Zhouyang Liu

Ziqing Wen, Zhouyang Liu, Jiahuan Wang et al.

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers such as Adam(W) provide per-parameter adaptivity, they do not explicitly account for module-level gradient heterogeneity, resulting in slower convergence, suboptimal performance, or training instability. Existing approaches typically rely on manually tuned module-specific learning rates or specific optimization strategies, which are computationally costly and difficult to generalize across tasks or models. To establish a more principled approach, we first analyze the noise-damping behavior of Adam in high-noise modules and introduce \textbf{Module-wise Learning Rate Scaling via SNR (MoLS)}. MoLS estimates module-level SNRs to scale Adam updates, allowing automated module-wise learning rate allocation without manual tuning. Empirical results through multiple LLM training benchmarks demonstrate that MoLS improves convergence speed and generalization, achieving performance comparable to carefully tuned module-specific learning rates, while remaining compatible with memory-efficient training algorithms.

Zhouyang Liu, Ning Liu, Yixin Chen et al.

Subgraph matching is challenging as it necessitates time-consuming combinatorial searches. Recent Graph Neural Network (GNN)-based approaches address this issue by employing GNN encoders to extract graph information and hinge distance measures to ensure containment constraints in the embedding space. These methods significantly shorten the response time, making them promising solutions for subgraph retrieval. However, they suffer from scale differences between graph pairs during encoding, as they focus on feature counts but overlook the relative positions of features within node-rooted subtrees, leading to disturbed containment constraints and false predictions. Additionally, their hinge distance measures lack discriminative power for matched graph pairs, hindering ranking applications. We propose NC-Iso, a novel GNN architecture for neural subgraph matching. NC-Iso preserves the relative positions of features by building the hierarchical dependencies between adjacent echelons within node-rooted subtrees, ensuring matched graph pairs maintain consistent hierarchies while complying with containment constraints in feature counts. To enhance the ranking ability for matched pairs, we introduce a novel similarity dominance ratio-enhanced measure, which quantifies the dominance of similarity over dissimilarity between graph pairs. Empirical results on nine datasets validate the effectiveness, generalization ability, scalability, and transferability of NC-Iso while maintaining time efficiency, offering a more discriminative neural subgraph matching solution for subgraph retrieval. Code available at https://github.com/liuzhouyang/NC-Iso.

Zhouyang Liu, Yixin Chen, Ning Liu et al.

Graph similarity is critical in graph-related tasks such as graph retrieval, where metrics like maximum common subgraph (MCS) and graph edit distance (GED) are commonly used. However, exact computations of these metrics are known to be NP-Hard. Recent neural network-based approaches approximate the similarity score in embedding spaces to alleviate the computational burden, but they either involve expensive pairwise node comparisons or fail to effectively utilize structural and scale information of graphs. To tackle these issues, we propose a novel geometric-based graph embedding method called Graph2Region (G2R). G2R represents nodes as closed regions and recovers their adjacency patterns within graphs in the embedding space. By incorporating the node features and adjacency patterns of graphs, G2R summarizes graph regions, i.e., graph embeddings, where the shape captures the underlying graph structures and the volume reflects the graph size. Consequently, the overlap between graph regions can serve as an approximation of MCS, signifying similar node regions and adjacency patterns. We further analyze the relationship between MCS and GED and propose using disjoint parts as a proxy for GED similarity. This analysis enables concurrent computation of MCS and GED, incorporating local and global structural information. Experimental evaluation highlights G2R's competitive performance in graph similarity computation. It achieves up to a 60.0\% relative accuracy improvement over state-of-the-art methods in MCS similarity learning, while maintaining efficiency in both training and inference. Moreover, G2R showcases remarkable capability in predicting both MCS and GED similarities simultaneously, providing a holistic assessment of graph similarity. Code available at https://github.com/liuzhouyang/Graph2Region.

Zhouyang Liu, Ning Liu, Yixin Chen et al.

Graph Edit Distance (GED) offers a principled and flexible measure of graph similarity, as it quantifies the minimum cost needed to transform one graph into another with customizable edit operation costs. Despite recent learning-based efforts to approximate GED via vector space representations, existing methods struggle with adapting to varying operation costs. Furthermore, they suffer from inefficient, reactive mapping refinements due to reliance on isolated node-level distance as guidance. To address these issues, we propose GEN, a novel learning-based approach for flexible GED approximation. GEN addresses the varying costs adaptation by integrating operation costs prior to match establishment, enabling mappings to dynamically adapt to cost variations. Furthermore, GEN introduces a proactive guidance optimization strategy that captures graph-level dependencies between matches, allowing informed matching decisions in a single step without costly iterative refinements. Extensive evaluations on real-world and synthetic datasets demonstrate that GEN achieves up to 37.8% reduction in GED approximation error and 72.7% reduction in inference time compared with state-of-the-art methods, while consistently maintaining robustness under diverse cost settings and graph sizes.