Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical QueriesXiao Liu, Shiyu Zhao, Kai Su et al. · tsinghua
Knowledge graph (KG) embeddings have been a mainstream approach for reasoning over incomplete KGs. However, limited by their inherently shallow and static architectures, they can hardly deal with the rising focus on complex logical queries, which comprise logical operators, imputed edges, multiple source entities, and unknown intermediate entities. In this work, we present the Knowledge Graph Transformer (kgTransformer) with masked pre-training and fine-tuning strategies. We design a KG triple transformation method to enable Transformer to handle KGs, which is further strengthened by the Mixture-of-Experts (MoE) sparse activation. We then formulate the complex logical queries as masked prediction and introduce a two-stage masked pre-training strategy to improve transferability and generalizability. Extensive experiments on two benchmarks demonstrate that kgTransformer can consistently outperform both KG embedding-based baselines and advanced encoders on nine in-domain and out-of-domain reasoning tasks. Additionally, kgTransformer can reason with explainability via providing the full reasoning paths to interpret given answers.
20.6CEJul 15
Exploring the Alignment of Generation and Understanding in Protein Structure ModelingJunde Xu, Yuansheng Huang, Zijun Gao et al.
Understanding and generation are often treated as two separate paradigms in training deep neural networks, despite the fact that both are trained with closely related objectives such as denoising and masked prediction. While prior studies have shown that generative models often learn suboptimal representations for understanding tasks in vision, it is less understood whether a similar gap exists in the protein domain. In this work, we systematically investigate this question by benchmarking state-of-the-art protein generative models on widely-used protein understanding tasks, and observe that these models exhibit consistently poor performance compared to existing protein encoders. Furthermore, inspired by the Representation Alignment (REPA) framework, we propose to explicitly align generative protein diffusion models with pretrained protein understanding models during training. Experiments on the MotifBench demonstrate that representation alignment significantly improves functional protein generation, boosting the MotifBench score of Protpardelle-1c from 39.2 to 47.1, corresponding to a 20% relative improvement. Our results suggest that representation alignment provides a general and effective mechanism for bridging understanding and generation in protein structure modeling.
Multi-task Bioassay Pre-training for Protein-ligand Binding Affinity PredictionJiaxian Yan, Zhaofeng Ye, Ziyi Yang et al.
Protein-ligand binding affinity (PLBA) prediction is the fundamental task in drug discovery. Recently, various deep learning-based models predict binding affinity by incorporating the three-dimensional structure of protein-ligand complexes as input and achieving astounding progress. However, due to the scarcity of high-quality training data, the generalization ability of current models is still limited. In addition, different bioassays use varying affinity measurement labels (i.e., IC50, Ki, Kd), and different experimental conditions inevitably introduce systematic noise, which poses a significant challenge to constructing high-precision affinity prediction models. To address these issues, we (1) propose Multi-task Bioassay Pre-training (MBP), a pre-training framework for structure-based PLBA prediction; (2) construct a pre-training dataset called ChEMBL-Dock with more than 300k experimentally measured affinity labels and about 2.8M docked three-dimensional structures. By introducing multi-task pre-training to treat the prediction of different affinity labels as different tasks and classifying relative rankings between samples from the same bioassay, MBP learns robust and transferrable structural knowledge from our new ChEMBL-Dock dataset with varied and noisy labels. Experiments substantiate the capability of MBP as a general framework that can improve and be tailored to mainstream structure-based PLBA prediction tasks. To the best of our knowledge, MBP is the first affinity pre-training model and shows great potential for future development.
16.3IRNov 16, 2023
Chemist-X: Large Language Model-empowered Agent for Reaction Condition Recommendation in Chemical SynthesisKexin Chen, Jiamin Lu, Junyou Li et al.
