With the increasing demands of training graph neural networks (GNNs) on large-scale graphs, graph data condensation has emerged as a critical technique to relieve the storage and time costs during the training phase. It aims to condense the original large-scale graph to a much smaller synthetic graph while preserving the essential information necessary for efficiently training a downstream GNN. However, existing methods concentrate either on optimizing node features exclusively or endeavor to independently learn node features and the graph structure generator. They could not explicitly leverage the information of the original graph structure and failed to construct an interpretable graph structure for the synthetic dataset. To address these issues, we introduce a novel framework named Graph Data Condensation via Self-expressive Graph Structure Reconstruction (GCSR). Our method stands out by (1) explicitly incorporating the original graph structure into the condensing process and (2) capturing the nuanced interdependencies between the condensed nodes by reconstructing an interpretable self-expressive graph structure. Extensive experiments and comprehensive analysis validate the efficacy of the proposed method across diverse GNN models and datasets. Our code is available at https://github.com/zclzcl0223/GCSR.
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An Unsupervised Learning Framework Combined with Heuristics for the Maximum Minimal Cut Problem
PDF ↗The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting task for machine learning, especially without labeled instances. To deal with these problems, this work proposes an unsupervised learning framework combined with heuristics for MMCP that can provide valid and high-quality solutions. As far as we know, this is the first work that explores machine learning and heuristics to solve MMCP. The unsupervised solver is inspired by a relaxation-plus-rounding approach, the relaxed solution is parameterized by graph neural networks, and the cost and penalty of MMCP are explicitly written out, which can train the model end-to-end. A crucial observation is that each solution corresponds to at least one spanning tree. Based on this finding, a heuristic solver that implements tree transformations by adding vertices is utilized to repair and improve the solution quality of the unsupervised solver. Alternatively, the graph is simplified while guaranteeing solution consistency, which reduces the running time. We conduct extensive experiments to evaluate our framework and give a specific application. The results demonstrate the superiority of our method against two techniques designed.
Vehicle routing problems (VRP) are very important in many real-world applications and has been studied for several decades. Recently, neural combinatorial optimization (NCO) has attracted growing research effort. NCO is to train a neural network model to solve an optimization problem in question. However, existing NCO methods often build a different model for each routing problem, which significantly hinders their application in some areas where there are many different VRP variants to solve. In this work, we make a first attempt to tackle the crucial challenge of cross-problem generalization in NCO. We formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. In our experiments, the neural model is trained on five VRP variants and its performance is tested on eleven VRP variants. The experimental results show that the model demonstrates superior performance on these eleven VRP variants, reducing the average gap to around 5% from over 20% and achieving a notable performance boost on both benchmark datasets and real-world logistics scenarios.
CAD assembly modeling, which refers to using CAD software to design new products from a catalog of existing machine components, is important in the industrial field. The graph neural network (GNN) based recommender system for CAD assembly modeling can help designers make decisions and speed up the design process by recommending the next required component based on the existing components in CAD software. These components can be represented as a graph naturally. However, present recommender systems for CAD assembly modeling adopt fixed GNN architectures, which may be sub-optimal for different manufacturers with different data distribution. Therefore, to customize a well-suited recommender system for different manufacturers, we propose a novel neural architecture search (NAS) framework, dubbed CusGNN, which can design data-specific GNN automatically. Specifically, we design a search space from three dimensions (i.e., aggregation, fusion, and readout functions), which contains a wide variety of GNN architectures. Then, we develop an effective differentiable search algorithm to search high-performing GNN from the search space. Experimental results show that the customized GNNs achieve 1.5-5.1% higher top-10 accuracy compared to previous manual designed methods, demonstrating the superiority of the proposed approach. Code and data are available at https://github.com/BUPT-GAMMA/CusGNN.
