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Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future

Zheng ChuJingchang ChenQianglong ChenWeijiang YuTao HeHaotian WangWeihua PengMing LiuBing QinTing Liu

article2024ACL279 citations

Presents a structured taxonomy of generalized chain-of-thought reasoning in large language models, categorizing prompt construction techniques, topological variants, and enhancement methods alongside core benchmarks and emerging frontiers.

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As large language models become central to artificial intelligence, standard prompting often fails when addressing complex tasks requiring multi-step deduction, factual consistency, and explainability. Directly requesting answers can lead to incorrect reasoning steps and untrustworthy outputs. To address this challenge, researchers have advanced chain-of-thought prompting—a paradigm where models break problems into intermediate steps before reaching a final answer.

The article provides a systematic overview and taxonomy of generalized chain-of-thought methods, synthesizing advancements in prompt design, structural variations, optimization strategies, and emerging applications. The authors analyze a wide collection of studies across mathematical, logical, commonsense, symbolic, and multi-modal benchmarks, assessing empirical performance trends and implementation trade-offs across leading language models.

The primary finding is that step-by-step reasoning significantly improves model accuracy and interpretability across intricate domains compared to standard input-output prompting. For instance, few-shot chain-of-thought prompting on benchmark tasks such as standard grade-school math improves accuracy from baseline levels under 20% to over 60–80% depending on the model version. Second, representing intermediate rationales in structured formats—such as code or formal logic executed by external engines—substantially reduces execution inconsistencies. Third, advanced structures like tree- and graph-based reasoning allow models to explore multiple solution paths and backtrack, offering stronger problem-solving capabilities than linear chains at the cost of narrower task generalization. Finally, techniques such as self-consistency voting and question decomposition consistently lift performance, while distillation successfully transfers multi-step reasoning capabilities from larger foundation models to smaller, cost-effective models.

These findings indicate that generalized chain-of-thought reasoning is foundational for deploying reliable AI systems and autonomous agents capable of dynamic planning, tool use, and external knowledge integration. However, organizations face clear operational trade-offs: complex search strategies and sampling ensembles yield higher accuracy but multiply computational latency and inference costs. Additionally, relying solely on a model's internal self-feedback often fails to catch subtle hallucinations, creating operational risks if deployed without external verification.

Organizations should adopt semi-automated prompting or hybrid neuro-symbolic approaches that blend human supervision, programmatic execution, and external retrieval to balance cost, accuracy, and domain flexibility. For resource-constrained deployments, teams should leverage knowledge distillation from larger models rather than running computationally intensive multi-path reasoning in production. Future work must prioritize establishing robust intermediate verification frameworks, improving vision-text integration for multi-modal reasoning, and advancing the theoretical understanding of emergent reasoning capabilities.

Confidence in the broad utility of chain-of-thought reasoning is high, but readers should exercise caution when comparing reported benchmark numbers directly, as experimental configurations and model checkpoints vary across individual studies. Furthermore, significant uncertainty remains regarding how reliably models can detect and correct their own internal reasoning errors without external ground truth.

Harbin Institute of TechnologyHuaweiPeng Cheng Laboratorycognitive processreasoningtaxonomychain of thought reasoningthought promptingmultimodal reasoning
arXiv: 2309.15402zchuz/CoT-Reasoning-Survey
Cover for Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future

Abstract

Reasoning, a fundamental cognitive process integral to human intelligence, has garnered substantial interest within artificial intelligence. Notably, recent studies have revealed that chain-of-thought prompting significantly enhances LLM's reasoning capabilities, which attracts widespread attention from both academics and industry. In this paper, we systematically investigate relevant research, summarizing advanced methods through a meticulous taxonomy that offers novel perspectives. Moreover, we delve into the current frontiers and delineate the challenges and future directions, thereby shedding light on future research. Furthermore, we engage in a discussion about open questions. We hope this paper serves as an introduction for beginners and fosters future research. Resources have been made publicly available at https://github.com/zchuz/CoT-Reasoning-Survey.