Recent AI research plots a promising future of automatic chemical reactions within the chemistry society. This study proposes Chemist-X, a comprehensive AI agent that automates the reaction condition optimization (RCO) task in chemical synthesis with retrieval-augmented generation (RAG) technology and AI-controlled wet-lab experiment executions. To begin with, as an emulation on how chemical experts solve the RCO task, Chemist-X utilizes a novel RAG scheme to interrogate available molecular and literature databases to narrow the searching space for later processing. The agent then leverages a computer-aided design (CAD) tool we have developed through a large language model (LLM) supervised programming interface. With updated chemical knowledge obtained via RAG, as well as the ability in using CAD tools, our agent significantly outperforms conventional RCO AIs confined to the fixed knowledge within its training data. Finally, Chemist-X interacts with the physical world through an automated robotic system, which can validate the suggested chemical reaction condition without human interventions. The control of the robotic system was achieved with a novel algorithm we have developed for the equipment, which relies on LLMs for reliable script generation. Results of our automatic wet-lab experiments, achieved by fully LLM-supervised end-to-end operation with no human in the lope, prove Chemist-X's ability in self-driving laboratories.
Kimi-VL Technical ReportKimi Team, Angang Du, Bohong Yin et al. · pku, tsinghua
We present Kimi-VL, an efficient open-source Mixture-of-Experts (MoE) vision-language model (VLM) that offers advanced multimodal reasoning, long-context understanding, and strong agent capabilities - all while activating only 2.8B parameters in its language decoder (Kimi-VL-A3B). Kimi-VL demonstrates strong performance across challenging domains: as a general-purpose VLM, Kimi-VL excels in multi-turn agent tasks (e.g., OSWorld), matching flagship models. Furthermore, it exhibits remarkable capabilities across diverse challenging vision language tasks, including college-level image and video comprehension, OCR, mathematical reasoning, and multi-image understanding. In comparative evaluations, it effectively competes with cutting-edge efficient VLMs such as GPT-4o-mini, Qwen2.5-VL-7B, and Gemma-3-12B-IT, while surpassing GPT-4o in several key domains. Kimi-VL also advances in processing long contexts and perceiving clearly. With a 128K extended context window, Kimi-VL can process diverse long inputs, achieving impressive scores of 64.5 on LongVideoBench and 35.1 on MMLongBench-Doc. Its native-resolution vision encoder, MoonViT, further allows it to see and understand ultra-high-resolution visual inputs, achieving 83.2 on InfoVQA and 34.5 on ScreenSpot-Pro, while maintaining lower computational cost for common tasks. Building upon Kimi-VL, we introduce an advanced long-thinking variant: Kimi-VL-Thinking-2506. Developed through long chain-of-thought (CoT) supervised fine-tuning (SFT) and reinforcement learning (RL), the latest model exhibits strong long-horizon reasoning capabilities (64.0 on MMMU, 46.3 on MMMU-Pro, 56.9 on MathVision, 80.1 on MathVista, 65.2 on VideoMMMU) while obtaining robust general abilities. Code and models are publicly accessible at https://github.com/MoonshotAI/Kimi-VL.
MoBA: Mixture of Block Attention for Long-Context LLMsEnzhe Lu, Zhejun Jiang, Jingyuan Liu et al. · pku
Scaling the effective context length is essential for advancing large language models (LLMs) toward artificial general intelligence (AGI). However, the quadratic increase in computational complexity inherent in traditional attention mechanisms presents a prohibitive overhead. Existing approaches either impose strongly biased structures, such as sink or window attention which are task-specific, or radically modify the attention mechanism into linear approximations, whose performance in complex reasoning tasks remains inadequately explored. In this work, we propose a solution that adheres to the ``less structure'' principle, allowing the model to determine where to attend autonomously, rather than introducing predefined biases. We introduce Mixture of Block Attention (MoBA), an innovative approach that applies the principles of Mixture of Experts (MoE) to the attention mechanism. This novel architecture demonstrates superior performance on long-context tasks while offering a key advantage: the ability to seamlessly transition between full and sparse attention, enhancing efficiency without the risk of compromising performance. MoBA has already been deployed to support Kimi's long-context requests and demonstrates significant advancements in efficient attention computation for LLMs. Our code is available at https://github.com/MoonshotAI/MoBA.
8.1IRFeb 20, 2024Code
ChemMiner: A Large Language Model Agent System for Chemical Literature Data MiningKexin Chen, Yuyang Du, Junyou Li et al.