In recent years, Graph Neural Networks (GNNs) and Large Language Models (LLMs) have exhibited remarkable capability in addressing different graph learning and natural language tasks, respectively. Motivated by this, integrating LLMs with GNNs has been increasingly studied to acquire transferable knowledge across modalities, which leads to improved empirical performance in language and graph domains. However, existing studies mainly focused on a single-domain scenario by designing complicated integration techniques to manage multimodal data effectively. Therefore, a concise and generic learning framework for multi-domain tasks, i.e., graph and language domains, is highly desired yet remains under-exploited due to two major challenges. First, the language corpus of downstream tasks differs significantly from graph data, making it hard to bridge the knowledge gap between modalities. Second, not all knowledge demonstrates immediate benefits for downstream tasks, potentially introducing disruptive noise to context-sensitive models like LLMs. To tackle these challenges, we propose a novel plug-and-play framework for incorporating a lightweight cross-domain prompting method into both language and graph learning tasks. Specifically, we first convert the textual input into a domain-scalable prompt, which not only preserves the semantic and logical contents of the textual input, but also highlights related graph information as external knowledge for different domains. Then, we develop a reinforcement learning-based method to learn the optimal edge selection strategy for useful knowledge extraction, which profoundly sharpens the multi-domain model capabilities. In addition, we introduce a joint multi-view optimization module to regularize agent-level collaborative learning across two domains. Finally, extensive empirical justifications over 23 public and synthetic datasets demonstrate that our approach can be applied to diverse multi-domain tasks more accurately, robustly, and reasonably, and improve the performances of the state-of-the-art graph and language models in different learning paradigms.
Placement is a critical and challenging step of modern chip design, with routability being an essential indicator of placement quality. Current routability-oriented placers typically apply an iterative two-stage approach, wherein the first stage generates a placement solution, and the second stage provides non-differentiable routing results to heuristically improve the solution quality. This method hinders jointly optimizing the routability aspect during placement. To address this problem, this work introduces RoutePlacer, an end-to-end routability-aware placement method. It trains RouteGNN, a customized graph neural network, to efficiently and accurately predict routability by capturing and fusing geometric and topological representations of placements. Well-trained RouteGNN then serves as a differentiable approximation of routability, enabling end-to-end gradient-based routability optimization. In addition, RouteGNN can improve two-stage placers as a plug-and-play alternative to external routers. Our experiments on DREAMPlace, an open-source AI4EDA platform, show that RoutePlacer can reduce Total Overflow by up to 16% while maintaining routed wirelength, compared to the state-of-the-art; integrating RouteGNN within two-stage placers leads to a 44% reduction in Total Overflow without compromising wirelength.
Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a differentiable loss function that could directly optimize them. The lack of solutions to bridge this challenge not only hinders our ability to solve difficult tasks, such as imbalanced learning, but also requires the deployment of computationally expensive hyperparameter search processes in model selection. In this paper, we propose a general-purpose approach that transforms any confusion matrix-based metric into a loss function, AnyLoss, that is available in optimization processes. To this end, we use an approximation function to make a confusion matrix represented in a differentiable form, and this approach enables any confusion matrix-based metric to be directly used as a loss function. The mechanism of the approximation function is provided to ensure its operability and the differentiability of our loss functions is proved by suggesting their derivatives. We conduct extensive experiments under diverse neural networks with many datasets, and we demonstrate their general availability to target any confusion matrix-based metrics. Our method, especially, shows outstanding achievements in dealing with imbalanced datasets, and its competitive learning speed, compared to multiple baseline models, underscores its efficiency.
The burgeoning volume of graph data presents significant computational challenges in training graph neural networks (GNNs), critically impeding their efficiency in various applications. To tackle this challenge, graph condensation (GC) has emerged as a promising acceleration solution, focusing on the synthesis of a compact yet representative graph for efficiently training GNNs while retaining performance. Despite the potential to promote scalable use of GNNs, existing GC methods are limited to aligning the condensed graph with merely the observed static graph distribution. This limitation significantly restricts the generalization capacity of condensed graphs, particularly in adapting to dynamic distribution changes. In real-world scenarios, however, graphs are dynamic and constantly evolving, with new nodes and edges being continually integrated. Consequently, due to the limited generalization capacity of condensed graphs, applications that employ GC for efficient GNN training end up with sub-optimal GNNs when confronted with evolving graph structures and distributions in dynamic real-world situations. To overcome this issue, we propose open-world graph condensation (OpenGC), a robust GC framework that integrates structure-aware distribution shift to simulate evolving graph patterns and exploit the temporal environments for invariance condensation. This approach is designed to extract temporal invariant patterns from the original graph, thereby enhancing the generalization capabilities of the condensed graph and, subsequently, the GNNs trained on it. Furthermore, to support the periodic re-condensation and expedite condensed graph updating in life-long graph learning, OpenGC reconstructs the sophisticated optimization scheme with kernel ridge regression and non-parametric graph convolution, significantly accelerating the condensation process while ensuring the exact solutions. Extensive experiments on both real-world and synthetic evolving graphs demonstrate that OpenGC outperforms state-of-the-art (SOTA) GC methods in adapting to dynamic changes in open-world graph environments.
