Dynamic recommendation systems aim to provide personalized suggestions by modeling temporal user-item interactions across time-series behavioral data. Recent studies have leveraged pre-trained dynamic graph neural networks (GNNs) to learn user-item representations over temporal snapshot graphs. However, fine-tuning GNNs on these graphs often results in generalization issues due to temporal discrepancies between pre-training and fine-tuning stages, limiting the model’s ability to capture evolving user preferences. To address this, we propose TarDGR, a task-aware retrieval-augmented framework designed to enhance generalization capability by incorporating task-aware model and retrieval-augmentation. Specifically, TarDGR introduces a Task-Aware Evaluation Mechanism to identify semantically relevant historical subgraphs, enabling the construction of task-specific datasets without manual labeling. It also presents a Graph Transformer-based Task-Aware Model that integrates semantic and structural encodings to assess subgraph relevance. During inference, TarDGR retrieves and fuses task-aware subgraphs with the query subgraph, enriching its representation and mitigating temporal generalization issues. Experiments on multiple large-scale dynamic graph datasets demonstrate that TarDGR consistently outperforms state-of-the-art methods, with extensive empirical evidence underscoring its superior accuracy and generalization capabilities.

Large Language Models (LLMs) hold promise in automating data analysis tasks, yet open-source models face significant limitations in these kinds of reasoning-intensive scenarios. In this work, we investigate strategies to enhance the data analysis capabilities of open-source LLMs. By curating a seed dataset of diverse, realistic scenarios, we evaluate models across three dimensions: data understanding, code generation, and strategic planning. Our analysis reveals three key findings: (1) Strategic planning quality serves as the primary determinant of model performance; (2) Interaction design and task complexity significantly influence reasoning capabilities; (3) Data quality demonstrates a greater impact than diversity in achieving optimal performance. We leverage these insights to develop a data synthesis methodology, demonstrating significant improvements in open-source LLMs' analytical reasoning capabilities.

Jingsheng Zheng, Jintian Zhang, Yujie Luo, Yuren Mao, Yunjun Gao, Lun Du, Huajun Chen, Ningyu Zhang. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Homophily, the tendency of similar nodes to connect, is a fundamental phenomenon in network science and a critical factor in the performance of graph neural networks (GNNs). While existing studies primarily explore homophily in homogeneous graphs, where nodes share the same type, real-world networks are often more accurately modeled as heterogeneous graphs (HGs) with diverse node types and intricate cross-type interactions. This structural diversity complicates the analysis of homophily, as traditional homophily metrics fail to account for distinct label spaces across node types. To address this limitation, we introduce the Cross-Type Homophily Ratio (CHR), a novel metric that quantifies homophily based on the similarity of target information across different node types. Additionally, we propose Cross-Type Homophily-guided Graph Editing (CTHGE), a novel method for improving heterogeneous graph neural networks (HGNNs) performance by optimizing cross-type connectivity using Cross-Type Homophily Ratio. Extensive experiments on five HG datasets with nine HGNNs validate the effectiveness of CTHGE, which delivers a maximum relative performance improvement of over 25% for HGNNs on node classification tasks, offering a fresh perspective on cross-type homophily in HGs learning.

As global e-commerce platforms continue to expand, companies are entering new markets where they encounter cold-start challenges due to limited human labels and user behaviors. In this paper, we share our experiences in Coupang to provide a competitive cold-start performance of relevance matching for emerging e-commerce markets. Specifically, we present a Cold-Start Relevance Matching (CSRM) framework, utilizing a multilingual Large Language Model (LLM) to address three challenges: (1) activating cross-lingual transfer learning abilities of LLMs through machine translation tasks; (2) enhancing query understanding and incorporating e-commerce knowledge by retrieval-based query augmentation; (3) mitigating the impact of training label errors through a multi-round self-distillation training strategy. Our experiments demonstrate the effectiveness of CSRM-LLM and the proposed techniques, resulting in successful real-world deployment and significant online gains, with a 45.8% reduction in defect ratio and a 0.866% uplift in session purchase rate.

Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, Ningyu Zhang. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

Large Language Models (LLMs) demonstrate exceptional performance in textual understanding and tabular reasoning tasks. However, their ability to comprehend and analyze hybrid text, containing textual and tabular data, remains unexplored. The hybrid text often appears in the form of hybrid long documents (HLDs), which far exceed the token limit of LLMs. Consequently, we apply an Automated Information Extraction framework (AIE) to enable LLMs to process the HLDs and carry out experiments to analyse four important aspects of information extraction from HLDs. Given the findings: 1) The effective way to select and summarize the useful part of a HLD. 2) An easy table serialization way is enough for LLMs to understand tables. 3) The naive AIE has adaptability in many complex scenarios. 4) The useful prompt engineering to enhance LLMs on HLDs. To address the issue of dataset scarcity in HLDs and support future work, we also propose the Financial Reports Numerical Extraction (FINE) dataset. The dataset and code are publicly available in the attachments.

Code retrieval, which retrieves code snippets based on users' natural language descriptions, is widely used by devel-opers and plays a pivotal role in real-world software development. The advent of deep learning has shifted the retrieval paradigm from lexical-based matching towards leveraging deep learning models to encode source code and queries into vector represen-tations, facilitating code retrieval according to vector similarity. Despite the effectiveness of these models, managing large-scale code database presents significant challenges. Previous research proposes deep hashing-based methods, which generate hash codes for queries and code snippets and use Hamming distance for rapid recall of code candidates. However, this approach's reliance on linear scanning of the entire code base limits its scalability. To further improve the efficiency of large-scale code retrieval, we propose a novel approach SECRET (Scalable and Efficient Code Retrieval via SegmEnTed deep hashing). SECRET converts long hash codes calculated by existing deep hashing approaches into several short hash code segments through an iterative training strategy. After training, SECRET recalls code candidates by looking up the hash tables for each segment, the time complexity of recall can thus be greatly reduced. Extensive experimental results demonstrate that SECRET can drastically reduce the retrieval time by at least 95 % while achieving comparable or even higher performance of existing deep hashing approaches. Besides, SECRET also exhibits superior performance and efficiency compared to the classical hash table-based approach known as LSH under the same number of hash tables.