Topics

cognitive processreasoningtaxonomy

Keywords

chain of thought reasoningthought promptingmultimodal reasoningmulti-hop reasoningsymbolic reasoningtable-based reasoningtemporal reasoningdeductive reasoninginductive reasoningintermediate reasoning

Table of Contents

  • 1 Introduction
  • 2 Background and Preliminary
  • 2.1 Background
  • 2.2 Preliminary
  • 2.3 Advantages of CoT Reasoning
  • 3 Benchmarks
  • 4 Advanced Methods
  • 4.1 XoT Prompt Construction
  • 4.1.1 Manual Prompting
  • 4.1.2 Automatic Prompting
  • 4.1.3 Semi-automatic Prompting
  • 4.1.4 Pros and Cons of Three Approaches
  • 4.2 XoT Topological Variants
  • 4.3 XoT Enhancement Methods
  • 4.3.1 Verify and Refine
  • 4.3.2 Question Decomposition
  • 4.3.3 Knowledge Enhancement
  • 4.3.4 Self-Ensemble
  • 4.3.5 Efficient Reasoning
  • 5 Frontiers of Research
  • 5.1 Tool Use
  • 5.2 Planning
  • 5.3 Distillation of Reasoning Capabilities
  • 6 Future Directions
  • 6.1 Multi-modal Reasoning
  • 6.2 Faithful Reasoning
  • 6.3 Theoretical Perspective
  • 7 Discussion
  • 8 Conclusion
  • Limitations
  • Acknowledgements
  • References
  • A Appendix
  • A.1 Related Survey
  • A.2 Further Discussion
  • A.3 Early Attempts and Efforts in Specific Domains
  • A.4 Empirical Results
  • B Details of Benchmarks
  • B.1 Mathematical Reasoning
  • B.2 Commonsense Reasoning
  • B.3 Symbolic Reasoning
  • B.4 Logical Reasoning
  • B.5 Multi-modal Reasoning
  • B.6 Comprehensive Benchmarks

Knowls

  1. Knowl 1 — Probabilistic Formulation of Standard and Chain-of-Thought Prompting

    equation

    In standard few-shot prompting, the prompt TSPT_{SP} contains an instruction II and nn input-output demonstration pairs (x1,y1),…,(xn,yn)(x_1, y_1), \dots, (x_n, y_n):

    TSP={I,(x1,y1),…,(xn,yn)}T_{SP} = \{I, (x_1, y_1), \dots, (x_n, y_n)\}

    Given question QQ and prompt TSPT_{SP}, a probabilistic language model pLMp_{LM} autoregressively predicts the answer sequence A=(a1,…,a∣A∣)A = (a_1, \dots, a_{|A|}) without explicit intermediate steps:

    p(A∣TSP,Q)=∏i=1∣A∣pLM(ai∣TSP,Q,a<i)p(A \mid T_{SP}, Q) = \prod_{i=1}^{|A|} p_{LM}(a_i \mid T_{SP}, Q, a_{<i})

    In few-shot chain-of-thought (CoT) prompting, the prompt TCoTT_{CoT} augments each demonstration with an intermediate reasoning rationale eie_i:

    TCoT={I,(x1,e1,y1),…,(xn,en,yn)}T_{CoT} = \{I, (x_1, e_1, y_1), \dots, (x_n, e_n, y_n)\}

    The model generates an intermediate reasoning trajectory R=(r1,…,r∣R∣)R = (r_1, \dots, r_{|R|}) before producing the final answer AA. The joint probability factorizes as:

    p(A,R∣TCoT,Q)=p(A∣TCoT,Q,R)⋅p(R∣TCoT,Q)p(A, R \mid T_{CoT}, Q) = p(A \mid T_{CoT}, Q, R) \cdot p(R \mid T_{CoT}, Q)

    where the trajectory and answer tokens are modeled by:

    p(R∣TCoT,Q)=∏i=1∣R∣pLM(ri∣TCoT,Q,r<i)p(R \mid T_{CoT}, Q) = \prod_{i=1}^{|R|} p_{LM}(r_i \mid T_{CoT}, Q, r_{<i})

    p(A∣TCoT,Q,R)=∏j=1∣A∣pLM(aj∣TCoT,Q,R,a<j)p(A \mid T_{CoT}, Q, R) = \prod_{j=1}^{|A|} p_{LM}(a_j \mid T_{CoT}, Q, R, a_{<j})

