大语言模型在数学推理中的研究进展

doi:10.19678/j.issn.1000-3428.0069590

摘要/Abstract

摘要： 【目的】全面概述大语言模型在数学推理中的研究进展、机制原理以及应用趋势，为后续开展相关研究提供参考借鉴。【文献范围】选取与大语言模型在数学推理领域相关的122篇文献。【方法】系统描述了数学推理问题的类型及其数据集，分别从增强模型推理能力的策略和思维链提示方法这两方面深入解析各技术的原理、应用价值和存在问题。通过定性分析，并提出未来可能的研究方向。【局限】大语言模型相关研究发展迅速，相关调研工作可能未覆盖完整。【结论】基于思维链提示技术、微调、利用编程语言等外部工具和验证机制等方法可以有效提升大语言模型的数学推理能力，特别是基于思维链提示的技术成为了当前大语言模型的主要研究热点。未来研究工作可在进一步提升大语言模型的推理能力，解决数学推理问题方法展开深入研究。

Abstract: 【Objective】This review comprehensively outlines the current state, underlying mechanisms, and trends in applications of large language models in mathematical reasoning capabilities, offering references for future research in this area. 【Scope】This analysis incorporates 122 publications related to mathematical reasoning with large language models. 【Method】The paper systematically describes the types of mathematical reasoning issues and their datasets, delving into the principles, utility, and strategies for enhancing model reasoning capabilities and methods of chain-of-thought prompting. Through qualitative analysis, it provides a thorough overview of research progress in the field of mathematical reasoning with large language models and suggests potential future research directions. 【Limitations】Rapid developments in research related to large models may mean this review does not cover all pertinent studies. 【Conclusion】Methods such as chain-of-thought prompting, fine-tuning, the utilization of programming languages and other external tools, and verification mechanisms can effectively enhance the mathematical reasoning capabilities of large language models, with chain-of-thought prompting techniques in particular becoming a major focus of current research in large language models. Future studies could further enhance the reasoning capabilities of large language models and develop methods for solving mathematical problems.

罗焕坤, 葛一烽, 刘帅. 大语言模型在数学推理中的研究进展[J]. 计算机工程, doi: 10.19678/j.issn.1000-3428.0069590.

Luo HuanKun, Ge YiFeng , Liu Shuai. Research Progress of Large Language Models in Mathematical Reasoning[J]. Computer Engineering, doi: 10.19678/j.issn.1000-3428.0069590.

