LOG INPub Date : 2022-12-18DOI: 10.48550/arXiv.2212.09083
J. Gasteiger, Chen Qian, Stephan Gunnemann
{"title":"Influence-Based Mini-Batching for Graph Neural Networks","authors":"J. Gasteiger, Chen Qian, Stephan Gunnemann","doi":"10.48550/arXiv.2212.09083","DOIUrl":"https://doi.org/10.48550/arXiv.2212.09083","url":null,"abstract":"Using graph neural networks for large graphs is challenging since there is no clear way of constructing mini-batches. To solve this, previous methods have relied on sampling or graph clustering. While these approaches often lead to good training convergence, they introduce significant overhead due to expensive random data accesses and perform poorly during inference. In this work we instead focus on model behavior during inference. We theoretically model batch construction via maximizing the influence score of nodes on the outputs. This formulation leads to optimal approximation of the output when we do not have knowledge of the trained model. We call the resulting method influence-based mini-batching (IBMB). IBMB accelerates inference by up to 130x compared to previous methods that reach similar accuracy. Remarkably, with adaptive optimization and the right training schedule IBMB can also substantially accelerate training, thanks to precomputed batches and consecutive memory accesses. This results in up to 18x faster training per epoch and up to 17x faster convergence per runtime compared to previous methods.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128949866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-12-16DOI: 10.48550/arXiv.2212.08689
Tianxiang Zhao, Dongsheng Luo, Xiang Zhang, Suhang Wang
{"title":"TopoImb: Toward Topology-level Imbalance in Learning from Graphs","authors":"Tianxiang Zhao, Dongsheng Luo, Xiang Zhang, Suhang Wang","doi":"10.48550/arXiv.2212.08689","DOIUrl":"https://doi.org/10.48550/arXiv.2212.08689","url":null,"abstract":"Graph serves as a powerful tool for modeling data that has an underlying structure in non-Euclidean space, by encoding relations as edges and entities as nodes. Despite developments in learning from graph-structured data over the years, one obstacle persists: graph imbalance. Although several attempts have been made to target this problem, they are limited to considering only class-level imbalance. In this work, we argue that for graphs, the imbalance is likely to exist at the sub-class topology group level. Due to the flexibility of topology structures, graphs could be highly diverse, and learning a generalizable classification boundary would be difficult. Therefore, several majority topology groups may dominate the learning process, rendering others under-represented. To address this problem, we propose a new framework {method} and design (1 a topology extractor, which automatically identifies the topology group for each instance with explicit memory cells, (2 a training modulator, which modulates the learning process of the target GNN model to prevent the case of topology-group-wise under-representation. {method} can be used as a key component in GNN models to improve their performances under the data imbalance setting. Analyses on both topology-level imbalance and the proposed {method} are provided theoretically, and we empirically verify its effectiveness with both node-level and graph-level classification as the target tasks.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123156761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-12-16DOI: 10.48550/arXiv.2212.08541
Euan Ong, Petar Velickovic
{"title":"Learnable Commutative Monoids for Graph Neural Networks","authors":"Euan Ong, Petar Velickovic","doi":"10.48550/arXiv.2212.08541","DOIUrl":"https://doi.org/10.48550/arXiv.2212.08541","url":null,"abstract":"Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their $O(V)$ depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of $O(log V)$ depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"48 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127447161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-12-12DOI: 10.48550/arXiv.2212.05810
Sara Hahner, Felix Kerkhoff, J. Garcke
{"title":"Transfer Learning using Spectral Convolutional Autoencoders on Semi-Regular Surface Meshes","authors":"Sara Hahner, Felix Kerkhoff, J. Garcke","doi":"10.48550/arXiv.2212.05810","DOIUrl":"https://doi.org/10.48550/arXiv.2212.05810","url":null,"abstract":"The underlying dynamics and patterns of 3D surface meshes deforming over time can be discovered by unsupervised learning, especially autoencoders, which calculate low-dimensional embeddings of the surfaces. To study the deformation patterns of unseen shapes by transfer learning, we want to train an autoencoder that can analyze new surface meshes without training a new network. Here, most state-of-the-art autoencoders cannot handle meshes of different connectivity and therefore have limited to no generalization capacities to new meshes. Also, reconstruction errors strongly increase in comparison to the errors for the training shapes. To address this, we propose a novel spectral CoSMA (Convolutional Semi-Regular Mesh Autoencoder) network. This patch-based approach is combined with a surface-aware training. It reconstructs surfaces not presented during training and generalizes the deformation behavior of the surfaces' patches. The novel approach reconstructs unseen meshes from different datasets in superior quality compared to state-of-the-art autoencoders that have been trained on these shapes. Our transfer learning errors on unseen shapes are 40% lower than those from models learned directly on the data. Furthermore, baseline autoencoders detect deformation patterns of unseen mesh sequences only for the whole shape. In contrast, due to the employed regional patches and stable reconstruction quality, we can localize where on the surfaces these deformation patterns manifest.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121835439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-12-11DOI: 10.48550/arXiv.2212.05606