With the increasing use of time series data, particularly in critical applications and high-risk decision-making contexts, understanding and improving the explainability of time-series clustering(TSC) techniques is essential. While machine learning models excel in processing time series data, their explainability often needs enhancement, challenging human comprehension and trust. Time series data clustering, as an unsupervised learning method, extracts valuable patterns from complex datasets without prior knowledge, spanning various domains like biology and finance. However, the complexity of clustering models and their opaque decision-making processes raise concerns about understanding and trusting the results. Research in this area aims to enhance the explainability of TSC by developing new interpretation methods that not only ensure the accuracy of clustering results but also make them user-friendly and comprehensible to human users. This is crucial for overcoming challenges related to understanding and trusting the decision-making processes and outcomes of the model. In this study, we embarked on two significant endeavors: (a) We explored the use of explainable artificial intelligence (XAI) for TSC for the first time, conducting a comprehensive literature review. (b) We subdivided the research field through innovative classification methods, categorizing the explainability methods of TSC into three main categories: data preprocessing techniques based on time series data, single or hybrid methods based model training, and instance-based visualization algorithm applications. This analytical framework aims to elucidate how the explainability of TSC can be enhanced across these three dimensions, thereby improving its credibility. Our work not only opens new research avenues but also provides robust strategies for enhancing the explainability and credibility of TSC methods.

Tabular data analysis is crucial in various fields, and large language models show promise in this area. However, current research mostly focuses on rudimentary tasks like Text2SQL and TableQA, neglecting advanced analysis like forecasting and chart generation. To address this gap, we developed the Text2Analysis benchmark, incorporating advanced analysis tasks that go beyond the SQL-compatible operations and require more in-depth analysis. We also develop five innovative and effective annotation methods, harnessing the capabilities of large language models to enhance data quality and quantity. Additionally, we include unclear queries that resemble real-world user questions to test how well models can understand and tackle such challenges. Finally, we collect 2249 query-result pairs with 347 tables. We evaluate five state-of-the-art models using three different metrics and the results show that our benchmark presents introduces considerable challenge in the field of tabular data analysis, paving the way for more advanced research opportunities.

Recent years have witnessed the substantial progress of large-scale models across various domains, such as natural language processing and computer vision, facilitating the expression of concrete concepts. Unlike concrete concepts that are usually directly associated with physical objects, expressing abstract concepts through natural language requires considerable effort since they are characterized by intricate semantics and connotations. An alternative approach is to leverage images to convey rich visual information as a supplement. Nevertheless, existing Text-to-Image (T2I) models are primarily trained on concrete physical objects and often struggle to visualize abstract concepts. Inspired by the three-layer artwork theory that identifies critical factors, intent, object and form during artistic creation, we propose a framework of Text-to-Image generation for Abstract Concepts (TIAC). The abstract concept is clarified into a clear intent with a detailed definition to avoid ambiguity. LLMs then transform it into semantic-related physical objects, and the concept-dependent form is retrieved from an LLM-extracted form pattern set. Information from these three aspects will be integrated to generate prompts for T2I models via LLM. Evaluation results from human assessments and our newly designed metric concept score demonstrate the effectiveness of our framework in creating images that can sufficiently express abstract concepts.

Code search with natural language helps us reuse existing code snippets. Thanks to the Transformer-based pretraining models, the performance of code search has been improved significantly. However, due to the quadratic complexity of multi-head self-attention, there is a limit on the input token length. For efficient training on standard GPUs like V100, existing pretrained code models, including GraphCodeBERT, CodeBERT, RoBERTa (code), take the first 256 tokens by default, which makes them unable to represent the complete information of long code that is greater than 256 tokens. To tackle the long code problem, we propose a new baseline SEA (Split, Encode and Aggregate), which splits long code into code blocks, encodes these blocks into embeddings, and aggregates them to obtain a comprehensive long code representation. With SEA, we could directly use Transformer-based pretraining models to model long code without changing their internal structure and re-pretraining. We also compare SEA with sparse Trasnformer methods. With GraphCodeBERT as the encoder, SEA achieves an overall mean reciprocal ranking score of 0.785, which is 10.1% higher than GraphCodeBERT on the CodeSearchNet benchmark, justifying SEA as a strong baseline for long code search.

Person-job fit is an essential part of online recruitment platforms in serving various downstream applications like Job Search and Candidate Recommendation. Recently, pretrained large language models have further enhanced the effectiveness by leveraging richer textual information in user profiles and job descriptions apart from user behavior features and job metadata. However, the general domain-oriented design struggles to capture the unique structural information within user profiles and job descriptions, leading to a loss of latent semantic correlations. We propose TAROT, a hierarchical multitask co-pretraining framework, to better utilize structural and semantic information for informative text embeddings. TAROT targets semi-structured text in profiles and jobs, and it is co-pretained with multi-grained pretraining tasks to constrain the acquired semantic information at each level. Experiments on a real-world LinkedIn dataset show significant performance improvements, proving its effectiveness in person-job fit tasks.

Online recruitment platforms typically employ Person-Job Fit models in the core service that automatically match suitable job seekers with appropriate job positions. While existing works leverage historical or contextual information, they often disregard a crucial aspect: job seekers' social relationships in professional networks. This paper emphasizes the importance of incorporating professional networks into the Person-Job Fit model. Our innovative approach consists of two stages: (1) defining a Workplace Heterogeneous Information Network (WHIN) to capture heterogeneous knowledge, including professional connections and pre-training representations of various entities using a heterogeneous graph neural network; (2) designing a Contextual Social Attention Graph Neural Network (CSAGNN) that supplements users' missing information with professional connections' contextual information. We introduce a job-specific attention mechanism in CSAGNN to handle noisy professional networks, leveraging pre-trained entity representations from WHIN. We demonstrate the effectiveness of our approach through experimental evaluations conducted across three real-world recruitment datasets from LinkedIn, showing superior performance compared to baseline models.