参考文献

[1] Achiam J, Adler S, Agarwal S, et al. Gpt-4 technical report[J]. arXiv preprint arXiv:2303.08774, 2023.
[2] Lu P, Qiu L, Yu W, et al. A Survey of Deep Learning for Mathematical Reasoning[C]//The 61st Annual Meeting Of The Association For Computational Linguistics. 2023.
[ 3 ] Miao S Y, Liang C C, Su K Y. A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers[C]//Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020: 975-984.
[4] Patel A, Bhattamishra S, Goyal N. Are NLP Models really able to Solve Simple Math Word Problems?[C]//Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. Association for Computational Linguistics, 2021.
[5] Mishra S, Finlayson M, Lu P, et al. LĪLA: A Unified Benchmark for Mathematical Reasoning[C]//2022 Conference on Empirical Methods in Natural Language Processing, EMNLP 2022. 2022.
[6] Wei T, Luan J, Liu W, et al. CMATH: can your language model pass chinese elementary school math test[J]. arXiv preprint arXiv:2306.16636, 2023.
[7] Zhong W, Cui R, Guo Y, et al. Agieval: A human-centric benchmark for evaluating foundation models[J]. arXiv preprint arXiv:2304.06364, 2023.
[8]Raiyan S R, Faiyaz M N, Kabir S M J, et al. Math Word Problem Solving by Generating Linguistic Variants of Problem Statements[C]//Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 4: Student Research Workshop). 2023: 362-378.
[9] Koncel-Kedziorski R, Roy S, Amini A, et al. MAWPS: A math word problem repository[C]//Proceedings of the 2016 conference of the north american chapter of the association for computational linguistics: human language technologies. 2016: 1152-1157.
[10] Amini A, Gabriel S, Lin S, et al. MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms[C]//Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers). 2019: 2357-2367.
[11] Qin J, Liang X, Hong Y, et al. Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks[C]//Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021: 5870-5881.
[12] Cobbe K, Kosaraju V, Bavarian M, et al. Training verifiers to solve math word problems[J]. arXiv preprint arXiv:2110.14168, 2021.[13] Gao L, Madaan A, Zhou S, et al. Pal: Program-aided language models[C]//International Conference on Machine Learning. PMLR, 2023: 10764-10799.
[14] Hendrycks D, Burns C, Kadavath S, et al. Measuring Mathematical Problem Solving With the MATH Dataset[C]//Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2). 2021.
[ 15 ] Zhang B, Zhou K, Wei X, et al. Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning[C]//Thirty-seventh Conference on Neural Information Processing Systems Datasets and Benchmarks Track. 2023.
[16]Lightman H, Kosaraju V, Burda Y, et al. Let's Verify Step by Step[C]//The Twelfth International Conference on Learning Representations. 2023.
[17]Sawada T, Paleka D, Havrilla A, et al. ARB: Advanced Reasoning Benchmark for Large Language Models[C]//The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'23. 2023.
[18] Frieder S, Pinchetti L, Chevalier A, et al. Mathematical Capabilities of ChatGPT[C]//Thirty-seventh Conference on Neural Information Processing Systems Datasets and Benchmarks Track. 2023.
[19]Chen W, Yin M, Ku M, et al. TheoremQA: A Theorem-driven Question Answering Dataset[C]//Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing. 2023: 7889-7901.
[20]Yue X, Qu X, Zhang G, et al. MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning[C]//The Twelfth International Conference on Learning Representations. 2023.
[ 21 ] Lu P, Qiu L, Chang K W, et al. Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning[C]//The Eleventh International Conference on Learning Representations. 2022.
[22] Robinson J A. A machine-oriented logic based on the resolution principle[J]. Journal of the ACM (JACM), 1965, 12(1): 23-41.
[23] KNUTH D E, BENDIX P B. Simple Word Problems in Universal Algebras[C]//Computational Problems in Abstract Algebra: Proceedings of a Conference Held at Oxford Under the Auspices of the Science Research Council Atlas Computer Laboratory, 29th August to 2nd September 1967. Elsevier, 2014: 263.
[24] Megill N, Wheeler D A. Metamath: a computer language for mathematical proofs[M]. Lulu. com, 2019.
[25] de Moura L, Kong S, Avigad J, et al. The Lean theorem prover (system description)[C]//Automated Deduction-CADE-25: 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings 25. Springer International Publishing, 2015: 378-388.
[26] Isabelle: A generic theorem prover[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994.
[27] Polu S, Sutskever I. Generative language modeling for automated theorem proving[J]. arXiv preprint arXiv:2009.03393, 2020.
[28] Zheng K, Han J M, Polu S. miniF2F: a cross-system benchmark for formal Olympiad-level mathematics[C]//International Conference on Learning Representations. 2021.
[29] Megill N, Wheeler D A. Metamath: a computer language for mathematical proofs[M]. Lulu. com, 2019.