Zhen Tan, Song Wang, Kaize Ding, Jundong Li, Huan Liu
{"title":"Transductive Linear Probing: A Novel Framework for Few-Shot Node Classification","authors":"Zhen Tan, Song Wang, Kaize Ding, Jundong Li, Huan Liu","doi":"10.48550/arXiv.2212.05606","DOIUrl":"https://doi.org/10.48550/arXiv.2212.05606","url":null,"abstract":"Few-shot node classification is tasked to provide accurate predictions for nodes from novel classes with only few representative labeled nodes. This problem has drawn tremendous attention for its projection to prevailing real-world applications, such as product categorization for newly added commodity categories on an E-commerce platform with scarce records or diagnoses for rare diseases on a patient similarity graph. To tackle such challenging label scarcity issues in the non-Euclidean graph domain, meta-learning has become a successful and predominant paradigm. More recently, inspired by the development of graph self-supervised learning, transferring pretrained node embeddings for few-shot node classification could be a promising alternative to meta-learning but remains unexposed. In this work, we empirically demonstrate the potential of an alternative framework, textit{Transductive Linear Probing}, that transfers pretrained node embeddings, which are learned from graph contrastive learning methods. We further extend the setting of few-shot node classification from standard fully supervised to a more realistic self-supervised setting, where meta-learning methods cannot be easily deployed due to the shortage of supervision from training classes. Surprisingly, even without any ground-truth labels, transductive linear probing with self-supervised graph contrastive pretraining can outperform the state-of-the-art fully supervised meta-learning based methods under the same protocol. We hope this work can shed new light on few-shot node classification problems and foster future research on learning from scarcely labeled instances on graphs.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125068764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-12-07DOI: 10.48550/arXiv.2212.03978
Michal Pándy, Weikang Qiu, Gabriele Corso, Petar Velivckovi'c, Rex Ying, J. Leskovec, Pietro Lio'
{"title":"Learning Graph Search Heuristics","authors":"Michal Pándy, Weikang Qiu, Gabriele Corso, Petar Velivckovi'c, Rex Ying, J. Leskovec, Pietro Lio'","doi":"10.48550/arXiv.2212.03978","DOIUrl":"https://doi.org/10.48550/arXiv.2212.03978","url":null,"abstract":"Searching for a path between two nodes in a graph is one of the most well-studied and fundamental problems in computer science. In numerous domains such as robotics, AI, or biology, practitioners develop search heuristics to accelerate their pathfinding algorithms. However, it is a laborious and complex process to hand-design heuristics based on the problem and the structure of a given use case. Here we present PHIL (Path Heuristic with Imitation Learning), a novel neural architecture and a training algorithm for discovering graph search and navigation heuristics from data by leveraging recent advances in imitation learning and graph representation learning. At training time, we aggregate datasets of search trajectories and ground-truth shortest path distances, which we use to train a specialized graph neural network-based heuristic function using backpropagation through steps of the pathfinding process. Our heuristic function learns graph embeddings useful for inferring node distances, runs in constant time independent of graph sizes, and can be easily incorporated in an algorithm such as A* at test time. Experiments show that PHIL reduces the number of explored nodes compared to state-of-the-art methods on benchmark datasets by 58.5% on average, can be directly applied in diverse graphs ranging from biological networks to road networks, and allows for fast planning in time-critical robotics domains.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116291758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-11-30DOI: 10.48550/arXiv.2211.17113
P. Barceló, Mikhail Galkin, Christopher Morris, Miguel Romero Orth
{"title":"Weisfeiler and Leman Go Relational","authors":"P. Barceló, Mikhail Galkin, Christopher Morris, Miguel Romero Orth","doi":"10.48550/arXiv.2211.17113","DOIUrl":"https://doi.org/10.48550/arXiv.2211.17113","url":null,"abstract":"Knowledge graphs, modeling multi-relational data, improve numerous applications such as question answering or graph logical reasoning. Many graph neural networks for such data emerged recently, often outperforming shallow architectures. However, the design of such multi-relational graph neural networks is ad-hoc, driven mainly by intuition and empirical insights. Up to now, their expressivity, their relation to each other, and their (practical) learning performance is poorly understood. Here, we initiate the study of deriving a more principled understanding of multi-relational graph neural networks. Namely, we investigate the limitations in the expressive power of the well-known Relational GCN and Compositional GCN architectures and shed some light on their practical learning performance. By aligning both architectures with a suitable version of the Weisfeiler-Leman test, we establish under which conditions both models have the same expressive power in distinguishing non-isomorphic (multi-relational) graphs or vertices with different structural roles. Further, by leveraging recent progress in designing expressive graph neural networks, we introduce the $k$-RN architecture that provably overcomes the expressiveness limitations of the above two architectures. Empirically, we confirm our theoretical findings in a vertex classification setting over small and large multi-relational graphs.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126011128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-11-30DOI: 10.48550/arXiv.2211.16731
