arXiv subjects

Muhan Zhang

Publications and source records attributed to Muhan Zhang.

At least 109 records · Page 6Linked to original sources

arXiv2024

RulE: Knowledge Graph Reasoning with Rule Embedding

Knowledge graph (KG) reasoning is an important problem for knowledge graphs. In this paper, we propose a novel and principled framework called \textbf{RulE} (stands for {Rul}e {E}mbedding) to effectively leverage logical rules to enhance KG reasoning. Unlike knowledge graph embedding (KGE) methods, RulE learns rule embeddings from existing triplets and first-order {rules} by jointly representing \textbf{entities}, \textbf{relations} and \textbf{logical rules} in a unified embedding space. Based on the learned rule embeddings, a confidence score can be calculated for each rule, reflecting its consistency with the observed triplets. This allows us to perform logical rule inference in a soft way, thus alleviating the brittleness of logic. On the other hand, RulE injects prior logical rule information into the embedding space, enriching and regularizing the entity/relation embeddings. This makes KGE alone perform better too. RulE is conceptually simple and empirically effective. We conduct extensive experiments to verify each component of RulE. Results on multiple benchmarks reveal that our model outperforms the majority of existing embedding-based and rule-based approaches.

cs.AI↗

arXiv2024

SPGNN: Recognizing Salient Subgraph Patterns via Enhanced Graph Convolution and Pooling

Graph neural networks (GNNs) have revolutionized the field of machine learning on non-Euclidean data such as graphs and networks. GNNs effectively implement node representation learning through neighborhood aggregation and achieve impressive results in many graph-related tasks. However, most neighborhood aggregation approaches are summation-based, which can be problematic as they may not be sufficiently expressive to encode informative graph structures. Furthermore, though the graph pooling module is also of vital importance for graph learning, especially for the task of graph classification, research on graph down-sampling mechanisms is rather limited. To address the above challenges, we propose a concatenation-based graph convolution mechanism that injectively updates node representations to maximize the discriminative power in distinguishing non-isomorphic subgraphs. In addition, we design a novel graph pooling module, called WL-SortPool, to learn important subgraph patterns in a deep-learning manner. WL-SortPool layer-wise sorts node representations (i.e. continuous WL colors) to separately learn the relative importance of subtrees with different depths for the purpose of classification, thus better characterizing the complex graph topology and rich information encoded in the graph. We propose a novel Subgraph Pattern GNN (SPGNN) architecture that incorporates these enhancements. We test the proposed SPGNN architecture on many graph classification benchmarks. Experimental results show that our method can achieve highly competitive results with state-of-the-art graph kernels and other GNN approaches.

cs.LG↗

arXiv2024

4DBInfer: A 4D Benchmarking Toolbox for Graph-Centric Predictive Modeling on Relational DBs

Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks. From a delivery standpoint, we operationalize the above four dimensions (4D) of exploration within a unified, scalable open-source toolbox called 4DBInfer. We conclude by presenting evaluations using 4DBInfer, the results of which highlight the importance of considering each such dimension in the design of RDB predictive models, as well as the limitations of more naive approaches such as simply joining adjacent tables. Our source code is released at https://github.com/awslabs/multi-table-benchmark .

cs.LG↗

arXiv2024

Parrot Mind: Towards Explaining the Complex Task Reasoning of Pretrained Large Language Models with Template-Content Structure

The pre-trained large language models (LLMs) have shown their extraordinary capacity to solve reasoning tasks, even on tasks that require a complex process involving multiple sub-steps. However, given the vast possible generation space of all the tasks, how the pretrained model learns the reasoning ability remains an open question. We firstly propose that an intrinsic structural constraint on the generated sequence of language-based reasoning -- we called it template-content structure (T-C structure) -- is the key to explain why LLMs can solve a large number of complex reasoning problems with limited training data by showing this structure can reduce the possible space from exponential level to linear level. Furthermore, by generalizing this structure to the hierarchical case, we demonstrate that models can achieve task composition, further reducing the space needed to learn from linear to logarithmic, thereby effectively learning on complex reasoning involving multiple steps. We provide both examples and formal theory of our T-C structure. We also experimentally validate the existence of the T-C structure in some current LLMs and its effectiveness for reasoning.