Graph Neural Networks (GNNs) have achieved great success on a variety of tasks with graph-structural data, among which node classification is an essential one. Unsupervised Graph Domain Adaptation (UGDA) shows its practical value of reducing the labeling cost for node classification. It leverages knowledge from a labeled graph (i.e., source domain) to tackle the same task on another unlabeled graph (i.e., target domain). Most existing UGDA methods heavily rely on the labeled graph in the source domain. They utilize labels from the source domain as the supervision signal and are jointly trained on both the source graph and the target graph. However, in some real-world scenarios, the source graph is inaccessible because of privacy issues. Therefore, we propose a novel scenario named Source Free Unsupervised Graph Domain Adaptation (SFUGDA). In this scenario, the only information we can leverage from the source domain is the well-trained source model, without any exposure to the source graph and its labels. As a result, existing UGDA methods are not feasible anymore. To address the non-trivial adaptation challenges in this practical scenario, we propose a model-agnostic algorithm called SOGA for domain adaptation to fully exploit the discriminative ability of the source model while preserving the consistency of structural proximity on the target graph. We prove the effectiveness of the proposed algorithm both theoretically and empirically. The experimental results on four cross-domain tasks show consistent improvements in the Macro-F1 score and Macro-AUC.

Graph Neural Networks (GNNs) have shown superior performance in modeling graph data. Existing studies have shown that a lot of GNNs perform well on homophilic graphs while performing poorly on heterophilic graphs. Recently, researchers have turned their attention to design GNNs for heterophilic graphs by specific model design. Different from existing methods that mitigate heterophily by model design, we propose to study heterophilic graphs from an orthogonal perspective by rewiring the graph to reduce heterophily and make GNNs perform better. Through comprehensive empirical analysis, we verify the potential of graph rewiring methods. Then we propose a method namedDeepHeterophilyGraphRewiring (DHGR) to rewire graphs by adding homophilic edges and pruning heterophilic edges. The rewiring operation is implemented by comparing the similarity of neighborhood label/feature distribution of node pairs. Besides, we design a scalable implementation for DHGR to guarantee a high efficiency. DHRG can be easily used as a plug-in module, i.e., a graph pre-processing step, for any GNNs, including both GNNs for homophily and heterophily, to boost their performance on the node classification task. To the best of our knowledge, it is the first work studying graph rewiring for heterophilic graphs. Extensive experiments on 11 public graph datasets demonstrate the superiority of our proposed methods.

Spreadsheets are an important and unique type of business document for data storage, analysis and presentation. The distinction between spreadsheets and most other types of digital documents lies in that spreadsheets provide users with high flexibility of data organization on the grid. Existing related techniques mainly focus on the tabular data and are incompetent in understanding the entire sheet. On the one hand, spreadsheets have no explicit separation across tabular data and other information, leaving a gap for the deployment of such techniques. On the other hand, pervasive data dependence and semantic relations across the sheet require comprehensive modeling of all the information rather than only the tables. In this paper, we propose SheetPT, the first pre-training technique on spreadsheets to enable effective representation learning under this scenario. For computational effectiveness and efficiency, we propose the coherent chunk, an intermediate semantic unit of sheet structure; and we accordingly devise a hierarchical attention-based architecture to capture contextual information across different structural granularities. Three pre-training objectives are also designed to ensure sufficient training against millions of spreadsheets. Two representative downstream tasks, formula prediction and sheet structure recognition are utilized to evaluate its capability and the prominent results reveal its superiority over existing state-of-the-art methods.

The recent prevalence of pretrained language models (PLMs) has dramatically shifted the paradigm of semantic parsing, where the mapping from natural language utterances to structured logical forms is now formulated as a Seq2Seq task. Despite the promising performance, previous PLM-based approaches often suffer from hallucination problems due to their negligence of the structural information contained in the sentence, which essentially constitutes the key semantics of the logical forms. Furthermore, most works treat PLM as a black box in which the generation process of the target logical form is hidden beneath the decoder modules, which greatly hinders the model's intrinsic interpretability. To address these two issues, we propose to incorporate the current PLMs with a hierarchical decoder network. By taking the first-principle structures as the semantic anchors, we propose two novel intermediate supervision tasks, namely Semantic Anchor Extraction and Semantic Anchor Alignment, for training the hierarchical decoders and probing the model intermediate representations in a self-adaptive manner alongside the fine-tuning process. We conduct intensive experiments on several semantic parsing benchmarks and demonstrate that our approach can consistently outperform the baselines. More importantly, by analyzing the intermediate representations of the hierarchical decoders, our approach also makes a huge step toward the interpretability of PLMs in the domain of semantic parsing.

Recent years, Pre-trained Language models (PLMs) have swept into various fields of artificial intelligence and achieved great success. However, most PLMs, such as T5 and GPT3, have a huge amount of parameters, fine-tuning them is often expensive and time consuming, and storing them takes up a lot of space. Therefore, it is necessary to adopt a parameter-efficient approach to reduce parameters of PLMs in fine-tuning without compromising their performance in downstream tasks. In this paper, we design a novel adapter which only acts on self-attention outputs in PLMs. This adapter adopts element-wise linear transformation using Hadamard product, hence named as Hadamard adapter, requires the fewest parameters compared to previous parameter-efficient adapters. In addition, we also summarize some tuning patterns for Hadamard adapter shared by various downstream tasks, expecting to provide some guidance for further parameter reduction with shared adapters in future studies. The experiments conducted on the widely-used GLUE benchmark with several SOTA PLMs prove that the Hadamard adapter achieves competitive performance with only 0.033% parameters compared with full fine-tuning, and it has the fewest parameters compared with other adapters. Moreover, we further find that there is also some redundant layers in the Hadamard adapter which can be removed to achieve more parameter efficiency with only 0.022% parameters.

Code search aims to retrieve semantically relevant code snippets for a given natural language query. Recently, many approaches employing contrastive learning have shown promising results on code representation learning and greatly improved the performance of code search. However, there is still a lot of room for improvement in using contrastive learning for code search. In this paper, we propose CoCoSoDa to effectively utilize contrastive learning for code search via two key factors in contrastive learning: data augmentation and negative samples. Specifically, soft data augmentation is to dynamically masking or replacing some tokens with their types for input sequences to generate positive samples. Momentum mechanism is used to generate large and consistent representations of negative samples in a mini-batch through maintaining a queue and a momentum encoder. In addition, multimodal contrastive learning is used to pull together representations of code-query pairs and push apart the unpaired code snippets and queries. We conduct extensive experiments to evaluate the effectiveness of our approach on a large-scale dataset with six programming languages. Experimental results show that: (1) CoCoSoDa outperforms 18 baselines and especially exceeds CodeBERT, GraphCodeBERT, and UniXcoder by 13.3%, 10.5%, and 5.9% on average MRR scores, respectively. (2) The ablation studies show the effectiveness of each component of our approach. (3) We adapt our techniques to several different pre-trained models such as RoBERTa, CodeBERT, and GraphCodeBERT and observe a significant boost in their performance in code search. (4) Our model performs robustly under different hyper-parameters. Furthermore, we perform qualitative and quantitative analyses to explore reasons behind the good performance of our model.