  2. Knowl 2 — Taxonomy of Generalized Chain-of-Thought Reasoning

    model/method

    Generalized Chain-of-Thought (XoT) organizes step-by-step problem-solving methods along three principal dimensions:

    1. Advanced Methods:

      • Prompt Construction: Manual Prompting (human-annotated rationales or program formulations), Automatic Prompting (zero-shot trigger instructions, automatic demonstration clustering and sampling), and Semi-automatic Prompting (bootstrapping, synthetic demonstration generation, policy-guided demonstration selection).
      • Topological Variants: Chain Structures (sequential natural language, code, or formal logic), Tree Structures (branching search via BFS, DFS, and Monte Carlo tree evaluation with backtracking), and Graph Structures (cyclic connections, NN-to-11 aggregation, and network-based premise dependencies).
      • Enhancement Methods: Verify and Refine (iterative feedback, critic models, deductive filtering), Question Decomposition (hierarchical top-down sub-question solving and bottom-up aggregation), Knowledge Enhancement (internal parametric recall and external retrieval augmentation), Self-Ensemble (majority voting, complexity-weighted aggregation, multi-agent debate), and Efficient Reasoning (parallel sub-problem decoding, speculative draft verification, adaptive sample budgeting).

    2. Frontiers of Research:

      • Tool Use: Integrating external APIs, calculators, search engines, and python interpreters to execute actions beyond pure language modeling.
      • Planning: Utilizing formal description languages (e.g., PDDL) and search algorithms (DFS, MCTS, A*) for goal decomposition and environment state tracking.
      • Distillation: Transferring teacher-generated step-by-step rationales into compact models via self-distillation, multi-chain training, and process reward optimization.

    3. Future Directions & Challenges:

      • Multimodal and video reasoning, faithful error detection and correction, and uncovering theoretical mechanisms governing emergence and computational expressivity.

  3. Knowl 3 — Trade-Offs in XoT Prompt Construction Paradigms

    model/method

    Prompt construction approaches for Generalized Chain-of-Thought fall into three paradigms with distinct operational trade-offs:

    • Manual Prompting: Employs human annotators to write explicit reasoning chains in natural language (e.g., Few-shot CoT) or code/logic (e.g., Program-aided Language models, Program of Thoughts). While it achieves strong task accuracy by providing clear reasoning demonstrations, it incurs substantial manual labor costs and exhibits poor cross-domain transferability.
    • Automatic Prompting: Generates reasoning steps without human annotation using zero-shot triggers (e.g., appending "Let's think step by step") or by clustering model-generated rationales (e.g., Auto-CoT, RePrompting). It eliminates labor costs and enables cross-domain adaptation, but suffers from instability and error cascading due to the absence of supervised guidance.
    • Semi-automatic Prompting: Combines a minimal seed set of human annotations with automated bootstrapping, iterative expansion, or reinforcement learning/policy gradient optimization (e.g., AutoMate CoT, Synthetic Prompting). This paradigm strikes a practical balance by maintaining competitive reasoning accuracy while minimizing human annotation requirements.

  4. Knowl 4 — Topological Reasoning Variants Across Chain, Tree, and Graph Structures

    model/method

    Generalized Chain-of-Thought (XoT) extends sequential reasoning across three primary topological structures:

    • Chain Structures: Linear step-by-step generation. Beyond natural language, reasoning steps can be formalized in programming languages (e.g., Program of Thoughts / PoT, Program-Aided Language models / PAL) or declarative logic (e.g., LINC, SatLM). Decoupling intermediate reasoning from execution via deterministic external interpreters eliminates arithmetic and logical calculation errors. However, linear chains cannot explore alternative reasoning branches or backtrack.
    • Tree Structures: Organize reasoning into branching decision trees where models explore multiple intermediate paths using search algorithms such as breadth-first search, depth-first search, or Monte Carlo Tree Search (e.g., Tree-of-Thoughts / ToT, ProbTree). Tree structures allow global exploration and backtracking to resolve dead ends, but require explicit state definitions and problem-specific decomposition rules, limiting generalizability.
    • Graph Structures: Introduce multi-parent links, cycles, and NN-to-11 aggregation nodes (e.g., Graph of Thoughts / GoT, ResPrompt). Graphs permit merging multiple intermediate findings and performing self-verification over complex relational dependencies, but introduce complex control flow overhead and depend heavily on custom state representations.

  5. Knowl 5 — Reasoning Enhancement Paradigms for Generalized Chain-of-Thought

    model/method

    Five primary enhancement paradigms improve reasoning fidelity, efficiency, and robustness in Generalized Chain-of-Thought:

    • Verify and Refine: Employs self-critique, secondary critic models, backward (abductive) verification, or deductive filtering (e.g., Natural Program, Deductive Beam Search) to detect intermediate inconsistencies and iteratively refine flawed reasoning chains.
    • Question Decomposition: Divides complex queries into a sequence of simpler sub-questions via top-down hierarchical splitting (e.g., Least-to-Most prompting, Decomposed Prompting) or bottom-up prerequisite aggregation (e.g., Socratic Questioning), passing resolved sub-answers to downstream reasoning steps.
    • Knowledge Enhancement: Mitigates factual hallucinations by prompting the model for introspective parametric recall or integrating non-parametric external retrieval (retriever modules, web search, knowledge graphs), interleaving retrieval queries directly within reasoning steps.
    • Self-Ensemble: Leverages generation stochasticity by sampling multiple reasoning paths and aggregating final answers via majority voting (Self-Consistency), complexity weighting, step-level filtering, multi-prompt ensembling, or multi-agent debate (MAD).
    • Efficient Reasoning: Reduces latency and computational cost through parallel sub-problem execution (Skeleton-of-Thought), draft-model speculative decoding, dynamic sampling frequency adaptation, and uncertainty-based selective annotation.

  6. Knowl 6 — Distillation of Step-by-Step Reasoning Capabilities into Smaller Language Models

    model/method

    While chain-of-thought capabilities emerge primarily in large-scale language models (typically ≥100B\ge 100\text{B} parameters), step-by-step reasoning can be distilled into compact models using specialized training paradigms:

    • Multi-Chain Distillation: Sampling diverse reasoning trajectories per instance from teacher LLMs and filtering them via self-consistency to train student models on step-by-step rationales (e.g., Distilling Step-by-Step, Symbolic CoT Distillation).
    • Counterfactual and Contrastive Objectives: Employing contrastive decoding or counterfactual reasoning objectives during student supervision to prevent small models from memorizing superficial rationale shortcuts (e.g., SCOTT).
    • Trajectory Preference Optimization: Optimizing student reasoning paths using Proximal Policy Optimization (PPO) or Direct Preference Optimization (DPO) guided by step-level process reward models or Monte Carlo tree search evaluations (e.g., DialCoT, Math-Shepherd).
    • Hybrid Natural Language and Code Supervision: Distilling reasoning rationales across both textual explanations and executable code representations.
    • Specialization Trade-off: Fine-tuning compact models on domain-specific reasoning chains can improve task-specific accuracy but risks degrading general out-of-domain conversational and zero-shot capabilities.