cs.AI↗

arXiv2024

VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs

GNN-to-MLP distillation aims to utilize knowledge distillation (KD) to learn computationally-efficient multi-layer perceptron (student MLP) on graph data by mimicking the output representations of teacher GNN. Existing methods mainly make the MLP to mimic the GNN predictions over a few class labels. However, the class space may not be expressive enough for covering numerous diverse local graph structures, thus limiting the performance of knowledge transfer from GNN to MLP. To address this issue, we propose to learn a new powerful graph representation space by directly labeling nodes' diverse local structures for GNN-to-MLP distillation. Specifically, we propose a variant of VQ-VAE to learn a structure-aware tokenizer on graph data that can encode each node's local substructure as a discrete code. The discrete codes constitute a codebook as a new graph representation space that is able to identify different local graph structures of nodes with the corresponding code indices. Then, based on the learned codebook, we propose a new distillation target, namely soft code assignments, to directly transfer the structural knowledge of each node from GNN to MLP. The resulting framework VQGraph achieves new state-of-the-art performance on GNN-to-MLP distillation in both transductive and inductive settings across seven graph datasets. We show that VQGraph with better performance infers faster than GNNs by 828x, and also achieves accuracy improvement over GNNs and stand-alone MLPs by 3.90% and 28.05% on average, respectively. Code: https://github.com/YangLing0818/VQGraph.

cs.LG↗

arXiv2024

Highly Accurate Disease Diagnosis and Highly Reproducible Biomarker Identification with PathFormer

Biomarker identification is critical for precise disease diagnosis and understanding disease pathogenesis in omics data analysis, like using fold change and regression analysis. Graph neural networks (GNNs) have been the dominant deep learning model for analyzing graph-structured data. However, we found two major limitations of existing GNNs in omics data analysis, i.e., limited-prediction (diagnosis) accuracy and limited-reproducible biomarker identification capacity across multiple datasets. The root of the challenges is the unique graph structure of biological signaling pathways, which consists of a large number of targets and intensive and complex signaling interactions among these targets. To resolve these two challenges, in this study, we presented a novel GNN model architecture, named PathFormer, which systematically integrate signaling network, priori knowledge and omics data to rank biomarkers and predict disease diagnosis. In the comparison results, PathFormer outperformed existing GNN models significantly in terms of highly accurate prediction capability ( 30% accuracy improvement in disease diagnosis compared with existing GNN models) and high reproducibility of biomarker ranking across different datasets. The improvement was confirmed using two independent Alzheimer's Disease (AD) and cancer transcriptomic datasets. The PathFormer model can be directly applied to other omics data analysis studies.

q-bio.GN↗

arXiv2024

CktGNN: Circuit Graph Neural Network for Electronic Design Automation

The electronic design automation of analog circuits has been a longstanding challenge in the integrated circuit field due to the huge design space and complex design trade-offs among circuit specifications. In the past decades, intensive research efforts have mostly been paid to automate the transistor sizing with a given circuit topology. By recognizing the graph nature of circuits, this paper presents a Circuit Graph Neural Network (CktGNN) that simultaneously automates the circuit topology generation and device sizing based on the encoder-dependent optimization subroutines. Particularly, CktGNN encodes circuit graphs using a two-level GNN framework (of nested GNN) where circuits are represented as combinations of subgraphs in a known subgraph basis. In this way, it significantly improves design efficiency by reducing the number of subgraphs to perform message passing. Nonetheless, another critical roadblock to advancing learning-assisted circuit design automation is a lack of public benchmarks to perform canonical assessment and reproducible research. To tackle the challenge, we introduce Open Circuit Benchmark (OCB), an open-sourced dataset that contains $10$K distinct operational amplifiers with carefully-extracted circuit specifications. OCB is also equipped with communicative circuit generation and evaluation capabilities such that it can help to generalize CktGNN to design various analog circuits by producing corresponding datasets. Experiments on OCB show the extraordinary advantages of CktGNN through representation-based optimization frameworks over other recent powerful GNN baselines and human experts' manual designs. Our work paves the way toward a learning-based open-sourced design automation for analog circuits. Our source code is available at \url{https://github.com/zehao-dong/CktGNN}.

cs.LG↗

arXiv2024

Rethinking the Power of Graph Canonization in Graph Representation Learning with Stability