[ 30 ] Bansal K, Loos S, Rabe M, et al. Holist: An environment for machine learning of higher order logic theorem proving[C]//International Conference on Machine Learning. PMLR, 2019: 454-463.
[31] Yang K, Deng J. Learning to prove theorems via interacting with proof assistants[C]//International Conference on Machine Learning. PMLR, 2019: 6984-6994.
[32] Gelernter H, Hansen J R, Loveland D W. Empirical explorations of the geometry theorem machine[C]//Papers presented at the May 3-5, 1960, western joint IRE-AIEE-ACM computer conference. 1960: 143-149.
[33] Trinh T H, Wu Y, Le Q V, et al. Solving olympiad geometry without human demonstrations[J]. Nature, 2024, 625(7995): 476-482.
[34] Seo M, Hajishirzi H, Farhadi A, et al. Solving geometry problems: Combining text and diagram interpretation[C]//Proceedings of the 2015 conference on empirical methods in natural language processing. 2015: 1466-1476.
[35] Alvin C, Gulwani S, Majumdar R, et al. Synthesis of solutions for shaded area geometry problems[C]//The Thirtieth International Flairs Conference. 2017.
[36] Sachan M, Dubey K, Xing E. From textbooks to knowledge: A case study in harvesting axiomatic knowledge from textbooks to solve geometry problems[C]//Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing. 2017:773-784.
[37] Sachan M, Xing E. Learning to solve geometry problems from natural language demonstrations in textbooks[C]//Proceedings of the 6th Joint Conference on Lexical and Computational Semantics (* SEM 2017). 2017: 251-261.
[38] Lu P, Gong R, Jiang S, et al. Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning[C]//Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021: 6774-6786.
[39] Chen J, Tang J, Qin J, et al. GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning[C]//Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021. 2021: 513-523.
[ 40 ] Chen J, Li T, Qin J, et al. UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression[C]//Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing. 2022: 3313-3323.
[41]Lu P, Bansal H, Xia T, et al. MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts[C]//The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'23. 2023.
[42] Masry A, Do X L, Tan J Q, et al. ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning[C]//Findings of the Association for Computational Linguistics: ACL 2022. 2022: 2263-2279.
[43] Kafle K, Price B, Cohen S, et al. Dvqa: Understanding data visualizations via question answering[C]//Proceedings of the IEEE conference on computer vision and pattern recognition. 2018: 5648-5656.
[44] Chaudhry R, Shekhar S, Gupta U, et al. Leaf-qa: Locate, encode & attend for figure question answering[C]//Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. 2020: 3512-3521.
[45] Rashkin H, Sap M, Allaway E, et al. Event2Mind: Commonsense Inference on Events, Intents, and Reactions[C]//Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics. 2018.
[ 46 ] Wang C, Liang S, Zhang Y, et al. Does it Make Sense? And Why? A Pilot Study for Sense Making and Explanation[C]//Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. 2019: 4020-4026.
[47] Talmor A, Herzig J, Lourie N, et al. COMMONSENSEQA: A Question Answering Challenge Targeting Commonsense Knowledge[C]//Proceedings of NAACL-HLT. 2019: 4149-4158.
[48] Zellers R, Holtzman A, Bisk Y, et al. HellaSwag: Can a Machine Really Finish Your Sentence?[C]//Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. Association for Computational Linguistics, 2019.
[49] Zhou B, Khashabi D, Ning Q, et al. “Going on a vacation” takes longer than “Going for a walk”: A Study of Temporal Commonsense Understanding[C]//Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). Association for Computational Linguistics, 2019.
[50] Geva M, Khashabi D, Segal E, et al. Did aristotle use a laptop? a question answering benchmark with implicit reasoning strategies[J]. Transactions of the Association for Computational Linguistics, 2021, 9: 346-361.
[51] Talmor A, Yoran O, Le Bras R, et al. CommonsenseQA 2.0: Exposing the Limits of AI through Gamification[C]//Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 1). 2021.
[52] Wei J, Wang X, Schuurmans D, et al. Chain-of-Thought Prompting Elicits Reasoning in Large Language Models[C]//Advances in Neural Information Processing Systems. 2022.
[53] Srivastava A, Rastogi A, Rao A, et al. Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models[J]. Transactions on Machine Learning Research, 2023.
[ 54 ] Suzgun M, Scales N, Schärli N, et al. Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them[C]//Findings of the Association for Computational Linguistics: ACL 2023. 2023: 13003-13051.
[ 55 ] Liu J, Cui L, Liu H, et al. LogiQA: a challenge dataset for machine reading comprehension with logical reasoning[C]//Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence. 2021: 3622-3628.
[56] Yu W, Jiang Z, Dong Y, et al. ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning[C]//International Conference on Learning Representations. 2019.
