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Zijian Li

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19 papers

2 author rows

IJCAI Conference 2025 Conference Paper

Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism

Ruichu Cai
Kaitao Zheng
Junxian Huang
Zijian Li
Zhengming Chen
Boyan Xu
Zhifeng Hao

Time series imputation is one of the most challenging problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the generation process from the observed time series data. In real-world scenarios, different types of missing mechanisms, like MAR (Missing At Random) and MNAR (Missing Not At Random), can occur in time series data. However, existing methods often overlook the difference among the aforementioned missing mechanisms and use a single model for time series imputation, which can easily lead to misleading results due to mechanism mismatching. In this paper, we propose a framework for the time series imputation problem by exploring Different Missing Mechanisms (DMM in short) and tailoring solutions accordingly. Specifically, we first analyze the data generation processes with temporal latent states and missing cause variables for different mechanisms. Sequentially, we model these generation processes via variational inference and estimate prior distributions of latent variables via a normalizing flow-based neural architecture. Furthermore, we establish identifiability results under the nonlinear independent component analysis framework to show that latent variables are identifiable. Experimental results show that our method surpasses existing time series imputation techniques across various datasets with different missing mechanisms, demonstrating its effectiveness in real-world applications.

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NeurIPS Conference 2025 Conference Paper

CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulations

Guangyi Chen
Yunlong Deng
Peiyuan Zhu
Yan Li
Yifan Shen
Zijian Li
Kun Zhang

Causal Representation Learning (CRL) aims to uncover the data-generating process and identify the underlying causal variables and relations, whose evaluation remains inherently challenging due to the requirement of known ground-truth causal variables and causal structure. Existing evaluations often rely on either simplistic synthetic datasets or downstream performance on real-world tasks, generally suffering a dilemma between realism and evaluative precision. In this paper, we introduce a new benchmark for CRL using high-fidelity simulated visual data that retains both realistic visual complexity and, more importantly, access to ground-truth causal generating processes. The dataset comprises around 200 thousand images and 3 million video frames across 24 sub-scenes in four domains: static image generation, dynamic physical simulations, robotic manipulations, and traffic situation analysis. These scenarios range from static to dynamic settings, simple to complex structures, and single to multi-agent interactions, offering a comprehensive testbed that hopefully bridges the gap between rigorous evaluation and real-world applicability. In addition, we provide flexible access to the underlying causal structures, allowing users to modify or configure them to align with the required assumptions in CRL, such as available domain labels, temporal dependencies, or intervention histories. Leveraging this benchmark, we evaluated representative CRL methods across diverse paradigms and offered empirical insights to assist practitioners and newcomers in choosing or extending appropriate CRL frameworks to properly address specific types of real problems that can benefit from the CRL perspective. Welcome to visit our: Project page: https: //causal-verse. github. io/, Dataset: https: //huggingface. co/CausalVerse

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AAAI Conference 2025 Conference Paper

Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting

Ruichu Cai
Haiqin Huang
Zhifan Jiang
Zijian Li
Changze Zhou
Yuequn Liu
Yuming Liu
Zhifeng Hao

Current methods for time series forecasting struggle in the online scenario, since it is difficult to preserve long-term dependency while adapting short-term changes when data are arriving sequentially. Although some recent methods solve this problem by controlling the updates of latent states, they cannot disentangle the long/short-term states, leading to the inability to effectively adapt to nonstationary. To tackle this challenge, we propose a general framework to disentangle long/short-term states for online time series forecasting. Our idea is inspired by the observations where short-term changes can be led by unknown interventions like abrupt policies in the stock market. Based on this insight, we formalize a data generation process with unknown interventions on short-term states. Under mild assumptions, we further leverage the independence of short-term states led by unknown interventions to establish the identification theory to achieve the disentanglement of long/short-term states. Built on this theory, we develop a Long Short-Term Disentanglement model (LSTD) to extract the long/short-term states with long/short term encoders, respectively. Furthermore, the LSTD model incorporates a smooth constraint to preserve the long-term dependencies and an interrupted dependency constraint to enforce the forgetting of short-term dependencies, together boosting the disentanglement of long/short-term states. Experimental results on several benchmark datasets show that our LSTD model outperforms existing methods for online time series forecasting, validating its efficacy in real-world applications.