Recent years have witnessed the great potential of attention mechanism in graph representation learning. However, while variants of attention-based GNNs are setting new benchmarks for numerous real-world datasets, recent works have pointed out that their induced attentions are less robust and generalizable against noisy graphs due to lack of direct supervision. In this paper, we present a new framework which utilizes the tool of causality to provide a powerful supervision signal for the learning process of attention functions. Specifically, we estimate the direct causal effect of attention to the final prediction, and then maximize such effect to guide attention attending to more meaningful neighbors. Our method can serve as a plug-and-play module for any canonical attention-based GNNs in an end-to-end fashion. Extensive experiments on a wide range of benchmark datasets illustrated that, by directly supervising attention functions, the model is able to converge faster with a clearer decision boundary, and thus yields better performances.

Recently, fine-tuning pre-trained code models such as CodeBERT on downstream tasks has achieved great success in many software testing and analysis tasks. While effective and prevalent, fine-tuning the pre-trained parameters incurs a large computational cost. In this paper, we conduct an extensive experimental study to explore what happens to layer-wise pre-trained representations and their encoded code knowledge during fine-tuning. We then propose efficient alternatives to fine-tune the large pre-trained code model based on the above findings. Our experimental study shows that (1) lexical, syntactic and structural properties of source code are encoded in the lower, intermediate, and higher layers, respectively, while the semantic property spans across the entire model. (2) The process of fine-tuning preserves most of the code properties. Specifically, the basic code properties captured by lower and intermediate layers are still preserved during fine-tuning. Furthermore, we find that only the representations of the top two layers change most during fine-tuning for various downstream tasks. (3) Based on the above findings, we propose Telly to efficiently fine-tune pre-trained code models via layer freezing. The extensive experimental results on five various downstream tasks demonstrate that training parameters and the corresponding time cost are greatly reduced, while performances are similar or better.

Temporal data representing chronological observations of complex systems can be ubiquitously collected in smart industry, medicine, finance and etc. In the last decade, many tasks have been studied for mining temporal data and offered significant value for various applications. Among these tasks, causal discovery aims to understand the underlying generation mechanism of temporal data and has attracted much research attention. According to whether the data is calibrated, existing causal discovery approaches can be divided into two subtasks, i.e., multivariate time-series causal discovery, and event sequence causal discovery. Previous tutorials or surveys have primarily focused on causal discovery from time-series data and disregarded the second ones. In this tutorial, we elucidate the correlation between the two subtasks and provide a comprehensive review of the existing solutions. Moreover, we offer some potential applications and summarize new perspectives for discovering causal relations from temporal data. We hope the audiences can obtain a systematic overview of this topic and inspire some new ideas for their own research.

Collaborative filtering (CF) is an important research direction in recommender systems that aims to make recommendations given the information on user-item interactions. Graph CF has attracted more and more attention in recent years due to its effectiveness in leveraging high-order information in the user-item bipartite graph for better recommendations. Specifically, recent studies show the success of graph neural networks (GNN) for CF is attributed to its low-pass filtering effects. However, current researches lack a study of how different signal components contributes to recommendations, and how to design strategies to properly use them well. To this end, from the view of spectral transformation, we analyze the important factors that a graph filter should consider to achieve better performance. Based on the discoveries, we design JGCF, an efficient and effective method for CF based on Jacobi polynomial bases and frequency decomposition strategies. Extensive experiments on four widely used public datasets show the effectiveness and efficiency of the proposed methods, which brings at most 27.06% performance gain on Alibaba-iFashion. Besides, the experimental results also show that JGCF is better at handling sparse datasets, which shows potential in making recommendations for cold-start users.

Tables are widely used for data storage and presentation due to their high flexibility in layout. The importance of tables as information carriers and the complexity of tabular data understanding attract a great deal of research on large-scale pre-training for tabular data. However, most of the works design models for specific types of tables, such as relational tables and tables with well-structured headers, neglecting tables with complex layouts. In real-world scenarios, there are many such tables beyond their target scope that cannot be well supported. In this paper, we propose GetPt, a unified pre-training architecture for general table representation applicable even to tables with complex structures and layouts. First, we convert a table to a heterogeneous graph with multiple types of edges to represent the layout of the table. Based on the graph, a specially designed transformer is applied to jointly model the semantics and structure of the table. Second, we devise the Alternate Attention Network (AAN) to better model the contextual information across multiple granularities of a table including tokens, cells, and the table. To better support a wide range of downstream tasks, we further employ three pre-training objectives and pre-train the model on a large table dataset. We fine-tune and evaluate GetPt model on two representative tasks, table type classification, and table structure recognition. Experiments show that GetPt outperforms existing state-of-the-art methods on these tasks.

Graph Neural Networks (GNNs) have shown expressive performance on graph representation learning by aggregating information from neighbors. Recently, some studies have discussed the importance of modeling neighborhood distribution on the graph. However, most existing GNNs aggregate neighbors' features through single statistic (e.g., mean, max, sum), which loses the information related to neighbor's feature distribution and therefore degrades the model performance. In this paper, inspired by the method of moment in statistical theory, we propose to model neighbor's feature distribution with multi-order moments. We design a novel GNN model, namely Mix-Moment Graph Neural Network (MM-GNN), which includes a Multi-order Moment Embedding (MME) module and an Element-wise Attention-based Moment Adaptor module. MM-GNN first calculates the multi-order moments of the neighbors for each node as signatures, and then use an Element-wise Attention-based Moment Adaptor to assign larger weights to important moments for each node and update node representations. We conduct extensive experiments on 15 real-world graphs (including social networks, citation networks and web-page networks etc.) to evaluate our model, and the results demonstrate the superiority of MM-GNN over existing state-of-the-art models.