The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet rarely adopted when developing expressive GNNs. This paper proposes to maximize the expressivity of GNNs by graph canonization, then the power of such GNNs is studies from the perspective of model stability. A stable GNN will map similar graphs to close graph representations in the vectorial space, and the stability of GNNs is critical to generalize their performance to unseen graphs. We theoretically reveal the trade-off of expressivity and stability in graph-canonization-enhanced GNNs. Then we introduce a notion of universal graph canonization as the general solution to address the trade-off and characterize a widely applicable sufficient condition to solve the universal graph canonization. A comprehensive set of experiments demonstrates the effectiveness of the proposed method. In many popular graph benchmark datasets, graph canonization successfully enhances GNNs and provides highly competitive performance, indicating the capability and great potential of proposed method in general graph representation learning. In graph datasets where the sufficient condition holds, GNNs enhanced by universal graph canonization consistently outperform GNN baselines and successfully improve the SOTA performance up to $31\%$, providing the optimal solution to numerous challenging real-world graph analytical tasks like gene network representation learning in bioinformatics.

cs.LG↗

arXiv2024

Extending the Design Space of Graph Neural Networks by Rethinking Folklore Weisfeiler-Lehman

Message passing neural networks (MPNNs) have emerged as the most popular framework of graph neural networks (GNNs) in recent years. However, their expressive power is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Some works are inspired by $k$-WL/FWL (Folklore WL) and design the corresponding neural versions. Despite the high expressive power, there are serious limitations in this line of research. In particular, (1) $k$-WL/FWL requires at least $O(n^k)$ space complexity, which is impractical for large graphs even when $k=3$; (2) The design space of $k$-WL/FWL is rigid, with the only adjustable hyper-parameter being $k$. To tackle the first limitation, we propose an extension, $(k,t)$-FWL. We theoretically prove that even if we fix the space complexity to $O(n^k)$ (for any $k\geq 2$) in $(k,t)$-FWL, we can construct an expressiveness hierarchy up to solving the graph isomorphism problem. To tackle the second problem, we propose $k$-FWL+, which considers any equivariant set as neighbors instead of all nodes, thereby greatly expanding the design space of $k$-FWL. Combining these two modifications results in a flexible and powerful framework $(k,t)$-FWL+. We demonstrate $(k,t)$-FWL+ can implement most existing models with matching expressiveness. We then introduce an instance of $(k,t)$-FWL+ called Neighborhood$^2$-FWL (N$^2$-FWL), which is practically and theoretically sound. We prove that N$^2$-FWL is no less powerful than 3-WL, and can encode many substructures while only requiring $O(n^2)$ space. Finally, we design its neural version named N$^2$-GNN and evaluate its performance on various tasks. N$^2$-GNN achieves record-breaking results on ZINC-Subset (0.059), outperforming previous SOTA results by 10.6%. Moreover, N$^2$-GNN achieves new SOTA results on the BREC dataset (71.8%) among all existing high-expressive GNN methods.

cs.LG↗

arXiv2024

Distance-Restricted Folklore Weisfeiler-Leman GNNs with Provable Cycle Counting Power

The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive power of GNNs. Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from the input graph, generating representations for each subgraph, and using them to augment the representation of the input graph. However, those methods require heavy preprocessing, and suffer from high time and memory costs. In this paper, we overcome the aforementioned limitations of subgraph GNNs by proposing a novel class of GNNs -- $d$-Distance-Restricted FWL(2) GNNs, or $d$-DRFWL(2) GNNs. $d$-DRFWL(2) GNNs use node pairs whose mutual distances are at most $d$ as the units for message passing to balance the expressive power and complexity. By performing message passing among distance-restricted node pairs in the original graph, $d$-DRFWL(2) GNNs avoid the expensive subgraph extraction operations in subgraph GNNs, making both the time and space complexity lower. We theoretically show that the discriminative power of $d$-DRFWL(2) GNNs strictly increases as $d$ increases. More importantly, $d$-DRFWL(2) GNNs have provably strong cycle counting power even with $d=2$: they can count all 3, 4, 5, 6-cycles. Since 6-cycles (e.g., benzene rings) are ubiquitous in organic molecules, being able to detect and count them is crucial for achieving robust and generalizable performance on molecular tasks. Experiments on both synthetic datasets and molecular datasets verify our theory. To the best of our knowledge, our model is the most efficient GNN model to date (both theoretically and empirically) that can count up to 6-cycles.