The development of AI-assisted chemical synthesis tools requires comprehensive datasets covering diverse reaction types, yet current high-throughput experimental (HTE) approaches are expensive and limited in scope. Chemical literature represents a vast, underexplored data source containing thousands of reactions published annually. However, extracting reaction information from literature faces significant challenges including varied writing styles, complex coreference relationships, and multimodal information presentation. This paper proposes ChemMiner, a novel end-to-end framework leveraging multiple agents powered by large language models (LLMs) to extract high-fidelity chemical data from literature. ChemMiner incorporates three specialized agents: a text analysis agent for coreference mapping, a multimodal agent for non-textual information extraction, and a synthesis analysis agent for data generation. Furthermore, we developed a comprehensive benchmark with expert-annotated chemical literature to evaluate both extraction efficiency and precision. Experimental results demonstrate reaction identification rates comparable to human chemists while significantly reducing processing time, with high accuracy, recall, and F1 scores. Our open-sourced benchmark facilitates future research in chemical literature data mining.
Modeling Protein Using Large-scale Pretrain Language ModelYijia Xiao, Jiezhong Qiu, Ziang Li et al.
Protein is linked to almost every life process. Therefore, analyzing the biological structure and property of protein sequences is critical to the exploration of life, as well as disease detection and drug discovery. Traditional protein analysis methods tend to be labor-intensive and time-consuming. The emergence of deep learning models makes modeling data patterns in large quantities of data possible. Interdisciplinary researchers have begun to leverage deep learning methods to model large biological datasets, e.g. using long short-term memory and convolutional neural network for protein sequence classification. After millions of years of evolution, evolutionary information is encoded in protein sequences. Inspired by the similarity between natural language and protein sequences, we use large-scale language models to model evolutionary-scale protein sequences, encoding protein biology information in representation. Significant improvements are observed in both token-level and sequence-level tasks, demonstrating that our large-scale model can accurately capture evolution information from pretraining on evolutionary-scale individual sequences. Our code and model are available at https://github.com/THUDM/ProteinLM.
FastMoE: A Fast Mixture-of-Expert Training SystemJiaao He, Jiezhong Qiu, Aohan Zeng et al.
Mixture-of-Expert (MoE) presents a strong potential in enlarging the size of language model to trillions of parameters. However, training trillion-scale MoE requires algorithm and system co-design for a well-tuned high performance distributed training system. Unfortunately, the only existing platform that meets the requirements strongly depends on Google's hardware (TPU) and software (Mesh Tensorflow) stack, and is not open and available to the public, especially GPU and PyTorch communities. In this paper, we present FastMoE, a distributed MoE training system based on PyTorch with common accelerators. The system provides a hierarchical interface for both flexible model design and easy adaption to different applications, such as Transformer-XL and Megatron-LM. Different from direct implementation of MoE models using PyTorch, the training speed is highly optimized in FastMoE by sophisticated high-performance acceleration skills. The system supports placing different experts on multiple GPUs across multiple nodes, enabling enlarging the number of experts linearly against the number of GPUs. The source of FastMoE is available at https://github.com/laekov/fastmoe under Apache-2 license.
1.7CLDec 6, 2023
Holmes: Towards Distributed Training Across Clusters with Heterogeneous NIC EnvironmentFei Yang, Shuang Peng, Ning Sun et al.
Large language models (LLMs) such as GPT-3, OPT, and LLaMA have demonstrated remarkable accuracy in a wide range of tasks. However, training these models can incur significant expenses, often requiring tens of thousands of GPUs for months of continuous operation. Typically, this training is carried out in specialized GPU clusters equipped with homogeneous high-speed Remote Direct Memory Access (RDMA) network interface cards (NICs). The acquisition and maintenance of such dedicated clusters is challenging. Current LLM training frameworks, like Megatron-LM and Megatron-DeepSpeed, focus primarily on optimizing training within homogeneous cluster settings. In this paper, we introduce Holmes, a training framework for LLMs that employs thoughtfully crafted data and model parallelism strategies over the heterogeneous NIC environment. Our primary technical contribution lies in a novel scheduling method that intelligently allocates distinct computational tasklets in LLM training to specific groups of GPU devices based on the characteristics of their connected NICs. Furthermore, our proposed framework, utilizing pipeline parallel techniques, demonstrates scalability to multiple GPU clusters, even in scenarios without high-speed interconnects between nodes in distinct clusters. We conducted comprehensive experiments that involved various scenarios in the heterogeneous NIC environment. In most cases, our framework achieves performance levels close to those achievable with homogeneous RDMA-capable networks (InfiniBand or RoCE), significantly exceeding training efficiency within the pure Ethernet environment. Additionally, we verified that our framework outperforms other mainstream LLM frameworks under heterogeneous NIC environment in terms of training efficiency and can be seamlessly integrated with them.