V. Giunchiglia, Chirag Varun Shukla, Guadalupe Gonzalez, Chirag Agarwal
{"title":"Towards Training GNNs using Explanation Directed Message Passing","authors":"V. Giunchiglia, Chirag Varun Shukla, Guadalupe Gonzalez, Chirag Agarwal","doi":"10.48550/arXiv.2211.16731","DOIUrl":"https://doi.org/10.48550/arXiv.2211.16731","url":null,"abstract":"With the increasing use of Graph Neural Networks (GNNs) in critical real-world applications, several post hoc explanation methods have been proposed to understand their predictions. However, there has been no work in generating explanations on the fly during model training and utilizing them to improve the expressive power of the underlying GNN models. In this work, we introduce a novel explanation-directed neural message passing framework for GNNs, EXPASS (EXplainable message PASSing), which aggregates only embeddings from nodes and edges identified as important by a GNN explanation method. EXPASS can be used with any existing GNN architecture and subgraph-optimizing explainer to learn accurate graph embeddings. We theoretically show that EXPASS alleviates the oversmoothing problem in GNNs by slowing the layer wise loss of Dirichlet energy and that the embedding difference between the vanilla message passing and EXPASS framework can be upper bounded by the difference of their respective model weights. Our empirical results show that graph embeddings learned using EXPASS improve the predictive performance and alleviate the oversmoothing problems of GNNs, opening up new frontiers in graph machine learning to develop explanation-based training frameworks.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124674740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-11-29DOI: 10.48550/arXiv.2211.15839
Yu He, Petar Velivckovi'c, Pietro Lio', Andreea Deac
{"title":"Continuous Neural Algorithmic Planners","authors":"Yu He, Petar Velivckovi'c, Pietro Lio', Andreea Deac","doi":"10.48550/arXiv.2211.15839","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15839","url":null,"abstract":"Neural algorithmic reasoning studies the problem of learning algorithms with neural networks, especially with graph architectures. A recent proposal, XLVIN, reaps the benefits of using a graph neural network that simulates the value iteration algorithm in deep reinforcement learning agents. It allows model-free planning without access to privileged information about the environment, which is usually unavailable. However, XLVIN only supports discrete action spaces, and is hence nontrivially applicable to most tasks of real-world interest. We expand XLVIN to continuous action spaces by discretization, and evaluate several selective expansion policies to deal with the large planning graphs. Our proposal, CNAP, demonstrates how neural algorithmic reasoning can make a measurable impact in higher-dimensional continuous control settings, such as MuJoCo, bringing gains in low-data settings and outperforming model-free baselines.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128573367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LOG INPub Date : 2022-11-29DOI: 10.48550/arXiv.2211.15899
Kaiwen Dong, Yijun Tian, Zhichun Guo, Yang Yang, N. Chawla
{"title":"FakeEdge: Alleviate Dataset Shift in Link Prediction","authors":"Kaiwen Dong, Yijun Tian, Zhichun Guo, Yang Yang, N. Chawla","doi":"10.48550/arXiv.2211.15899","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15899","url":null,"abstract":"Link prediction is a crucial problem in graph-structured data. Due to the recent success of graph neural networks (GNNs), a variety of GNN-based models were proposed to tackle the link prediction task. Specifically, GNNs leverage the message passing paradigm to obtain node representation, which relies on link connectivity. However, in a link prediction task, links in the training set are always present while ones in the testing set are not yet formed, resulting in a discrepancy of the connectivity pattern and bias of the learned representation. It leads to a problem of dataset shift which degrades the model performance. In this paper, we first identify the dataset shift problem in the link prediction task and provide theoretical analyses on how existing link prediction methods are vulnerable to it. We then propose FakeEdge, a model-agnostic technique, to address the problem by mitigating the graph topological gap between training and testing sets. Extensive experiments demonstrate the applicability and superiority of FakeEdge on multiple datasets across various domains.","PeriodicalId":379381,"journal":{"name":"LOG IN","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129022939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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