Haoyu Wang

Yinan Huang, Haoyu Wang, Pan Li

Positional encodings (PEs) are essential for building powerful and expressive graph neural networks and graph transformers, as they effectively capture the relative spatial relationships between nodes. Although extensive research has been devoted to PEs in undirected graphs, PEs for directed graphs remain relatively unexplored. This work seeks to address this gap. We first introduce the notion of Walk Profile, a generalization of walk-counting sequences for directed graphs. A walk profile encompasses numerous structural features crucial for directed graph-relevant applications, such as program analysis and circuit performance prediction. We identify the limitations of existing PE methods in representing walk profiles and propose a novel Multi-q Magnetic Laplacian PE, which extends the Magnetic Laplacian eigenvector-based PE by incorporating multiple potential factors. The new PE can provably express walk profiles. Furthermore, we generalize prior basis-invariant neural networks to enable the stable use of the new PE in the complex domain. Our numerical experiments validate the expressiveness of the proposed PEs and demonstrate their effectiveness in solving sorting network satisfiability and performing well on general circuit benchmarks. Our code is available at https://github.com/Graph-COM/Multi-q-Maglap.

Shide Zhou, Tianlin Li, Yihao Huang et al.

Deep Neural networks (DNNs), extensively applied across diverse disciplines, are characterized by their integrated and monolithic architectures, setting them apart from conventional software systems. This architectural difference introduces particular challenges to maintenance tasks, such as model restructure (e.g., model compression), re-adaptation (e.g., fitting new samples), and incremental development (e.g., continual knowledge accumulation). Prior research addresses these challenges by identifying task-critical neuron layers, and dividing neural networks into semantically-similar sequential modules. However, such layer-level approaches fail to precisely identify and manipulate neuron-level semantic components, restricting their applicability to finer-grained model maintenance tasks. In this work, we implement NeuSemSlice, a novel framework that introduces the semantic slicing technique to effectively identify critical neuron-level semantic components in DNN models for semantic-aware model maintenance tasks. Specifically, semantic slicing identifies, categorizes and merges critical neurons across different categories and layers according to their semantic similarity, enabling their flexibility and effectiveness in the subsequent tasks. For semantic-aware model maintenance tasks, we provide a series of novel strategies based on semantic slicing to enhance NeuSemSlice. They include semantic components (i.e., critical neurons) preservation for model restructure, critical neuron tuning for model re-adaptation, and non-critical neuron training for model incremental development. A thorough evaluation has demonstrated that NeuSemSlice significantly outperforms baselines in all three tasks.