With a good code search engine, developers can reuse existing code snippets and accelerate software development process. Current code search methods can be divided into two categories: traditional information retrieval (IR) based and deep learning (DL) based approaches. DL-based approaches include the cross-encoder paradigm and the bi-encoder paradigm. However, both approaches have certain limitations. The inference of IR-based and bi-encoder models are fast; however, they are not accurate enough; while cross-encoder models can achieve higher search accuracy but consume more time. In this work, we propose TOSS, a two-stage fusion code search framework that can combine the advantages of different code search methods. TOSS first uses IR-based and bi-encoder models to efficiently recall a small number of top-K code candidates, and then uses fine-grained cross-encoders for finer ranking. Furthermore, we conduct extensive experiments on different code candidate volumes and multiple programming languages to verify the effectiveness of TOSS. We also compare TOSS with six data fusion methods. Experimental results show that TOSS is not only efficient, but also achieves state-of-the-art accuracy with an overall mean reciprocal ranking (MRR) score of 0.763, compared to the best baseline result on the CodeSearchNet benchmark of 0.713.

User engagement prediction plays a critical role in designing interaction strategies to grow user engagement and increase revenue in online social platforms. Through the in-depth analysis of the real-world data from the world's largest professional social platforms, i.e., LinkedIn, we find that users expose diverse engagement patterns, and a major reason for the differences in user engagement patterns is that users have different intents. That is, people have different intents when using LinkedIn, e.g., applying for jobs, building connections, or checking notifications, which shows quite different engagement patterns. Meanwhile, user intents and the corresponding engagement patterns may change over time. Although such pattern differences and dynamics are essential for user engagement prediction, differentiating user engagement patterns based on user dynamic intents for better user engagement forecasting has not received enough attention in previous works. In this paper, we proposed a Dynamic Intent Guided Meta Network (DIGMN), which can explicitly model user intent varying with time and perform differentiated user engagement forecasting. Specifically, we derive some interpretable basic user intents as prior knowledge from data mining and introduce prior intents to explicitly model dynamic user intent. Furthermore, based on the dynamic user intent representations, we propose a meta-predictor to perform differentiated user engagement forecasting. Through a comprehensive evaluation of LinkedIn anonymous user data, our method outperforms state-of-the-art baselines significantly, i.e., 2.96% and 3.48% absolute error reduction, on coarse-grained and fine-grained user engagement prediction tasks, respectively, demonstrating the effectiveness of our method.

With the rapid development of the World Wide Web (WWW), heterogeneous graphs (HG) have explosive growth. Recently, heterogeneous graph neural network (HGNN) has shown great potential in learning on HG. Current studies of HGNN mainly focus on some HGs with strong homophily properties (nodes connected by meta-path tend to have the same labels), while few discussions are made in those that are less homophilous. Recently, there have been many works on homogeneous graphs with heterophily. However, due to heterogeneity, it is non-trivial to extend their approach to deal with HGs with heterophily. In this work, based on empirical observations, we propose a meta-path-induced metric to measure the homophily degree of a HG. We also find that current HGNNs may have degenerated performance when handling HGs with less homophilous properties. Thus it is essential to increase the generalization ability of HGNNs on non-homophilous HGs. To this end, we propose HDHGR, a homophily-oriented deep heterogeneous graph rewiring approach that modifies the HG structure to increase the performance of HGNN. We theoretically verify HDHGR. In addition, experiments on real-world HGs demonstrate the effectiveness of HDHGR, which brings at most more than 10% relative gain.

Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.

Wenchao Gu, Yanlin Wang, Lun Du, Hongyu Zhang, Shi Han, Dongmei Zhang, Michael Lyu. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

Learning rate is one of the most important hyper-parameters that has significant influence for neural network training. Learning rate schedules are widely used in real practice to adjust the learning rate according to pre-defined schedules for the fast convergence and good generalization. However, existing learning rate schedules are all heuristic algorithms and lack theoretical support. Therefore, people usually choose the learning rate schedules through multiple ad-hoc trial, and the obtained learning rate schedules are sub-optimal. To boost the performance of the obtained sub-optimal learning rate schedule, we propose a generic learning rate schedule plugin, called LEArning Rate Perturbation (LEAP), which can be applied to various learning rate schedules to improve the model training by introducing a certain perturbation to the learning rate. We found that, with such simple yet effective strategy, training processing exponentially favors flat minima rather than sharp minima with guaranteed convergence, which leads to better generalization ability. In addition, we conduct extensive experiments which show that training with LEAP can improve the performance of various deep learning models on diverse datasets using various learning rate schedules (including constant learning rate).

Commit messages are important for software development and maintenance.Many neural network-based approaches have been proposed and shown promising results on automatic commit message generation.However, the generated commit messages could be repetitive or redundant.In this paper, we propose RACE, a new retrieval-augmented neural commit message generation method, which treats the retrieved similar commit as an exemplar and leverages it to generate an accurate commit message.As the retrieved commit message may not always accurately describe the content/intent of the current code diff, we also propose an exemplar guider, which learns the semantic similarity between the retrieved and current code diff and then guides the generation of commit message based on the similarity.We conduct extensive experiments on a large public dataset with five programming languages.Experimental results show that RACE can outperform all baselines.Furthermore, RACE can boost the performance of existing Seq2Seq models in commit message generation.

Source code summaries are important for program comprehension and maintenance. However, there are plenty of programs with missing, outdated, or mismatched summaries. Recently, deep learning techniques have been exploited to automatically generate summaries for given code snippets. To achieve a profound understanding of how far we are from solving this problem and provide suggestions to future research, in this paper, we conduct a systematic and in-depth analysis of 5 state-of-the-art neural code summarization models on 6 widely used BLEU variants, 4 pre-processing operations and their combinations, and 3 widely used datasets. The evaluation results show that some important factors have a great influence on the model evaluation, especially on the performance of models and the ranking among the models. However, these factors might be easily overlooked. Specifically, (1) the BLEU metric widely used in existing work of evaluating code summarization models has many variants. Ignoring the differences among these variants could greatly affect the validity of the claimed results. Besides, we discover and resolve an important and previously unknown bug in BLEU calculation in a commonly-used software package. Furthermore, we conduct human evaluations and find that the metric BLEU-DC is most correlated to human perception; (2) code preprocessing choices can have a large (from -18% to +25%) impact on the summarization performance and should not be neglected. We also explore the aggregation of pre-processing combinations and boost the performance of models; (3) some important characteristics of datasets (corpus sizes, data splitting methods, and duplication ratios) have a significant impact on model evaluation. Based on the experimental results, we give actionable suggestions for evaluating code summarization and choosing the best method in different scenarios. We also build a shared code summarization toolbox to facilitate future research.