11.4LGJun 3, 2025
Protein Inverse Folding From Structure FeedbackJunde Xu, Zijun Gao, Xinyi Zhou et al.
The inverse folding problem, aiming to design amino acid sequences that fold into desired three-dimensional structures, is pivotal for various biotechnological applications. Here, we introduce a novel approach leveraging Direct Preference Optimization (DPO) to fine-tune an inverse folding model using feedback from a protein folding model. Given a target protein structure, we begin by sampling candidate sequences from the inverse-folding model, then predict the three-dimensional structure of each sequence with the folding model to generate pairwise structural-preference labels. These labels are used to fine-tune the inverse-folding model under the DPO objective. Our results on the CATH 4.2 test set demonstrate that DPO fine-tuning not only improves sequence recovery of baseline models but also leads to a significant improvement in average TM-Score from 0.77 to 0.81, indicating enhanced structure similarity. Furthermore, iterative application of our DPO-based method on challenging protein structures yields substantial gains, with an average TM-Score increase of 79.5\% with regard to the baseline model. This work establishes a promising direction for enhancing protein sequence design ability from structure feedback by effectively utilizing preference optimization.
1.2QMOct 3, 2025
InstructPLM-mu: 1-Hour Fine-Tuning of ESM2 Beats ESM3 in Protein Mutation PredictionsJunde Xu, Yapin Shi, Lijun Lang et al.
Multimodal protein language models deliver strong performance on mutation-effect prediction, but training such models from scratch demands substantial computational resources. In this paper, we propose a fine-tuning framework called InstructPLM-mu and try to answer a question: \textit{Can multimodal fine-tuning of a pretrained, sequence-only protein language model match the performance of models trained end-to-end? } Surprisingly, our experiments show that fine-tuning ESM2 with structural inputs can reach performance comparable to ESM3. To understand how this is achieved, we systematically compare three different feature-fusion designs and fine-tuning recipes. Our results reveal that both the fusion method and the tuning strategy strongly affect final accuracy, indicating that the fine-tuning process is not trivial. We hope this work offers practical guidance for injecting structure into pretrained protein language models and motivates further research on better fusion mechanisms and fine-tuning protocols.
1.2SIDec 2, 2021
Learning Large-scale Network Embedding from Representative SubgraphJunsheng Kong, Weizhao Li, Ben Liao et al.
We study the problem of large-scale network embedding, which aims to learn low-dimensional latent representations for network mining applications. Recent research in the field of network embedding has led to significant progress such as DeepWalk, LINE, NetMF, NetSMF. However, the huge size of many real-world networks makes it computationally expensive to learn network embedding from the entire network. In this work, we present a novel network embedding method called "NES", which learns network embedding from a small representative subgraph. NES leverages theories from graph sampling to efficiently construct representative subgraph with smaller size which can be used to make inferences about the full network, enabling significantly improved efficiency in embedding learning. Then, NES computes the network embedding from this representative subgraph, efficiently. Compared with well-known methods, extensive experiments on networks of various scales and types demonstrate that NES achieves comparable performance and significant efficiency superiority.
7.5LGOct 8, 2021
Stable Prediction on Graphs with Agnostic Distribution ShiftShengyu Zhang, Kun Kuang, Jiezhong Qiu et al.
