neural Networks

We investigate the vulnerability of Graph Neural Networks (GNNs) to bit-flip attacks (BFAs) by introducing an analytical framework to study the influence of architectural features, graph properties, and their interaction. The expressivity of GNNs refers to their ability to distinguish non-isomorphic graphs and depends on the encoding of node neighborhoods. We examine the vulnerability of neural multiset functions commonly used for this purpose and establish formal criteria to characterize a GNN's susceptibility to losing expressivity due to BFAs. This enables an analysis of the impact of homophily, graph structural variety, feature encoding, and activation functions on GNN robustness. We derive theoretical bounds for the number of bit flips required to degrade GNN expressivity on a dataset, identifying ReLU-activated GNNs operating on highly homophilous graphs with low-dimensional or one-hot encoded features as particularly susceptible. Empirical results using ten real-world datasets confirm the statistical significance of our key theoretical insights and offer actionable results to mitigate BFA risks in expressivity-critical applications.

Attacking Graph Neural Networks with Bit Flips: Weisfeiler and Lehman Go Indifferent

Prior attacks on graph neural networks have mostly focused on graph poisoning and evasion, neglecting the network's weights and biases. Traditional weight-based fault injection attacks, such as bit flip attacks used for convolutional neural networks, do not consider the unique properties of graph neural networks. We propose 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 losing the expressivity of the Weisfeiler-Lehman test. Our findings suggest that exploiting mathematical properties specific to certain graph neural network architectures can significantly increase their vulnerability to bit flip attacks. Injectivity Bit Flip Attacks can degrade the maximal expressive Graph Isomorphism Networks trained on various 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 a bit flip attack transferred from convolutional neural networks. Our attack is transparent and motivated by theoretical insights which are confirmed by extensive empirical results.

Non-Redundant Graph Neural Networks with Improved Expressiveness

Message passing graph neural networks iteratively compute node embeddings by aggregating messages from all neighbors. This procedure can be viewed as a neural variant of the Weisfeiler-Leman method, which limits their expressive power. Moreover, oversmoothing and oversquashing restrict the number of layers these networks can effectively utilize. The repeated exchange and encoding of identical information in message passing amplifies oversquashing. We propose a novel aggregation scheme based on neighborhood trees, which allows for controlling the redundancy by pruning branches of the unfolding trees underlying standard message passing. We prove that reducing redundancy improves expressivity and experimentally show that it alleviates oversquashing. We investigate the interaction between redundancy in message passing and redundancy in computation and propose a compact representation of neighborhood trees, from which we compute node and graph embeddings via a neural tree canonization technique. Our method is provably more expressive than the Weisfeiler-Leman method, less susceptible to oversquashing than message passing neural networks, and provides high classification accuracy on widely-used benchmark datasets.