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NeurIPS Conference 2025 Conference Paper

LLM Interpretability with Identifiable Temporal-Instantaneous Representation

Xiangchen Song
Jiaqi Sun
Zijian Li
Yujia Zheng
Kun Zhang

Despite Large Language Models' remarkable capabilities, understanding their internal representations remains challenging. Mechanistic interpretability tools such as sparse autoencoders (SAEs) were developed to extract interpretable features from LLMs but lack temporal dependency modeling, instantaneous relation representation, and more importantly theoretical guarantees—undermining both the theoretical foundations and the practical confidence necessary for subsequent analyses. While causal representation learning (CRL) offers theoretically-grounded approaches for uncovering latent concepts, existing methods cannot scale to LLMs' rich conceptual space due to inefficient computation. To bridge the gap, we introduce an identifiable temporal causal representation learning framework specifically designed for LLMs' high-dimensional concept space, capturing both time-delayed and instantaneous causal relations. Our approach provides theoretical guarantees and demonstrates efficacy on synthetic datasets scaled to match real-world complexity. By extending SAE techniques with our temporal causal framework, we successfully discover meaningful concept relationships in LLM activations. Our findings show that modeling both temporal and instantaneous conceptual relationships advances the interpretability of LLMs.

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IJCAI Conference 2025 Conference Paper

Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning

Ruichu Cai
Junjie Wan
Weilin Chen
Zeqin Yang
Zijian Li
Peng Zhen
Jiecheng Guo

Estimating long-term causal effects by combining long-term observational and short-term experimental data is a crucial but challenging problem in many real-world scenarios. In existing methods, several ideal assumptions, e. g. latent unconfoundedness assumption or additive equi-confounding bias assumption, are proposed to address the latent confounder problem raised by the observational data. However, in real-world applications, these assumptions are typically violated which limits their practical effectiveness. In this paper, we tackle the problem of estimating the long-term individual causal effects without the aforementioned assumptions. Specifically, we propose to utilize the natural heterogeneity of data, such as data from multiple sources, to identify latent confounders, thereby significantly avoiding reliance on idealized assumptions. Practically, we devise a latent representation learning-based estimator of long-term causal effects. Theoretically, we establish the identifiability of latent confounders, with which we further achieve long-term effect identification. Extensive experimental studies, conducted on multiple synthetic and semi-synthetic datasets, demonstrate the effectiveness of our proposed method.

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NeurIPS Conference 2025 Conference Paper

Online Time Series Forecasting with Theoretical Guarantees

Zijian Li
Changze Zhou
Minghao Fu
Sanjay Manjunath
Fan Feng
Guangyi Chen
Yingyao Hu
Ruichu Cai

This paper is concerned with online time series forecasting, where unknown distribution shifts occur over time, i. e. , latent variables influence the mapping from historical to future observations. To develop an automated way of online time series forecasting, we propose a Theoretical framework for Online Time-series forecasting (TOT in short) with theoretical guarantees. Specifically, we prove that supplying a forecaster with latent variables tightens the Bayes risk—the benefit endures under estimation uncertainty of latent variables and grows as the latent variables achieve a more precise identifiability. To better introduce latent variables into online forecasting algorithms, we further propose to identify latent variables with minimal adjacent observations. Based on these results, we devise a model-agnostic blueprint by employing a temporal decoder to match the distribution of observed variables and two independent noise estimators to model the causal inference of latent variables and mixing procedures of observed variables, respectively. Experiment results on synthetic data support our theoretical claims. Moreover, plug-in implementations built on several baselines yield general improvement across multiple benchmarks, highlighting the effectiveness in real-world applications.

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NeurIPS Conference 2025 Conference Paper

Thought Communication in Multiagent Collaboration

Yujia Zheng
Zhuokai Zhao
Zijian Li
Yaqi Xie
Mingze Gao
Lizhu Zhang
Kun Zhang

Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely on natural language, exchanging tokens or their embeddings. To go beyond language, we introduce a new paradigm, thought communication, which enables agents to interact directly mind-to-mind, akin to telepathy. To uncover these latent thoughts in a principled way, we formalize the process as a general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in a nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees. Guided by the established theory, we develop a framework that extracts latent thoughts from all agents prior to communication and assigns each agent the relevant thoughts, along with their sharing patterns. This paradigm naturally extends beyond LLMs to all modalities, as most observational data arise from hidden generative processes. Experiments on both synthetic and real-world benchmarks validate the theory and demonstrate the collaborative advantages of thought communication. We hope this work illuminates the potential of leveraging the hidden world, as many challenges remain unsolvable through surface-level observation alone, regardless of compute or data scale.