Computing trajectory similarities is a critical and fundamental task for various spatial-temporal applications, such as clustering, prediction, and anomaly detection. Traditional similarity metrics, i.e. DTW and Hausdorff, suffer from quadratic computation complexity, leading to their inability on large-scale data. To solve this problem, many trajectory representation learning techniques are proposed to approximate the metric space while reducing the complexity of similarity computation. Nevertheless, these works are designed based on RNN backend, resulting in a serious performance decline on long trajectories. In this paper, we propose a novel graph-based method, namely TrajGAT, to explicitly model the hierarchical spatial structure and improve the performance of long trajectory similarity computation. TrajGAT consists of two main modules, i.e. , graph construction and trajectory encoding. For graph construction, TrajGAT first employs PR quadtree to build the hierarchical structure of the whole spatial area, and then constructs a graph for each trajectory based on the original records and the leaf nodes of the quadtree. For trajectory encoding, we replace the self-attention in Transformer with graph attention and design an encoder to represent the generated graph trajectory. With these two modules, TrajGAT can capture the long-term dependencies of trajectories while reducing the GPU memory usage of Transformer. Our experiments on two real-life datasets show that TrajGAT not only improves the performance on long trajectories but also outperforms the state-of-the-art methods on mixture trajectories significantly.

Regularization can mitigate the generalization gap between training and inference by introducing inductive bias. Existing works have already proposed various inductive biases from diverse perspectives. However, none of them explores inductive bias from the perspective of class-dependent response distribution of individual neurons. In this paper, we conduct a substantial analysis of the characteristics of such distribution. Based on the analysis results, we articulate the Neuron Steadiness Hypothesis: the neuron with similar responses to instances of the same class leads to better generalization. Accordingly, we propose a new regularization method called Neuron Steadiness Regularization (NSR) to reduce neuron intra-class response variance. Based on the Complexity Measure, we theoretically guarantee the effectiveness of NSR for improving generalization. We conduct extensive experiments on Multilayer Perceptron, Convolutional Neural Networks, and Graph Neural Networks with popular benchmark datasets of diverse domains, which show that our Neuron Steadiness Regularization consistently outperforms the vanilla version of models with significant gain and low additional computational overhead.

Network Embedding aims to learn a function mapping the nodes to Euclidean space contribute to multiple learning analysis tasks on networks. However, both the noisy information behind the real-world networks and the overfitting problem negatively impact the quality of embedding vectors. To tackle these problems, researchers utilize Adversarial Perturbations on Parameters (APP) and achieve state-of-the-art performance. Unlike the mainstream methods introducing perturbations on the network structure or the data feature, Adversarial Training for Network Embedding (AdvTNE) adopts APP to directly perturb the model parameters, thus providing a new chance to understand the mechanism behind it. In this paper, we explain APP theoretically from an optimization perspective. Considering the Power-law property of networks and the optimization objective, we analyze the reason for its remarkable results on network embedding. Based on the above analysis and the Sigmoid saturation region problem, we propose a new Sine-base activation to enhance the performance of AdvTNE. We conduct extensive experiments on four real networks to validate the effectiveness of our method in node classification and link prediction. The results demonstrate that our method is competitive with state-of-the-art methods.

Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar), while their ability to capture heterophily property is often doubtful. This is partially caused by the design of the feature transformation with the same kernel for the nodes in the same hop and the followed aggregation operator. One kernel cannot model the similarity and the dissimilarity (i.e., the positive and negative correlation) between node features simultaneously even though we use attention mechanisms like Graph Attention Network (GAT), since the weight calculated by attention is always a positive value. In this paper, we propose a novel GNN model based on a bi-kernel feature transformation and a selection gate. Two kernels capture homophily and heterophily information respectively, and the gate is introduced to select which kernel we should use for the given node pairs. We conduct extensive experiments on various datasets with different homophily-heterophily properties. The experimental results show consistent and significant improvements against state-of-the-art GNN methods.

Recently, deep learning methods have become mainstream in code search since they do better at capturing semantic correlations between code snippets and search queries and have promising performance. However, code snippets have diverse information from different dimensions, such as business logic, specific algorithm, and hardware communication, so it is hard for a single code representation module to cover all the perspectives. On the other hand, as a specific query may focus on one or several perspectives, it is difficult for a single query representation module to represent different user intents. In this paper, we propose MuCoS, a multi-model ensemble learning architecture for semantic code search. It combines several individual learners, each of which emphasizes a specific perspective of code snippets. We train the individual learners on different datasets which contain different perspectives of code information, and we use a data augmentation strategy to get these different datasets. Then we ensemble the learners to capture comprehensive features of code snippets. The experiments show that MuCoS has better results than the existing state-of-the-art methods. Our source code and data are anonymously available at https://github.com/Xzh0u/MuCoS.

Graph Convolutional Networks (GCNs) have become the prevailing approach to efficiently learn representations from graph-structured data. Current GCN models adopt a neighborhood aggregation mechanism based on two primary operations, aggregation and combination. The workload of these two processes is determined by the input graph structure, making the graph input the bottleneck of processing GCN. Meanwhile, a large amount of task-irrelevant information in the graphs would hurt the model generalization performance. This brings the opportunity of studying how to remove the redundancy in the graphs. In this paper, we aim to accelerate GCN models by removing the task-irrelevant edges in the graph. We present AdaptiveGCN, an efficient and supervised graph sparsification framework. AdaptiveGCN adopts an edge predictor module to get edge selection strategies by learning the downstream task feedback signals for each GCN layer separately and adaptively in the training stage, then only inference with the selected edges in the test stage to speed up the GCN computation. The experimental results indicate that AdaptiveGCN could yield 43% (on CPU) and 39% (on GPU) GCN model speed-up averagely with comparable model performance on public graph learning benchmarks.