cs.LG↗

arXiv2023

SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning

Subgraph-based graph representation learning (SGRL) has recently emerged as a powerful tool in many prediction tasks on graphs due to its advantages in model expressiveness and generalization ability. Most previous SGRL models face computational challenges associated with the high cost of subgraph extraction for each training or test query. Recently, SUREL was proposed to accelerate SGRL, which samples random walks offline and joins these walks online as a proxy of subgraph for representation learning. Thanks to the reusability of sampled walks across different queries, SUREL achieves state-of-the-art performance in terms of scalability and prediction accuracy. However, SUREL still suffers from high computational overhead caused by node duplication in sampled walks. In this work, we propose a novel framework SUREL+ that upgrades SUREL by using node sets instead of walks to represent subgraphs. This set-based representation eliminates repeated nodes by definition but can also be irregular in size. To address this issue, we design a customized sparse data structure to efficiently store and access node sets and provide a specialized operator to join them in parallel batches. SUREL+ is modularized to support multiple types of set samplers, structural features, and neural encoders to complement the structural information loss after the reduction from walks to sets. Extensive experiments have been performed to validate SUREL+ in the prediction tasks of links, relation types, and higher-order patterns. SUREL+ achieves 3-11$\times$ speedups of SUREL while maintaining comparable or even better prediction performance; compared to other SGRL baselines, SUREL+ achieves $\sim$20$\times$ speedups and significantly improves the prediction accuracy.

cs.LG↗

arXiv2023

PyTorch Geometric High Order: A Unified Library for High Order Graph Neural Network

We introduce PyTorch Geometric High Order (PyGHO), a library for High Order Graph Neural Networks (HOGNNs) that extends PyTorch Geometric (PyG). Unlike ordinary Message Passing Neural Networks (MPNNs) that exchange messages between nodes, HOGNNs, encompassing subgraph GNNs and k-WL GNNs, encode node tuples, a method previously lacking a standardized framework and often requiring complex coding. PyGHO's main objective is to provide an unified and user-friendly interface for various HOGNNs. It accomplishes this through streamlined data structures for node tuples, comprehensive data processing utilities, and a flexible suite of operators for high-order GNN methodologies. In this work, we present a detailed in-depth of PyGHO and compare HOGNNs implemented with PyGHO with their official implementation on real-world tasks. PyGHO achieves up to $50\%$ acceleration and reduces the code needed for implementation by an order of magnitude. Our library is available at \url{https://github.com/GraphPKU/PygHO}.

cs.LG↗

arXiv2023

Chain of Images for Intuitively Reasoning

The human brain is naturally equipped to comprehend and interpret visual information rapidly. When confronted with complex problems or concepts, we use flowcharts, sketches, and diagrams to aid our thought process. Leveraging this inherent ability can significantly enhance logical reasoning. However, current Large Language Models (LLMs) do not utilize such visual intuition to help their thinking. Even the most advanced version language models (e.g., GPT-4V and LLaVA) merely align images into textual space, which means their reasoning processes remain purely verbal. To mitigate such limitations, we present a Chain of Images (CoI) approach, which can convert complex language reasoning problems to simple pattern recognition by generating a series of images as intermediate representations. Furthermore, we have developed a CoI evaluation dataset encompassing 15 distinct domains where images can intuitively aid problem-solving. Based on this dataset, we aim to construct a benchmark to assess the capability of future multimodal large-scale models to leverage images for reasoning. In supporting our CoI reasoning, we introduce a symbolic multimodal large language model (SyMLLM) that generates images strictly based on language instructions and accepts both text and image as input. Experiments on Geometry, Chess and Common Sense tasks sourced from the CoI evaluation dataset show that CoI improves performance significantly over the pure-language Chain of Thoughts (CoT) baselines. The code is available at https://github.com/GraphPKU/CoI.

cs.CV↗

arXiv2023

Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In the spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on the spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.