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NeurIPS Conference 2025 Conference Paper

Towards Identifiability of Hierarchical Temporal Causal Representation Learning

Zijian Li
Minghao Fu
Junxian Huang
Yifan Shen
Ruichu Cai
Yuewen Sun
Guangyi Chen
Kun Zhang

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from \textit{single-timestep observed variables}. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

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NeurIPS Conference 2024 Conference Paper

Causal Temporal Representation Learning with Nonstationary Sparse Transition

Xiangchen Song
Zijian Li
Guangyi Chen
Yujia Zheng
Yewen Fan
Xinshuai Dong
Kun Zhang

Causal Temporal Representation Learning (Ctrl) methods aim to identify the temporal causal dynamics of complex nonstationary temporal sequences. Despite the success of existing Ctrl methods, they require either directly observing the domain variables or assuming a Markov prior on them. Such requirements limit the application of these methods in real-world scenarios when we do not have such prior knowledge of the domain variables. To address this problem, this work adopts a sparse transition assumption, aligned with intuitive human understanding, and presents identifiability results from a theoretical perspective. In particular, we explore under what conditions on the significance of the variability of the transitions we can build a model to identify the distribution shifts. Based on the theoretical result, we introduce a novel framework, Causal Temporal Representation Learning with Nonstationary Sparse Transition (CtrlNS), designed to leverage the constraints on transition sparsity and conditional independence to reliably identify both distribution shifts and latent factors. Our experimental evaluations on synthetic and real-world datasets demonstrate significant improvements over existing baselines, highlighting the effectiveness of our approach.

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ICML Conference 2024 Conference Paper

DFlow: A Generative Model Combining Denoising AutoEncoder and Normalizing Flow for High Fidelity Waveform Generation

Chenfeng Miao
Qingying Zhu
Minchuan Chen
Wei Hu
Zijian Li
Shaojun Wang
Jing Xiao 0006

In this work, we present DFlow, a novel generative framework that combines Normalizing Flow (NF) with a Denoising AutoEncoder (DAE), for high-fidelity waveform generation. With a tactfully designed structure, DFlow seamlessly integrates the capabilities of both NF and DAE, resulting in a significantly improved performance compared to the standard NF models. Experimental results showcase DFlow’s superiority, achieving the highest MOS score among the existing methods on commonly used datasets and the fastest synthesis speed among all likelihood models. We further demonstrate the generalization ability of DFlow by generating high-quality out-of-distribution audio samples, such as singing and music audio. Additionally, we extend the model capacity of DFlow by scaling up both the model size and training set size. Our large-scale universal vocoder, DFlow-XL, achieves highly competitive performance against the best universal vocoder, BigVGAN.

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IJCAI Conference 2024 Conference Paper

Individual Causal Structure Learning from Population Data

Wei Chen
Xiaokai Huang
Zijian Li
Ruichu Cai
Zhiyi Huang
Zhifeng Hao

Learning the causal structure of each individual plays a crucial role in neuroscience, biology, and so on. Existing methods consider data from each individual separately, which may yield inaccurate causal structure estimations in limited samples. To leverage more samples, we consider incorporating data from all individuals as population data. We observe that the variables of all individuals are influenced by the common environment variables they share. These shared environment variables can be modeled as latent variables and serve as a bridge connecting data from different individuals. In particular, we propose an Individual Linear Acyclic Model (ILAM) for each individual from population data, which models the individual's variables as being linearly influenced by their parents, in addition to environment variables and noise terms. Theoretical analysis shows that the model is identifiable when all environment variables are non-Gaussian, or even if some are Gaussian with an adequate diversity in the variance of noises for each individual. We then develop an individual causal structures learning method based on the Share Independence Component Analysis technique. Experimental results on synthetic and real-world data demonstrate the correctness of the method even when the sample size of each individual's data is small.