Graph is a flexible and effective tool to represent complex structures in practice and graph neural networks (GNNs) have been shown to be effective on various graph tasks with randomly separated training and testing data. In real applications, however, the distribution of training graph might be different from that of the test one (e.g., users' interactions on the user-item training graph and their actual preference on items, i.e., testing environment, are known to have inconsistencies in recommender systems). Moreover, the distribution of test data is always agnostic when GNNs are trained. Hence, we are facing the agnostic distribution shift between training and testing on graph learning, which would lead to unstable inference of traditional GNNs across different test environments. To address this problem, we propose a novel stable prediction framework for GNNs, which permits both locally and globally stable learning and prediction on graphs. In particular, since each node is partially represented by its neighbors in GNNs, we propose to capture the stable properties for each node (locally stable) by re-weighting the information propagation/aggregation processes. For global stability, we propose a stable regularizer that reduces the training losses on heterogeneous environments and thus warping the GNNs to generalize well. We conduct extensive experiments on several graph benchmarks and a noisy industrial recommendation dataset that is collected from 5 consecutive days during a product promotion festival. The results demonstrate that our method outperforms various SOTA GNNs for stable prediction on graphs with agnostic distribution shift, including shift caused by node labels and attributes.
0.2CLSep 15, 2021
Fast Extraction of Word Embedding from Q-contextsJunsheng Kong, Weizhao Li, Zeyi Liu et al.
The notion of word embedding plays a fundamental role in natural language processing (NLP). However, pre-training word embedding for very large-scale vocabulary is computationally challenging for most existing methods. In this work, we show that with merely a small fraction of contexts (Q-contexts)which are typical in the whole corpus (and their mutual information with words), one can construct high-quality word embedding with negligible errors. Mutual information between contexts and words can be encoded canonically as a sampling state, thus, Q-contexts can be fast constructed. Furthermore, we present an efficient and effective WEQ method, which is capable of extracting word embedding directly from these typical contexts. In practical scenarios, our algorithm runs 11$\sim$13 times faster than well-established methods. By comparing with well-known methods such as matrix factorization, word2vec, GloVeand fasttext, we demonstrate that our method achieves comparable performance on a variety of downstream NLP tasks, and in the meanwhile maintains run-time and resource advantages over all these baselines.
46.6AIJun 14, 2021
Pre-Trained Models: Past, Present and FutureXu Han, Zhengyan Zhang, Ning Ding et al.
Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success and become a milestone in the field of artificial intelligence (AI). Owing to sophisticated pre-training objectives and huge model parameters, large-scale PTMs can effectively capture knowledge from massive labeled and unlabeled data. By storing knowledge into huge parameters and fine-tuning on specific tasks, the rich knowledge implicitly encoded in huge parameters can benefit a variety of downstream tasks, which has been extensively demonstrated via experimental verification and empirical analysis. It is now the consensus of the AI community to adopt PTMs as backbone for downstream tasks rather than learning models from scratch. In this paper, we take a deep look into the history of pre-training, especially its special relation with transfer learning and self-supervised learning, to reveal the crucial position of PTMs in the AI development spectrum. Further, we comprehensively review the latest breakthroughs of PTMs. These breakthroughs are driven by the surge of computational power and the increasing availability of data, towards four important directions: designing effective architectures, utilizing rich contexts, improving computational efficiency, and conducting interpretation and theoretical analysis. Finally, we discuss a series of open problems and research directions of PTMs, and hope our view can inspire and advance the future study of PTMs.
GLM: General Language Model Pretraining with Autoregressive Blank InfillingZhengxiao Du, Yujie Qian, Xiao Liu et al.
There have been various types of pretraining architectures including autoencoding models (e.g., BERT), autoregressive models (e.g., GPT), and encoder-decoder models (e.g., T5). However, none of the pretraining frameworks performs the best for all tasks of three main categories including natural language understanding (NLU), unconditional generation, and conditional generation. We propose a General Language Model (GLM) based on autoregressive blank infilling to address this challenge. GLM improves blank filling pretraining by adding 2D positional encodings and allowing an arbitrary order to predict spans, which results in performance gains over BERT and T5 on NLU tasks. Meanwhile, GLM can be pretrained for different types of tasks by varying the number and lengths of blanks. On a wide range of tasks across NLU, conditional and unconditional generation, GLM outperforms BERT, T5, and GPT given the same model sizes and data, and achieves the best performance from a single pretrained model with 1.25x parameters of BERT Large , demonstrating its generalizability to different downstream tasks.