Initialization plays a critical role in the training of deep neural networks (DNN). Existing initialization strategies mainly focus on stabilizing the training process to mitigate gradient vanish/explosion problems. However, these initialization methods are lacking in consideration about how to enhance generalization ability. The Information Bottleneck (IB) theory is a well-known understanding framework to provide an explanation about the generalization of DNN. Guided by the insights provided by IB theory, we design two criteria for better initializing DNN. And we further design a neuron campaign initialization algorithm to efficiently select a good initialization for a neural network on a given dataset. The experiments on MNIST dataset show that our method can lead to a better generalization performance with faster convergence.

Code summarization aims to generate concise natural language descriptions of source code, which can help improve program comprehension and maintenance.Recent studies show that syntactic and structural information extracted from abstract syntax trees (ASTs) is conducive to summary generation.However, existing approaches fail to fully capture the rich information in ASTs because of the large size/depth of ASTs.In this paper, we propose a novel model CAST that hierarchically splits and reconstructs ASTs.First, we hierarchically split a large AST into a set of subtrees and utilize a recursive neural network to encode the subtrees.Then, we aggregate the embeddings of subtrees by reconstructing the split ASTs to get the representation of the complete AST.Finally, AST representation, together with source code embedding obtained by a vanilla code token encoder, is used for code summarization.Extensive experiments, including the ablation study and the human evaluation, on benchmarks have demonstrated the power of CAST.To facilitate reproducibility, our code and data are available at https://github.com/ DeepSoftwareAnalytics/CAST.

Hierarchy preserving network embedding is a method that project nodes into feature space by preserving the hierarchy property of networks. Recently, researches on network representation have considerably profited from taking hierarchy into consideration. Among these works, SpaceNE1[1] stands out by preserving hierarchy with the help of subspace constraints on the hierarchy subspace system. However, like all other hierarchy preserving network embedding methods, SpaceNE is time-consuming and cannot generalize to new nodes. In this paper, we propose an inductive method, FastHGE, to learn node representations more efficiently and generalize to new nodes more easily. Empirically, the experiment of node classification demonstrates that the convergence speed of FastHGE is increased by 30 times in the case of the same accuracy with SpaceNE.

Commit messages are natural language descriptions of code changes, which are important for program understanding and maintenance. However, writing commit messages manually is time-consuming and laborious, especially when the code is updated frequently. Various approaches utilizing generation or retrieval techniques have been proposed to automatically generate commit messages. To achieve a better understanding of how the existing approaches perform in solving this problem, this paper conducts a systematic and in-depth analysis of the state-of-the-art models and datasets. We find that: (1) Different variants of the BLEU metric are used in previous works, which affects the evaluation and understanding of existing methods. (2) Most existing datasets are crawled only from Java repositories while repositories in other programming languages are not sufficiently explored. (3) Dataset splitting strategies can influence the performance of existing models by a large margin. Some models show better performance when the datasets are split by commit, while other models perform better when the datasets are split by timestamp or by project. Based on our findings, we conduct a human evaluation and find the BLEU metric that best correlates with the human scores for the task. We also collect a large-scale, information-rich, and multi-language commit message dataset MCMD and evaluate existing models on this dataset. Furthermore, we conduct extensive experiments under different dataset splitting strategies and suggest the suitable models under different scenarios. Based on the experimental results and findings, we provide feasible suggestions for comprehensively evaluating commit message generation models and discuss possible future research directions. We believe this work can help practitioners and researchers better evaluate and select models for automatic commit message generation. Our source code and data are available at https://github.com/DeepSoftwareAnalytics/CommitMsgEmpirical.

Tabular data are ubiquitous for the widespread applications of tables and hence have attracted the attention of researchers to extract underlying information. One of the critical problems in mining tabular data is how to understand their inherent semantic structures automatically. Existing studies typically adopt Convolutional Neural Network (CNN) to model the spatial information of tabular structures yet ignore more diverse relational information between cells, such as the hierarchical and paratactic relationships. To simultaneously extract spatial and relational information from tables, we propose a novel neural network architecture, TabularNet. The spatial encoder of TabularNet utilizes the row/column-level Pooling and the Bidirectional Gated Recurrent Unit (Bi-GRU) to capture statistical information and local positional correlation, respectively. For relational information, we design a new graph construction method based on the WordNet tree and adopt a Graph Convolutional Network (GCN) based encoder that focuses on the hierarchical and paratactic relationships between cells. Our neural network architecture can be a unified neural backbone for different understanding tasks and utilized in a multitask scenario. We conduct extensive experiments on three classification tasks with two real-world spreadsheet data sets, and the results demonstrate the effectiveness of our proposed TabularNet over state-of-the-art baselines.

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

Traffic flow forecasting is of great significance for improving the efficiency of transportation systems and preventing emergencies. Due to the highly non-linearity and intricate evolutionary patterns of short-term and long-term traffic flow, existing methods often fail to take full advantage of spatial-temporal information, especially the various temporal patterns with different period shifting and the characteristics of road segments. Besides, the globality representing the absolute value of traffic status indicators and the locality representing the relative value have not been considered simultaneously. This paper proposes a neural network model that focuses on the globality and locality of traffic networks as well as the temporal patterns of traffic data. The cycle-based dilated deformable convolution block is designed to capture different time-varying trends on each node accurately. Our model can extract both global and local spatial information since we combine two graph convolutional network methods to learn the representations of nodes and edges. Experiments on two real-world datasets show that the model can scrutinize the spatial-temporal correlation of traffic data, and its performance is better than the compared state-of-the-art methods. Further analysis indicates that the locality and globality of the traffic networks are critical to traffic flow prediction and the proposed TSSRGCN model can adapt to the various temporal traffic patterns.