cs.LG↗

arXiv2023

MAG-GNN: Reinforcement Learning Boosted Graph Neural Network

While Graph Neural Networks (GNNs) recently became powerful tools in graph learning tasks, considerable efforts have been spent on improving GNNs' structural encoding ability. A particular line of work proposed subgraph GNNs that use subgraph information to improve GNNs' expressivity and achieved great success. However, such effectivity sacrifices the efficiency of GNNs by enumerating all possible subgraphs. In this paper, we analyze the necessity of complete subgraph enumeration and show that a model can achieve a comparable level of expressivity by considering a small subset of the subgraphs. We then formulate the identification of the optimal subset as a combinatorial optimization problem and propose Magnetic Graph Neural Network (MAG-GNN), a reinforcement learning (RL) boosted GNN, to solve the problem. Starting with a candidate subgraph set, MAG-GNN employs an RL agent to iteratively update the subgraphs to locate the most expressive set for prediction. This reduces the exponential complexity of subgraph enumeration to the constant complexity of a subgraph search algorithm while keeping good expressivity. We conduct extensive experiments on many datasets, showing that MAG-GNN achieves competitive performance to state-of-the-art methods and even outperforms many subgraph GNNs. We also demonstrate that MAG-GNN effectively reduces the running time of subgraph GNNs.

cs.LG↗

arXiv2023

Neural Attention: Enhancing QKV Calculation in Self-Attention Mechanism with Neural Networks

In the realm of deep learning, the self-attention mechanism has substantiated its pivotal role across a myriad of tasks, encompassing natural language processing and computer vision. Despite achieving success across diverse applications, the traditional self-attention mechanism primarily leverages linear transformations for the computation of query, key, and value (QKV), which may not invariably be the optimal choice under specific circumstances. This paper probes into a novel methodology for QKV computation-implementing a specially-designed neural network structure for the calculation. Utilizing a modified Marian model, we conducted experiments on the IWSLT 2017 German-English translation task dataset and juxtaposed our method with the conventional approach. The experimental results unveil a significant enhancement in BLEU scores with our method. Furthermore, our approach also manifested superiority when training the Roberta model with the Wikitext-103 dataset, reflecting a notable reduction in model perplexity compared to its original counterpart. These experimental outcomes not only validate the efficacy of our method but also reveal the immense potential in optimizing the self-attention mechanism through neural network-based QKV computation, paving the way for future research and practical applications. The source code and implementation details for our proposed method can be accessed at https://github.com/ocislyjrti/NeuralAttention.

cs.CL↗

arXiv2023

Code Prompting: a Neural Symbolic Method for Complex Reasoning in Large Language Models

Large language models (LLMs) have scaled up to unlock a wide range of complex reasoning tasks with the aid of various prompting methods. However, current prompting methods generate natural language intermediate steps to help reasoning, which can cause imperfect task reduction and confusion. To mitigate such limitations, we explore code prompting, a neural symbolic prompting method with both zero-shot and few-shot versions which triggers code as intermediate steps. We conduct experiments on 7 widely-used benchmarks involving symbolic reasoning and arithmetic reasoning. Code prompting generally outperforms chain-of-thought (CoT) prompting. To further understand the performance and limitations of code prompting, we perform extensive ablation studies and error analyses, and identify several exclusive advantages of using symbolic promptings compared to natural language. We also consider the ensemble of code prompting and CoT prompting to combine the strengths of both. Finally, we show through experiments how code annotations and their locations affect code prompting.

cs.CL↗

arXiv2023

Graph Contrastive Learning Meets Graph Meta Learning: A Unified Method for Few-shot Node Tasks

Graph Neural Networks (GNNs) have become popular in Graph Representation Learning (GRL). One fundamental application is few-shot node classification. Most existing methods follow the meta learning paradigm, showing the ability of fast generalization to few-shot tasks. However, recent works indicate that graph contrastive learning combined with fine-tuning can significantly outperform meta learning methods. Despite the empirical success, there is limited understanding of the reasons behind it. In our study, we first identify two crucial advantages of contrastive learning compared to meta learning, including (1) the comprehensive utilization of graph nodes and (2) the power of graph augmentations. To integrate the strength of both contrastive learning and meta learning on the few-shot node classification tasks, we introduce a new paradigm: Contrastive Few-Shot Node Classification (COLA). Specifically, COLA employs graph augmentations to identify semantically similar nodes, which enables the construction of meta-tasks without the need for label information. Therefore, COLA can utilize all nodes to construct meta-tasks, further reducing the risk of overfitting. Through extensive experiments, we validate the essentiality of each component in our design and demonstrate that COLA achieves new state-of-the-art on all tasks.

cs.LG↗