Temporal graph representation learning has drawn considerable attention in recent years. Most existing works mainly focus on modeling local structural dependencies of temporal graphs. However, underestimating the inherent global structural role information in many real-world temporal graphs inevitably leads to sub-optimal graph representations. To overcome this shortcoming, we propose a novel Role-based Temporal Graph Convolution Network (RTGCN) that fully leverages the global structural role information in temporal graphs. Specifically, RTGCN can effectively capture the static global structural roles by using hypergraph convolution neural networks. To capture the evolution of nodes' structural roles, we further design structural role-based gated recurrent units. Finally, we integrate structural role proximity in our objective function to preserve global structural similarity, further promoting temporal graph representation learning. Experimental results on multiple real-world datasets demonstrate that RTGCN consistently outperforms state-of-the-art temporal graph representation learning methods by significant margins in various temporal link prediction and node classification tasks. Specifically, RTGCN achieves AUC improvement of up to 5.1% for link prediction and F1 improvement of up to 6.2% for new link prediction. In addition, RTGCN achieves AUC improvement up to 4.6% for node classification and 2.7% for structural role classification.
Graph Neural Networks (GNNs) have been increasingly deployed in a plethora of applications. However, the graph data used for training may contain sensitive personal information of the involved individuals. Once trained, GNNs typically encode such information in their learnable parameters. As a consequence, privacy leakage may happen when the trained GNNs are deployed and exposed to potential attackers. Facing such a threat, machine unlearning for GNNs has become an emerging technique that aims to remove certain personal information from a trained GNN. Among these techniques, certified unlearning stands out, as it provides a solid theoretical guarantee of the information removal effectiveness. Nevertheless, most of the existing certified unlearning methods for GNNs are only designed to handle node and edge unlearning requests. Meanwhile, these approaches are usually tailored for either a specific design of GNN or a specially designed training objective. These disadvantages significantly jeopardize their flexibility. In this paper, we propose a principled framework named IDEA to achieve flexible and certified unlearning for GNNs. Specifically, we first instantiate four types of unlearning requests on graphs, and then we propose an approximation approach to flexibly handle these unlearning requests over diverse GNNs. We further provide theoretical guarantee of the effectiveness for the proposed approach as a certification. Different from existing alternatives, IDEA is not designed for any specific GNNs or optimization objectives to perform certified unlearning, and thus can be easily generalized. Extensive experiments on real-world datasets demonstrate the superiority of IDEA in multiple key perspectives.
Deep neural network based Outlier Detection (DOD) has seen a recent surge of attention thanks to the many advances in deep learning. In this paper, we consider a critical-yet-understudied challenge with unsupervised DOD, that is, effective hyperparameter (HP) tuning/model selection. While several prior work report the sensitivity of OD models to HP settings, the issue is ever so critical for the modern DOD models that exhibit a long list of HPs. We introduce HYPER for tuning DOD models, tackling two fundamental challenges: (1) validation without supervision (due to lack of labeled outliers), and (2) efficient search of the HP/model space (due to exponential growth in the number of HPs). A key idea is to design and train a novel hypernetwork (HN) that maps HPs onto optimal weights of the main DOD model. In turn, HYPER capitalizes on a single HN that can dynamically generate weights for many DOD models (corresponding to varying HPs), which offers significant speed-up. In addition, it employs meta-learning on historical OD tasks with labels to train a proxy validation function, likewise trained with our proposed HN efficiently. Extensive experiments on different OD tasks show that HYPER achieves competitive performance against 8 baselines with significant efficiency gains.