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NeurIPS Conference 2024 Conference Paper

Learning Discrete Latent Variable Structures with Tensor Rank Conditions

Zhengming Chen
Ruichu Cai
Feng Xie
Jie Qiao
Anpeng Wu
Zijian Li
Zhifeng Hao
Kun Zhang

Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. To achieve this, we explore a tensor rank condition on contingency tables for an observed variable set $\mathbf{X}_p$, showing that the rank is determined by the minimum support of a specific conditional set (not necessary in $\mathbf{X}_p$) that d-separates all variables in $\mathbf{X}_p$. By this, one can locate the latent variable through probing the rank on different observed variables set, and further identify the latent causal structure under some structure assumptions. We present the corresponding identification algorithm and conduct simulated experiments to verify the effectiveness of our method. In general, our results elegantly extend the identification boundary for causal discovery with discrete latent variables and expand the application scope of causal discovery with latent variables.

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AAAI Conference 2024 Conference Paper

TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences

Yuequn Liu
Ruichu Cai
Wei Chen
Jie Qiao
Yuguang Yan
Zijian Li
Keli Zhang
Zhifeng Hao

Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). However, this i.i.d. assumption is often violated due to the inherent dependencies among the event sequences. Fortunately, in practice, we find these dependencies can be modeled by a topological network, suggesting a potential solution to the non-i.i.d. problem by introducing the prior topological network into Granger causal discovery. This observation prompts us to tackle two ensuing challenges: 1) how to model the event sequences while incorporating both the prior topological network and the latent Granger causal structure, and 2) how to learn the Granger causal structure. To this end, we devise a unified topological neural Poisson auto-regressive model with two processes. In the generation process, we employ a variant of the neural Poisson process to model the event sequences, considering influences from both the topological network and the Granger causal structure. In the inference process, we formulate an amortized inference algorithm to infer the latent Granger causal structure. We encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task. Experiments on simulated and real-world data demonstrate the effectiveness of our approach.

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NeurIPS Conference 2023 Conference Paper

Subspace Identification for Multi-Source Domain Adaptation

Zijian Li
Ruichu Cai
Guangyi Chen
Boyang Sun
Zhifeng Hao
Kun Zhang

Multi-source domain adaptation (MSDA) methods aim to transfer knowledge from multiple labeled source domains to an unlabeled target domain. Although current methods achieve target joint distribution identifiability by enforcing minimal changes across domains, they often necessitate stringent conditions, such as an adequate number of domains, monotonic transformation of latent variables, and invariant label distributions. These requirements are challenging to satisfy in real-world applications. To mitigate the need for these strict assumptions, we propose a subspace identification theory that guarantees the disentanglement of domain-invariant and domain-specific variables under less restrictive constraints regarding domain numbers and transformation properties and thereby facilitating domain adaptation by minimizing the impact of domain shifts on invariant variables. Based on this theory, we develop a Subspace Identification Guarantee (SIG) model that leverages variational inference. Furthermore, the SIG model incorporates class-aware conditional alignment to accommodate target shifts where label distributions change with the domain. Experimental results demonstrate that our SIG model outperforms existing MSDA techniques on various benchmark datasets, highlighting its effectiveness in real-world applications.

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TIST Journal 2021 Journal Article

Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical Systems

Zijian Li
Ruichu Cai
Hong Wei Ng
Marianne Winslett
Tom Z. J. Fu
Boyan Xu
Xiaoyan Yang
Zhenjie Zhang

Data-driven models are becoming essential parts in modern mechanical systems, commonly used to capture the behavior of various equipment and varying environmental characteristics. Despite the advantages of these data-driven models on excellent adaptivity to high dynamics and aging equipment, they are usually hungry for massive labels, mostly contributed by human engineers at a high cost. Fortunately, domain adaptation enhances the model generalization by utilizing the labeled source data and the unlabeled target data. However, the mainstream domain adaptation methods cannot achieve ideal performance on time series data, since they assume that the conditional distributions are equal. This assumption works well in the static data but is inapplicable for the time series data. Even the first-order Markov dependence assumption requires the dependence between any two consecutive time steps. In this article, we assume that the causal mechanism is invariant and present our Causal Mechanism Transfer Network (CMTN) for time series domain adaptation. By capturing causal mechanisms of time series data, CMTN allows the data-driven models to exploit existing data and labels from similar systems, such that the resulting model on a new system is highly reliable even with limited data. We report our empirical results and lessons learned from two real-world case studies, on chiller plant energy optimization and boiler fault detection, which outperform the existing state-of-the-art method.

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NeurIPS Conference 2021 Conference Paper

Domain Adaptation with Invariant Representation Learning: What Transformations to Learn?