  7. Knowl 7 — Benchmark Landscape for Evaluating Multi-Domain LLM Reasoning

    data/table

    Evaluation benchmarks for LLM reasoning are structured into five key reasoning domains, spanning distinct input modalities, output formalisms, and reasoning types:

    Domain Representative Datasets Formats Reasoning Focus
    Mathematical GSM8K, SVAMP, MATH, Text, Tables →\to Multi-step arithmetic, programmatic
    MultiArith, FinQA, DROP Numbers, Equations calculation, financial tabular reasoning
    Commonsense CommonsenseQA, ARC, Questions, Scenarios →\to Physical intuition, multi-hop world
    PIQA, StrategyQA Options, Yes/No knowledge, counterfactual commonsense
    Symbolic Last Letter Concat, Lists, Strings →\to Rule-based operations, coin flip,
    Coin Flip, BIG-bench Transformed Tokens algorithmic state simulation
    Logical LogiQA, ReClor, FOLIO, Premises, Rules →\to Deductive entailment proofs,
    ProofWriter, DEER Proofs, Classifications first-order logic, inductive rules
    Multimodal ScienceQA, VisualCOMET, Images/Videos + Text →\to Visual QA with rationales, video
    CLEVRER, STAR, NExT-QA Text, Event Predictions causal and temporal reasoning

    These benchmarks test capabilities ranging from exact symbolic execution and theorem-driven deductions to multi-hop contextual reasoning over text, tabular data, and video streams.

  8. Knowl 8 — Empirical Performance of XoT Reasoning Variants Across Foundation LLM Backbones

    data/table

    Empirical evaluations of generalized chain-of-thought methods across mathematical, commonsense, and symbolic benchmarks illustrate the impact of step-by-step decomposition, code rationales, and ensemble verification:

    Method Setting Backbone GSM8K SVAMP CSQA LastLetterConcat
    Standard I-O Prompting Few-shot text-davinci-002 19.7 69.9 79.5 5.8
    Few-shot CoT Few-shot text-davinci-002 63.1 76.4 73.5 77.5
    Program of Thoughts (PoT) Few-shot text-davinci-002 80.0 89.1 - -
    Few-shot CoT Few-shot text-davinci-003 66.8 69.1 - -
    Self-Consistency (SC) Few-shot text-davinci-003 67.9 83.1 - -
    Progressive-Hint (PHP) Few-shot text-davinci-003 79.0 84.7 - -
    FOBAR Few-shot text-davinci-003 79.5 86.0 - -
    Few-shot CoT Few-shot code-davinci-002 60.1 75.8 79.0 70.4
    Self-Consistency (SC) Few-shot code-davinci-002 78.0 86.8 81.5 73.4
    Program-Aided LM (PAL) Few-shot code-davinci-002 72.0 79.4 - -
    DIVERSE Few-shot code-davinci-002 82.3 87.0 79.9 -
    Least-to-Most Few-shot code-davinci-002 68.0 - - 94.0
    Few-shot CoT Few-shot gpt-3.5-turbo 76.5 81.9 78.0 73.2
    Self-Consistency (SC) Few-shot gpt-3.5-turbo 81.9 86.4 - -
    Verify CoT Few-shot gpt-3.5-turbo 86.0 - - 92.6
    RCoT Few-shot gpt-3.5-turbo 84.6 84.9 - -
    Zero-shot CoT Zero-shot text-davinci-002 40.5 63.7 64.0 57.6
    Auto-CoT Zero-shot text-davinci-002 47.9 69.5 74.4 59.7
    Plan-and-Solve Zero-shot text-davinci-003 58.2 72.0 65.2 64.8
    RCoT Zero-shot gpt-3.5-turbo 82.0 79.6 - -

    Key takeaways from these results:

    1. Standard few-shot input-output (I-O) prompting fails on multi-step arithmetic (GSM8K: 19.7%) and symbolic manipulation (LastLetterConcat: 5.8%), while natural language Few-shot CoT achieves massive gains (63.1% and 77.5%, respectively).
    2. Programmatic rationales executed via external interpreters (PoT, PAL) outperform standard text rationales on mathematical tasks by offloading calculation.
    3. Search, verification, and ensemble aggregation methods (Self-Consistency, DIVERSE, Verify CoT, RCoT) substantially improve accuracy over single-pass greedy generation across backbones.