Graph Neural Networks (GNN) have proven successful for graph-related tasks. However, many GNNs methods require labeled data, which is challenging to obtain. To tackle this, graph contrastive learning (GCL) have gained attention. GCL learns by contrasting similar nodes (positives) and dissimilar nodes (negatives). Current GCL methods, using data augmentation for positive samples and random selection for negative samples, can be sub-optimal due to limited positive samples and the possibility of false-negative samples. In this study, we propose an enhanced objective addressing these issues. We first introduce an ideal objective with all positive and no false-negative samples, then transform it probabilistically based on sampling distributions. We next model these distributions with node similarity and derive an enhanced objective. Comprehensive experiments have shown the effectiveness of the proposed enhanced objective for a broad set of GCL models.
Graph Neural Networks (GNNs) have demonstrated powerful capabilities in reasoning within Knowledge Graphs (KGs), gathering increasing attention. Our idea stems from the observation that the prior work typically employs hand-designed or sample-designed paradigms in the process of message propagation, engaging a set of adjacent entities at each step of propagation. As a result, such methods struggle with the increasing number of entities involved as propagation steps extend. Moreover, they neglect the message interactions between adjacent entities and propagation relations in KG reasoning, leading to semantic inconsistency during the message aggregation phase. To address these issues, we introduce a novel knowledge graph embedding method through a diffusion process, termed DiffusionE. Specifically, we reformulate the message propagation in knowledge reasoning as a diffusion process, regarding the message semantics as the diffusion signal. In this sense, guided by semantic information, messages can be transmitted between nodes effectively and adaptively. Furthermore, the theoretical analysis suggests our method can leverage an optimal diffusivity for message propagation in the semantic interactions of KGs. It shows that DiffusionE effectively leverages message interactions between entities and propagation relations, ensuring semantic consistency in KG reasoning. Comprehensive experiments reveal that our method attains state-of-the-art performance compared to prior work on several well-established benchmarks.
The sustainable training of modern neural network models represents an open challenge. Several existing methods approach this issue by identifying a subset of relevant data samples from the full training data to be used in model optimization with the goal of matching the performance of the full data training with that of the subset data training. Our work explores using memorization scores to find representative and atypical samples. We demonstrate that memorization-aware dataset summarization improves the subset construction performance. However, computing memorization scores is notably resource-intensive. To this end, we propose a novel method that leverages the discrepancy between sharpness-aware minimization and stochastic gradient descent to capture data points atypicality. We evaluate our metric over several efficient approximation functions for memorization scores - namely proxies -, empirically showing superior correlation and effectiveness. We explore the causes behind our approximation quality, highlighting how typical data points trigger a flatter loss landscape compared to atypical ones. Extensive experiments confirm the effectiveness of our proxy for dataset pruning and summarization tasks, surpassing state-of-the-art approaches both on canonical setups - where atypical data points benefit performance - and few-shot learning scenarios-where atypical data points can be detrimental.
Towards a Theory of Machine Learning on Graphs and its Applications in Combinatorial Optimization
PDF ↗Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across many disciplines, from life and physical to social and engineering sciences. Despite their practical success, our theoretical understanding of the properties of GNNs remains incomplete. Here, we survey the author's and his collaborators' progress in developing a deeper theoretical understanding of GNNs' expressive power and generalization abilities. In addition, we overview recent progress in using GNNs to speed up solvers for hard combinatorial optimization tasks.