Petar Stojanov
Zijian Li
Mingming Gong
Ruichu Cai
Jaime Carbonell
Kun Zhang

Unsupervised domain adaptation, as a prevalent transfer learning setting, spans many real-world applications. With the increasing representational power and applicability of neural networks, state-of-the-art domain adaptation methods make use of deep architectures to map the input features $X$ to a latent representation $Z$ that has the same marginal distribution across domains. This has been shown to be insufficient for generating optimal representation for classification, and to find conditionally invariant representations, usually strong assumptions are needed. We provide reasoning why when the supports of the source and target data from overlap, any map of $X$ that is fixed across domains may not be suitable for domain adaptation via invariant features. Furthermore, we develop an efficient technique in which the optimal map from $X$ to $Z$ also takes domain-specific information as input, in addition to the features $X$. By using the property of minimal changes of causal mechanisms across domains, our model also takes into account the domain-specific information to ensure that the latent representation $Z$ does not discard valuable information about $Y$. We demonstrate the efficacy of our method via synthetic and real-world data experiments. The code is available at: \texttt{https: //github. com/DMIRLAB-Group/DSAN}.

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AAAI Conference 2021 Conference Paper

Time Series Domain Adaptation via Sparse Associative Structure Alignment

Ruichu Cai
Jiawei Chen
Zijian Li
Wei Chen
Keli Zhang
Junjian Ye
Zhuozhang Li
Xiaoyan Yang

Domain adaptation on time series data is an important but challenging task. Most of the existing works in this area are based on the learning of the domain-invariant representation of the data with the help of restrictions like MMD. However, such extraction of the domain-invariant representation is a non-trivial task for time series data, due to the complex dependence among the timestamps. In detail, in the fully dependent time series, a small change of the time lags or the offsets may lead to difficulty in the domain invariant extraction. Fortunately, the stability of the causality inspired us to explore the domain invariant structure of the data. To reduce the difficulty in the discovery of causal structure, we relax it to the sparse associative structure and propose a novel sparse associative structure alignment model for domain adaptation. First, we generate the segment set to exclude the obstacle of offsets. Second, the intra-variables and inter-variables sparse attention mechanisms are devised to extract associative structure time-series data with considering time lags. Finally, the associative structure alignment is used to guide the transfer of knowledge from the source domain to the target one. Experimental studies not only verify the good performance of our methods on three real-world datasets but also provide some insightful discoveries on the transferred knowledge.

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IJCAI Conference 2019 Conference Paper

Learning Disentangled Semantic Representation for Domain Adaptation

Ruichu Cai
Zijian Li
Pengfei Wei
Jie Qiao
Kun Zhang
Zhifeng Hao

Domain adaptation is an important but challenging task. Most of the existing domain adaptation methods struggle to extract the domain-invariant representation on the feature space with entangling domain information and semantic information. Different from previous efforts on the entangled feature space, we aim to extract the domain invariant semantic information in the latent disentangled semantic representation (DSR) of the data. In DSR, we assume the data generation process is controlled by two independent sets of variables, i. e. , the semantic latent variables and the domain latent variables. Under the above assumption, we employ a variational auto-encoder to reconstruct the semantic latent variables and domain latent variables behind the data. We further devise a dual adversarial network to disentangle these two sets of reconstructed latent variables. The disentangled semantic latent variables are finally adapted across the domains. Experimental studies testify that our model yields state-of-the-art performance on several domain adaptation benchmark datasets.

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IJCAI Conference 2018 Conference Paper

An Encoder-Decoder Framework Translating Natural Language to Database Queries

Ruichu Cai
Boyan Xu
Zhenjie Zhang
Xiaoyan Yang
Zijian Li
Zhihao Liang

Machine translation is going through a radical revolution, driven by the explosive development of deep learning techniques using Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN). In this paper, we consider a special case in machine translation problems, targeting to convert natural language into Structured Query Language (SQL) for data retrieval over relational database. Although generic CNN and RNN learn the grammar structure of SQL when trained with sufficient samples, the accuracy and training efficiency of the model could be dramatically improved, when the translation model is deeply integrated with the grammar rules of SQL. We present a new encoder-decoder framework, with a suite of new approaches, including new semantic features fed into the encoder, grammar-aware states injected into the memory of decoder, as well as recursive state management for sub-queries. These techniques help the neural network better focus on understanding semantics of operations in natural language and save the efforts on SQL grammar learning. The empirical evaluation on real world database and queries show that our approach outperform state-of-the-art solution by a significant margin.

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