  9. Knowl 9 — Hypotheses on the Code-Data Origin and Emergence Mechanism of CoT Reasoning

    theoretical result

    The origin of chain-of-thought capabilities in large language models remains an active theoretical and empirical investigation centered on the following findings:

    • Impact of Code Pre-training: Early large language models trained predominantly on natural language text (e.g., original GPT-3 davinci, OPT) generally fail to perform effective multi-step chain-of-thought reasoning. Conversely, models pre-trained with substantial dedicated code corpora (e.g., GPT-3.5, LLaMA-2 with ~8% code) natively exhibit strong CoT reasoning capabilities. Pre-training on structured code enhances general reasoning and variable tracking, whereas incorporating code during instruction fine-tuning primarily provides task-specific reasoning improvements.
    • Theoretical Expressive Capacity: Incorporating intermediate reasoning tokens expands the computational expressivity of transformer architectures, allowing fixed-depth networks to solve problems outside the complexity classes computable in a single constant-depth forward pass.
    • Emergence Dynamics: Open questions persist regarding whether chain-of-thought reasoning represents a discontinuous emergent ability arising at critical parameter scales or an apparent artifact of non-linear multi-step evaluation metrics.

  10. Knowl 10 — Limitations of Self-Correction and Intermediate Reasoning Feedback in LLMs

    limitation

    Current Generalized Chain-of-Thought systems face core limitations in self-correction and feedback reliability:

    • Inability to Self-Correct Without External Grounding: When models evaluate their own intermediate steps without external execution or oracle feedback, they frequently fail to detect logical errors or reinforce invalid initial premises due to self-hallucination and confirmation bias within their capability boundaries.
    • Error Cascading: Reasoning steps in linear or deep branching structures depend sequentially on antecedent outputs. A single undetected factual or deductive error in an early step leads to irrecoverable cascading errors throughout downstream sub-problems.
    • Constraint of Rule-Based Verification: While external tools (deductive verifiers, code interpreters, task-specific critics) prevent calculation errors, defining comprehensive, generalizable verification rules for open-ended, multi-domain, and non-symbolic tasks remains an open challenge.

Coverage note — None was omitted; all major contributions including the XoT taxonomy, mathematical formulations, prompt construction trade-offs, topological variants, enhancement paradigms, distillation methods, benchmark classifications, empirical data, theoretical code-origin hypotheses, and self-correction limitations are fully covered.

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Citation

MLA
Chu, Z., et al. “Navigate Through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future”. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2024, pp. 1173–203, https://doi.org/10.18653/v1/2024.acl-long.65.
APA
Chu, Z., Chen, J., Chen, Q., Yu, W., He, T., Wang, H., Peng, W., Liu, M., (秦兵), B. Q., & Liu, T. (2024). Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 1173–1203. https://doi.org/10.18653/v1/2024.acl-long.65
Chicago
Chu, Z., J. Chen, Q. Chen, et al. 2024. “Navigate Through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future”. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 1173–1203. https://doi.org/10.18653/v1/2024.acl-long.65.
Harvard
Chu, Z. et al. (2024) “Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future”, Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). Association for Computational Linguistics, pp. 1173–1203. Available at: https://doi.org/10.18653/v1/2024.acl-long.65.
Vancouver
1. Chu Z, Chen J, Chen Q, Yu W, He T, Wang H, Peng W, Liu M, (秦兵) BQ, Liu T (2024) Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future. In: Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). Association for Computational Linguistics, pp 1173–1203

BibTeX

@inproceedings{chu-etal-2024-navigate,
    title = "Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future",
    author = "Chu, Zheng  and
      Chen, Jingchang  and
      Chen, Qianglong  and
      Yu, Weijiang  and
      He, Tao  and
      Wang, Haotian  and
      Peng, Weihua  and
      Liu, Ming  and
      Qin, Bing  and
      Liu, Ting",
    editor = "Ku, Lun-Wei  and
      Martins, Andre  and
      Srikumar, Vivek",
    booktitle = "Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = aug,
    year = "2024",
    address = "Bangkok, Thailand",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2024.acl-long.65/",
    doi = "10.18653/v1/2024.acl-long.65",
    pages = "1173--1203"
}
Metadata:ACL Anthology

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