5.8MLAug 6, 2020
A Matrix Chernoff Bound for Markov Chains and Its Application to Co-occurrence MatricesJiezhong Qiu, Chi Wang, Ben Liao et al.
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued function on its state space. Our result gives exponentially decreasing bounds on the tail distributions of the extreme eigenvalues of the sample mean matrix. Our proof is based on the matrix expander (regular undirected graph) Chernoff bound [Garg et al. STOC '18] and scalar Chernoff-Hoeffding bounds for Markov chains [Chung et al. STACS '12]. Our matrix Chernoff bound for Markov chains can be applied to analyze the behavior of co-occurrence statistics for sequential data, which have been common and important data signals in machine learning. We show that given a regular Markov chain with $n$ states and mixing time $τ$, we need a trajectory of length $O(τ(\log{(n)}+\log{(τ)})/ε^2)$ to achieve an estimator of the co-occurrence matrix with error bound $ε$. We conduct several experiments and the experimental results are consistent with the exponentially fast convergence rate from theoretical analysis. Our result gives the first bound on the convergence rate of the co-occurrence matrix and the first sample complexity analysis in graph representation learning.
Blockwise Self-Attention for Long Document UnderstandingJiezhong Qiu, Hao Ma, Omer Levy et al.
We present BlockBERT, a lightweight and efficient BERT model for better modeling long-distance dependencies. Our model extends BERT by introducing sparse block structures into the attention matrix to reduce both memory consumption and training/inference time, which also enables attention heads to capture either short- or long-range contextual information. We conduct experiments on language model pre-training and several benchmark question answering datasets with various paragraph lengths. BlockBERT uses 18.7-36.1% less memory and 12.0-25.1% less time to learn the model. During testing, BlockBERT saves 27.8% inference time, while having comparable and sometimes better prediction accuracy, compared to an advanced BERT-based model, RoBERTa.
Alchemy: A Quantum Chemistry Dataset for Benchmarking AI ModelsGuangyong Chen, Pengfei Chen, Chang-Yu Hsieh et al.
We introduce a new molecular dataset, named Alchemy, for developing machine learning models useful in chemistry and material science. As of June 20th 2019, the dataset comprises of 12 quantum mechanical properties of 119,487 organic molecules with up to 14 heavy atoms, sampled from the GDB MedChem database. The Alchemy dataset expands the volume and diversity of existing molecular datasets. Our extensive benchmarks of the state-of-the-art graph neural network models on Alchemy clearly manifest the usefulness of new data in validating and developing machine learning models for chemistry and material science. We further launch a contest to attract attentions from researchers in the related fields. More details can be found on the contest website \footnote{https://alchemy.tencent.com}. At the time of benchamrking experiment, we have generated 119,487 molecules in our Alchemy dataset. More molecular samples are generated since then. Hence, we provide a list of molecules used in the reported benchmarks.
DeepInf: Social Influence Prediction with Deep LearningJiezhong Qiu, Jian Tang, Hao Ma et al.
Social and information networking activities such as on Facebook, Twitter, WeChat, and Weibo have become an indispensable part of our everyday life, where we can easily access friends' behaviors and are in turn influenced by them. Consequently, an effective social influence prediction for each user is critical for a variety of applications such as online recommendation and advertising. Conventional social influence prediction approaches typically design various hand-crafted rules to extract user- and network-specific features. However, their effectiveness heavily relies on the knowledge of domain experts. As a result, it is usually difficult to generalize them into different domains. Inspired by the recent success of deep neural networks in a wide range of computing applications, we design an end-to-end framework, DeepInf, to learn users' latent feature representation for predicting social influence. In general, DeepInf takes a user's local network as the input to a graph neural network for learning her latent social representation. We design strategies to incorporate both network structures and user-specific features into convolutional neural and attention networks. Extensive experiments on Open Academic Graph, Twitter, Weibo, and Digg, representing different types of social and information networks, demonstrate that the proposed end-to-end model, DeepInf, significantly outperforms traditional feature engineering-based approaches, suggesting the effectiveness of representation learning for social applications.
Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vecJiezhong Qiu, Yuxiao Dong, Hao Ma et al.
Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.