Language Models (LMs) often encounter knowledge conflicts when parametric memory contradicts contextual knowledge. Previous works attribute this conflict to the interplay between "memory heads" and "context heads", attention heads assumed to promote either memory or context exclusively. In this study, we go beyond this fundamental assumption by uncovering a critical phenomenon we term the *superposition of contextual information and parametric memory*, where highly influential attention heads simultaneously contribute to both memory and context. Building upon this insight, we propose Just Run Twice (JuICE), a test-time attention intervention method that steers LMs toward either parametric beliefs or contextual knowledge without requiring fine-tuning. JuICE identifies a set of reliable attention heads and leverages a dual-run approach to mitigate the superposition effects. Extensive experiments across 11 datasets and 6 model architectures demonstrate that JuICE sets the new state-of-the-art performance and robust generalization, achieving significant and consistent improvement across different domains under various conflict types. Finally, we theoretically analyze knowledge conflict and the superposition of contextual information and parametric memory in attention heads, which further elucidates the effectiveness of JuICE in these settings. Our code is available at https://github.com/GaotangLi/JUICE.

We address the key challenge of size-induced distribution shifts in graph neural networks (GNNs) and their impact on the generalization of GNNs to larger graphs. Existing literature operates under diverse assumptions about distribution shifts, resulting in varying conclusions about the generalizability of GNNs. In contrast to prior work, we adopt a data-driven approach to identify and characterize the types of size-induced distribution shifts and explore their impact on GNN performance from a spectral standpoint, a perspective that has been largely underexplored. Leveraging the significant variance in graph sizes in real biological datasets, we analyze biological graphs and find that spectral differences-driven by subgraph patterns (e.g., average cycle length)-strongly correlate with GNN performance on larger, unseen graphs. Based on these insights, we propose three model-agnostic strategies to enhance GNNs' awareness of critical subgraph patterns, identifying size-intensive attention as the most effective approach. Extensive experiments with six GNN architectures and seven model-agnostic strategies across five datasets show that our size-intensive attention strategy significantly improves graph classification on test graphs 2 to 10 times larger than the training graphs, boosting F1 scores by up to 8% over strong baselines.

Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node classification when class labels display strong heterophily are well understood, it is unclear how heterophily affects GNN performance in other important graph learning tasks where class labels are not available. In this work, we focus on the link prediction task and systematically analyze the impact of heterophily in node features on GNN performance. We first introduce formal definitions of homophilic and heterophilic link prediction tasks, and present a theoretical framework that highlights the different optimizations needed for the respective tasks. We then analyze how different link prediction encoders and decoders adapt to varying levels of feature homophily and introduce designs for improved performance. Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges. Our empirical analysis on a variety of synthetic and real-world datasets confirms our theoretical insights and highlights the importance of adopting learnable decoders and GNN encoders with ego- and neighbor-embedding separation in message passing for link prediction tasks beyond homophily.

Brain graphs, which model the structural and functional relationships between brain regions, are crucial in neuroscientific and clinical applications that can be formulated as graph classification tasks. However, dense brain graphs pose computational challenges such as large time and memory consumption and poor model interpretability. In this paper, we investigate effective designs in Graph Neural Networks (GNNs) to sparsify brain graphs by eliminating noisy edges. Many prior works select noisy edges based on explainability or task-irrelevant properties, but this does not guarantee performance improvement when using the sparsified graphs. Additionally, the selection of noisy edges is often tailored to each individual graph, making it challenging to sparsify multiple graphs collectively using the same approach.