Heterogeneous Information Networks (HINs) are ubiquitous structures in that they can depict complex relational data. Due to their complexity, it is hard to obtain sufficient labeled data on HINs, hampering classification on HINs. While domain adaptation (DA) techniques have been widely utilized in images and texts, the heterogeneity and complex semantics pose specific challenges towards domain adaptive classification on HINs. On one hand, HINs involve multiple levels of semantics, making it demanding to do domain alignment among them. On the other hand, the trade-off between domain similarity and distinguishability must be elaborately chosen, in that domain invariant features have been shown to be homogeneous and uninformative for classification. In this paper, we propose Multi-space Domain Adaptive Classification (MuSDAC) to handle the problem of DA on HINs. Specifically, we utilize multi-channel shared weight GCNs, projecting nodes in HINs to multiple spaces where pairwise alignment is carried out. In addition, we propose a heuristic sampling algorithm that efficiently chooses the combination of channels featuring distinguishability, and moving-averaged weighted voting scheme to fuse the selected channels, minimizing both transfer and classification loss. Extensive experiments on pairwise datasets endorse not only our model's performance on domain adaptive classification on HINs and contributions by individual components.

To depict ubiquitous relational data in real world, network data have been widely applied in modeling complex relationships. Projecting vertices to low dimensional spaces, quoted as Network Embedding, would thus be applicable to diverse real-world predicative tasks. Numerous works exploiting pairwise proximities, one characteristic owned by real networks, the clustering property, namely vertices are inclined to form communities of various ranges and hence form a hierarchy consisting of communities, has barely received attention from researchers. In this paper, we propose our network embedding framework, abbreviated SpaceNE, preserving hierarchies formed by communities through subspaces, manifolds with flexible dimensionalities and are inherently hierarchical. Moreover, we propose that subspaces are able to address further problems in representing hierarchical communities, including sparsity and space warps. Last but not least, we proposed constraints on dimensions of subspaces to denoise, which are further approximated by differentiable functions such that joint optimization is enabled, along with a layer-wise scheme to alleviate the overhead cause by the vast number of parameters. We conduct various experiments with results demonstrating our model's effectiveness in addressing community hierarchies.

Keyword-based tags (referred to as tags) are used to represent additional attributes of nodes in addition to what is explicitly stated in their contents, like the hashtags in YouTube. Aside of being auxiliary information for node representation, tags can also be used for retrieval, recommendation, content organization, and event analysis. Therefore, tag representation learning is of great importance. However, to learn satisfactory tag representations is challenging because 1) traditional representation methods generally fail when it comes to representing tags, 2) bidirectional interactions between nodes and tags should be modeled, which are generally not dealt within existing research works. In this paper, we propose a tag representation learning model which takes tag-related node interaction into consideration, named Tag2Gauss. Specifically, since tags represent node communities with intricate overlapping relationships, we propose that Gaussian distributions would be appropriate in modeling tags. Considering the bidirectional interactions between nodes and tags, we propose a tag representation learning model mapping tags to distributions consisting of two embedding tasks, namely Tag-view embedding and Node-view embedding. Extensive evidence demonstrates the effectiveness of representing tag as a distribution, and the advantages of the proposed architecture in many applications, such as the node classification and the network visualization.

Recent works reveal that network embedding techniques enable many machine learning models to handle diverse downstream tasks on graph structured data. However, as previous methods usually focus on learning embeddings for a single network, they can not learn representations transferable on multiple networks. Hence, it is important to design a network embedding algorithm that supports downstream model transferring on different networks, known as domain adaptation. In this paper, we propose a novel Domain Adaptive Network Embedding framework, which applies graph convolutional network to learn transferable embeddings. In DANE, nodes from multiple networks are encoded to vectors via a shared set of learnable parameters so that the vectors share an aligned embedding space. The distribution of embeddings on different networks are further aligned by adversarial learning regularization. In addition, DANE's advantage in learning transferable network embedding can be guaranteed theoretically. Extensive experiments reflect that the proposed framework outperforms other state-of-the-art network embedding baselines in cross-network domain adaptation tasks.

Network embedding is a method to learn low-dimensional representation vectors for nodes in complex networks. In real networks, nodes may have multiple tags but existing methods ignore the abundant semantic and hierarchical information of tags. This information is useful to many network applications and usually very stable. In this paper, we propose a tag representation learning model, Tag2Vec, which mixes nodes and tags into a hybrid network. Firstly, for tag networks, we define semantic distance as the proximity between tags and design a novel strategy, parameterized random walk, to generate context with semantic and hierarchical information of tags adaptively. Then, we propose hyperbolic Skip-gram model to express the complex hierarchical structure better with lower output dimensions. We evaluate our model on the NBER U.S. patent dataset and WordNet dataset. The results show that our model can learn tag representations with rich semantic information and it outperforms other baselines.

Recently, real-time air quality estimation has attracted more and more attention from all over the world, which is close to our daily life. With the prevalence of mobile sensors, there is an emerging way to monitor the air quality with mobile sensors on vehicles. Compared with traditional expensive monitor stations, mobile sensors are cheaper and more abundant, but observations from these sensors have unstable spatial and temporal distributions, which results in the existing model could not work very well on this type of data. In this article, taking advantage of air quality data from mobile sensors, we propose an real-time urban air quality estimation method based on the Gaussian Process Regression for air pollution of the unmonitored areas, pivoting on the diffusion effect and the accumulation effect of air pollution. In order to meet the real-time demands, we propose a two-layer ensemble learning framework and a self-adaptivity mechanism to improve computational efficiency and adaptivity. We evaluate our model with real data from mobile sensor system located in Beijing, China. And the experiments show that our proposed model is superior to the state-of-the-art spatial regression methods in both precision and time performances.

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification and network visualization. The source code of GNE is available online.

Network embedding, as an approach to learn low-dimensional representations of vertices, has been proved extremely useful in many applications. Lots of state-of-the-art network embedding methods based on Skip-gram framework are efficient and effective. However, these methods mainly focus on the static network embedding and cannot naturally generalize to the dynamic environment. In this paper, we propose a stable dynamic embedding framework with high efficiency. It is an extension for the Skip-gram based network embedding methods, which can keep the optimality of the objective in the Skip-gram based methods in theory. Our model can not only generalize to the new vertex representation, but also update the most affected original vertex representations during the evolvement of the network. Multi-class classification on three real-world networks demonstrates that, our model can update the vertex representations efficiently and achieve the performance of retraining simultaneously. Besides, the visualization experimental result illustrates that, our model is capable of avoiding the embedding space drifting.