Credit card fraud imposes significant costs on both cardholders and issuing banks. Fraudsters often disguise their crimes, such as using legitimate transactions through several benign users to bypass anti-fraud detection. Existing graph neural network (GNN) models struggle with learning features of camouflaged, indirect multi-hop transactions due to their inherent over-smoothing issues in deep multi-layer aggregation, presenting a major challenge in detecting disguised relationships. Therefore, in this paper, we propose a novel High-order Graph Representation Learning model (HOGRL) to avoid incorporating excessive noise during the multi-layer aggregation process. In particular, HOGRL learns different orders of \emph{pure} representations directly from high-order transaction graphs. We realize this goal by effectively constructing high-order transaction graphs first and then learning the \emph{pure} representations of each order so that the model could identify fraudsters' multi-hop indirect transactions via multi-layer \emph{pure} feature learning. In addition, we introduce a mixture-of-expert attention mechanism to automatically determine the importance of different orders for jointly optimizing fraud detection performance. We conduct extensive experiments in both the open source and real-world datasets, the result demonstrates the significant improvements of our proposed HOGRL compared with state-of-the-art fraud detection baselines. HOGRL's superior performance also proves its effectiveness in addressing high-order fraud camouflage criminals.
Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy
PDF ↗Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high efficiency and less requirement for expert knowledge. However, many neural construction methods for Vehicle Routing Problems~(VRPs) focus on synthetic problem instances with specified node distributions and limited scales, leading to poor performance on real-world problems which usually involve complex and unknown node distributions together with large scales. To make neural VRP solvers more practical, we design an auxiliary policy that learns from the local transferable topological features, named local policy, and integrate it with a typical construction policy (which learns from the global information of VRP instances) to form an ensemble policy. With joint training, the aggregated policies perform cooperatively and complementarily to boost generalization. The experimental results on two well-known benchmarks, TSPLIB and CVRPLIB, of travelling salesman problem and capacitated VRP show that the ensemble policy significantly improves both cross-distribution and cross-scale generalization performance, and even performs well on real-world problems with several thousand nodes.
Incremental scene reconstruction is essential to the navigation in robotics. Most of the conventional methods typically make use of either TSDF (truncated signed distance functions) volume or neural networks to implicitly represent the surface. Due to the voxel representation or involving with time-consuming sampling, they have difficulty in balancing speed, memory storage, and surface quality. In this paper, we propose a novel hybrid voxel-octree approach to effectively fuse octree with voxel structures so that we can take advantage of both implicit surface and explicit triangular mesh representation. Such sparse structure preserves triangular faces in the leaf nodes and produces partial meshes sequentially for incremental reconstruction. This storage scheme allows us to naturally optimize the mesh in explicit 3D space to achieve higher surface quality. We iteratively deform the mesh towards the target and recovers vertex colors by optimizing a shading model. Experimental results on several datasets show that our proposed approach is capable of quickly and accurately reconstructing a scene with realistic colors. Code is available at https://github.com/Frankuzi/HVOFusion
ConstrainedZero: Chance-Constrained POMDP Planning Using Learned Probabilistic Failure Surrogates and Adaptive Safety Constraints
PDF ↗To plan safely in uncertain environments, agents must balance utility with safety constraints. Safe planning problems can be modeled as a chance-constrained partially observable Markov decision process (CC-POMDP) and solutions often use expensive rollouts or heuristics to estimate the optimal value and action-selection policy. This work introduces the ConstrainedZero policy iteration algorithm that solves CC-POMDPs in belief space by learning neural network approximations of the optimal value and policy with an additional network head that estimates the failure probability given a belief. This failure probability guides safe action selection during online Monte Carlo tree search (MCTS). To avoid overemphasizing search based on the failure estimates, we introduce Δ-MCTS, which uses adaptive conformal inference to update the failure threshold during planning. The approach is tested on a safety-critical POMDP benchmark, an aircraft collision avoidance system, and the sustainability problem of safe CO₂ storage. Results show that by separating safety constraints from the objective we can achieve a target level of safety without optimizing the balance between rewards and costs.
We propose a new approach based on ranking to learn to guide Greedy Best-First Search (GBFS). As previous ranking approaches, ours is based on the observation that directly learning a heuristic function is overly restrictive, and that GBFS is capable of efficiently finding good plans for a much more flexible class of total quasi-orders over states. In order to learn an optimal ranking function, we introduce a new ranking framework capable of leveraging any neural network regression model and efficiently handling the training data through batching. Compared with previous ranking approaches for planning, ours does not require complex loss functions and allows training on states outside the optimal plan with minimal overhead. Our experiments on the domains of the latest planning competition learning track show that our approach substantially improves the coverage of the underlying neural network models without degrading plan quality.