ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design process. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs). This paper introduces Language Hyper-Heuristics (LHHs), an emerging variant of Hyper-Heuristics that leverages LLMs for heuristic generation, featuring minimal manual intervention and open-ended heuristic spaces. To empower LHHs, we present Reflective Evolution (ReEvo), a generic searching framework that emulates the reflective design approach of human experts while far surpassing human capabilities with its scalable LLM inference, Internet-scale domain knowledge, and powerful evolutionary search. Evaluations across 12 COP settings show that 1) verbal reflections for evolution lead to smoother fitness landscapes, explicit inference of black-box COP settings, and better search results; 2) heuristics generated by ReEvo in minutes can outperform state-of-the-art human designs and neural solvers; 3) LHHs enable efficient algorithm design automation even when challenged with black-box COPs, demonstrating its potential for complex and novel real-world applications. Our code is available: https://github.com/ai4co/LLM-as-HH.

On Structural Expressive Power of Graph Transformers

Graph Transformer has recently received wide attention in the research community with its outstanding performance, yet its structural expressive power has not been well analyzed. Inspired by the connections between Weisfeiler-Lehman (WL) graph isomorphism test and graph neural network (GNN), we introduce \textbf{SEG-WL test} (\textbf{S}tructural \textbf{E}ncoding enhanced \textbf{G}lobal \textbf{W}eisfeiler-\textbf{L}ehman test), a generalized graph isomorphism test algorithm as a powerful theoretical tool for exploring the structural discriminative power of graph Transformers. We theoretically prove that the SEG-WL test is an expressivity upper bound on a wide range of graph Transformers, and the representational power of SEG-WL test can be approximated by a simple Transformer network arbitrarily under certain conditions. With the SEG-WL test, we show how graph Transformers' expressive power is determined by the design of structural encodings, and present conditions that make the expressivity of graph Transformers beyond WL test and GNNs. Moreover, motivated by the popular shortest path distance encoding, we follow the theory-oriented principles and develop a provably stronger structural encoding method, Shortest Path Induced Subgraph (\textit{SPIS}) encoding. Our theoretical findings provide a novel and practical paradigm for investigating the expressive power of graph Transformers, and extensive synthetic and real-world experiments empirically verify the strengths of our proposed methods.

Continual Learning on Dynamic Graphs via Parameter Isolation

Many real-world graph learning tasks require handling dynamic graphs where new nodes and edges emerge. Dynamic graph learning methods commonly suffer from the catastrophic forgetting problem, where knowledge learned for previous graphs is overwritten by updates for new graphs. To alleviate the problem, continual graph learning methods are proposed. However, existing continual graph learning methods aim to learn new patterns and maintain old ones with the same set of parameters of fixed size, and thus face a fundamental tradeoff between both goals. In this paper, we propose Parameter Isolation GNN (PI-GNN) for continual learning on dynamic graphs that circumvents the tradeoff via parameter isolation and expansion. Our motivation lies in that different parameters contribute to learning different graph patterns. Based on the idea, we expand model parameters to continually learn emerging graph patterns. Meanwhile, to effectively preserve knowledge for unaffected patterns, we find parameters that correspond to them via optimization and freeze them to prevent them from being rewritten. Experiments on eight real-world datasets corroborate the effectiveness of PI-GNN compared to state-of-the-art baselines.

Dual Intent Enhanced Graph Neural Network for Session-based New Item Recommendation

Recommender systems are essential to various fields, e.g., e-commerce, e-learning, and streaming media. At present, graph neural networks (GNNs) for session-based recommendations normally can only recommend items existing in users' historical sessions. As a result, these GNNs have difficulty recommending items that users have never interacted with (new items), which leads to a phenomenon of information cocoon. Therefore, it is necessary to recommend new items to users. As there is no interaction between new items and users, we cannot include new items when building session graphs for GNN session-based recommender systems. Thus, it is challenging to recommend new items for users when using GNN-based methods. We regard this challenge as '\textbf{G}NN \textbf{S}ession-based \textbf{N}ew \textbf{I}tem \textbf{R}ecommendation (GSNIR)'. To solve this problem, we propose a dual-intent enhanced graph neural network for it. Due to the fact that new items are not tied to historical sessions, the users' intent is difficult to predict. We design a dual-intent network to learn user intent from an attention mechanism and the distribution of historical data respectively, which can simulate users' decision-making process in interacting with a new item. To solve the challenge that new items cannot be learned by GNNs, inspired by zero-shot learning (ZSL), we infer the new item representation in GNN space by using their attributes. By outputting new item probabilities, which contain recommendation scores of the corresponding items, the new items with higher scores are recommended to users. Experiments on two representative real-world datasets show the superiority of our proposed method. The case study from the real-world verifies interpretability benefits brought by the dual-intent module and the new item reasoning module. The code is available at Github: https://github.com/Ee1s/NirGNN

Hierarchical Transformer for Scalable Graph Learning

Graph Transformer is gaining increasing attention in the field of machine learning and has demonstrated state-of-the-art performance on benchmarks for graph representation learning. However, as current implementations of Graph Transformer primarily focus on learning representations of small-scale graphs, the quadratic complexity of the global self-attention mechanism presents a challenge for full-batch training when applied to larger graphs. Additionally, conventional sampling-based methods fail to capture necessary high-level contextual information, resulting in a significant loss of performance. In this paper, we introduce the Hierarchical Scalable Graph Transformer (HSGT) as a solution to these challenges. HSGT successfully scales the Transformer architecture to node representation learning tasks on large-scale graphs, while maintaining high performance. By utilizing graph hierarchies constructed through coarsening techniques, HSGT efficiently updates and stores multi-scale information in node embeddings at different levels. Together with sampling-based training methods, HSGT effectively captures and aggregates multi-level information on the hierarchical graph using only Transformer blocks. Empirical evaluations demonstrate that HSGT achieves state-of-the-art performance on large-scale benchmarks with graphs containing millions of nodes with high efficiency.

LEReg: Empower Graph Neural Networks with Local Energy Regularization

Researches on analyzing graphs with Graph Neural Networks (GNNs) have been receiving more and more attention because of the great expressive power of graphs. GNNs map the adjacency matrix and node features to node representations by message passing through edges on each convolution layer. However, the message passed through GNNs is not always beneficial for all parts in a graph. Specifically, as the data distribution is different over the graph, the receptive field (the farthest nodes that a node can obtain information from) needed to gather information is also different. Existing GNNs treat all parts of the graph uniformly, which makes it difficult to adaptively pass the most informative message for each unique part. To solve this problem, we propose two regularization terms that consider message passing locally: (1) Intra-Energy Reg and (2) Inter-Energy Reg. Through experiments and theoretical discussion, we first show that the speed of smoothing of different parts varies enormously and the topology of each part affects the way of smoothing. With Intra-Energy Reg, we strengthen the message passing within each part, which is beneficial for getting more useful information. With Inter-Energy Reg, we improve the ability of GNNs to distinguish different nodes. With the proposed two regularization terms, GNNs are able to filter the most useful information adaptively, learn more robustly and gain higher expressiveness. Moreover, the proposed LEReg can be easily applied to other GNN models with plug-and-play characteristics. Extensive experiments on several benchmarks verify that GNNs with LEReg outperform or match the state-of-the-art methods. The effectiveness and efficiency are also empirically visualized with elaborate experiments.

Meta-Weight Graph Neural Network: Push the Limits Beyond Global Homophily

Graph Neural Networks (GNNs) show strong expressive power on graph data mining, by aggregating information from neighbors and using the integrated representation in the downstream tasks. The same aggregation methods and parameters for each node in a graph are used to enable the GNNs to utilize the homophily relational data. However, not all graphs are homophilic, even in the same graph, the distributions may vary significantly. Using the same convolution over all nodes may lead to the ignorance of various graph patterns. Furthermore, many existing GNNs integrate node features and structure identically, which ignores the distributions of nodes and further limits the expressive power of GNNs. To solve these problems, we propose Meta Weight Graph Neural Network (MWGNN) to adaptively construct graph convolution layers for different nodes. First, we model the Node Local Distribution (NLD) from node feature, topological structure and positional identity aspects with the Meta-Weight. Then, based on the Meta-Weight, we generate the adaptive graph convolutions to perform a node-specific weighted aggregation and boost the node representations. Finally, we design extensive experiments on real-world and synthetic benchmarks to evaluate the effectiveness of MWGNN. These experiments show the excellent expressive power of MWGNN in dealing with graph data with various distributions.

Deep Molecular Representation Learning via Fusing Physical and Chemical Information

Molecular representation learning is the first yet vital step in combining deep learning and molecular science. To push the boundaries of molecular representation learning, we present PhysChem, a novel neural architecture that learns molecular representations via fusing physical and chemical information of molecules. PhysChem is composed of a physicist network (PhysNet) and a chemist network (ChemNet). PhysNet is a neural physical engine that learns molecular conformations through simulating molecular dynamics with parameterized forces; ChemNet implements geometry-aware deep message-passing to learn chemical / biomedical properties of molecules. Two networks specialize in their own tasks and cooperate by providing expertise to each other. By fusing physical and chemical information, PhysChem achieved state-of-the-art performances on MoleculeNet, a standard molecular machine learning benchmark. The effectiveness of PhysChem was further corroborated on cutting-edge datasets of SARS-CoV-2.

Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring it to a most intractable challenge. Existing works typically utilize shallow graph convolution networks (GNNs) and temporal extracting modules to model spatial and temporal dependencies respectively. However, the representation ability of such models is limited due to: (1) shallow GNNs are incapable to capture long-range spatial correlations, (2) only spatial connections are considered and a mass of semantic connections are ignored, which are of great importance for a comprehensive understanding of traffic networks. To this end, we propose Spatial-Temporal Graph Ordinary Differential Equation Networks (STGODE). Specifically, we capture spatial-temporal dynamics through a tensor-based ordinary differential equation (ODE), as a result, deeper networks can be constructed and spatial-temporal features are utilized synchronously. To understand the network more comprehensively, semantical adjacency matrix is considered in our model, and a well-design temporal dialated convolution structure is used to capture long term temporal dependencies. We evaluate our model on multiple real-world traffic datasets and superior performance is achieved over state-of-the-art baselines.

HamNet: Conformation-Guided Molecular Representation with Hamiltonian Neural Networks

Well-designed molecular representations (fingerprints) are vital to combine medical chemistry and deep learning. Whereas incorporating 3D geometry of molecules (i.e. conformations) in their representations seems beneficial, current 3D algorithms are still in infancy. In this paper, we propose a novel molecular representation algorithm which preserves 3D conformations of molecules with a Molecular Hamiltonian Network (HamNet). In HamNet, implicit positions and momentums of atoms in a molecule interact in the Hamiltonian Engine following the discretized Hamiltonian equations. These implicit coordinations are supervised with real conformations with translation- & rotation-invariant losses, and further used as inputs to the Fingerprint Generator, a message-passing neural network. Experiments show that the Hamiltonian Engine can well preserve molecular conformations, and that the fingerprints generated by HamNet achieve state-of-the-art performances on MoleculeNet, a standard molecular machine learning benchmark.