[57] Zhong W, Wang S, Tang D, et al. Analytical reasoning of text[C]//Findings of the Association for Computational Linguistics: NAACL 2022. 2022: 2306-2319.
[58] Kasneci E, Sessler K, Küchemann S, et al. ChatGPT for good? On opportunities and challenges of large language models for education[J]. Learning and Individual Differences, 2023, 103: 102274.
[59] Chowdhery A, Narang S, Devlin J, et al. Palm: Scaling language modeling with pathways[J]. Journal of Machine Learning Research, 2023, 24(240): 1-113.
[60]Touvron H, Lavril T, Izacard G, et al. Llama: Open and efficient foundation language models[J]. arXiv preprint arXiv:2302.13971, 2023.
[61] Team G, Anil R, Borgeaud S, et al. Gemini: a family of highly capable multimodal models[J]. arXiv preprint arXiv:2312.11805, 2023.
[62] Vaswani A, Shazeer N, Parmar N, et al. Attention is all you need[J]. Advances in neural information processing systems, 2017, 30.
[63] Brown T, Mann B, Ryder N, et al. Language models are few-shot learners[J]. Advances in neural information processing systems, 2020, 33: 1877-1901.
[64] Christiano P F, Leike J, Brown T, et al. Deep reinforcement learning from human preferences[J]. Advances in neural information processing systems, 2017, 30.
[65] Chung H W, Hou L, Longpre S, et al. Scaling instruction-finetuned language models[J]. Journal of Machine Learning Research, 2024, 25(70): 1-53.
[66] Penedo G, Malartic Q, Hesslow D, et al. The RefinedWeb dataset for Falcon LLM: outperforming curated corpora with web data, and web data only[J]. arXiv preprint arXiv:2306.01116, 2023.
[67] Du Z, Qian Y, Liu X, et al. GLM: General Language Model Pretraining with Autoregressive Blank Infilling[C]//Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022: 320-335.
[68] Yang A, Xiao B, Wang B, et al. Baichuan 2: Open large-scale language models[J]. arXiv preprint arXiv:2309.10305, 2023.
[69] Touvron H, Martin L, Stone K, et al. Llama 2: Open Foundation and Fine-Tuned Chat Models[J]. arXiv e-prints, 2023: arXiv: 2307.09288.
[70] Zeng A, Liu X, Du Z, et al. GLM-130B: An Open Bilingual Pre-trained Model[C]//The Eleventh International Conference on Learning Representations. 2022.
[71] meta-llama. llama3[EB/OL]. [2024-04-18]. https://github.com/meta-llama/llama3.
[72] Sun Y, Wang S, Feng S, et al. Ernie 3.0: Large-scale knowledge enhanced pre-training for language understanding and generation[J]. arXiv preprint arXiv:2107.02137, 2021.
[73] Zeng W, Ren X, Su T, et al. PanGu-$\alpha $: Large-scale Autoregressive Pretrained Chinese Language Models with Auto-parallel Computation[J]. arXiv e-prints, 2021: arXiv: 2104.12369.
[74]Radford A, Wu J, Child R, et al. Language Models are Unsupervised Multitask Learners[C]//OSDI'04: Sixth Symposium on Operating System Design and Implementation. 137-150.
[75] Brown T B, Mann B, Ryder N, et al. Language Models are Few-Shot Learners[J]. arXiv preprint arXiv:2005.14165, 2020.
[76] Zong M, Krishnamachari B. Solving math word problems concerning systems of equations with gpt-3[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2023, 37(13): 15972-15979.
[77] Wu T, He S, Liu J, et al. A Brief Overview of ChatGPT: The History, Status Quo and Potential Future Development[J]. IEEE/CAA Journal of Automatica Sinica, 2023, 10(5): 1122-1136.
[78] Shakarian P, Koyyalamudi A, Ngu N, et al. An Independent Evaluation of ChatGPT on MathematicalWord Problems (MWP)[C]//CEUR Workshop Proceedings. CEUR-WS, 2023, 3433.
[79] Cheng V, Zhang Y. Analyzing ChatGPT’s mathematical deficiencies: Insights and contributions[C]//Proceedings of the 35th Conference on Computational Linguistics and Speech Processing (ROCLING 2023). 2023: 188-193.
[80] Ouyang L, Wu J, Jiang X, et al. Training language models to follow instructions with human feedback[J]. Advances in NeuralInformation Processing Systems, 2022, 35: 27730-27744.
[81] Lewkowycz A, Andreassen A J, Dohan D, et al. Solving Quantitative Reasoning Problems with Language Models[C]//Advances in Neural Information Processing Systems. 2022.
[82] Gu S. Llms as potential brainstorming partners for math and science problems[J]. arXiv preprint arXiv:2310.10677, 2023.
[83] Yang Z, Li L, Lin K, et al. The dawn of lmms: Preliminary explorations with gpt-4v (ision)[J]. arXiv preprint arXiv:2309.17421, 2023, 9(1): 1.
[ 84 ]Zhang M, Wang Z, Yang Z, et al. Interpretable Math Word Problem Solution Generation via Step-by-step Planning[C]//Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.
[85] Yue X, Qu X, Zhang G, et al. MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning[C]//The Twelfth International Conference on Learning Representations. 2023.
[86] Wang Y, Liu X, Shi S. Deep neural solver for math word problems[C]//Proceedings of the 2017 conference on empirical methods in natural language processing. 2017: 845-854.
[87] Ling W, Yogatama D, Dyer C, et al. Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems[C]//Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2017: 158-167.
[88] He-Yueya J, Poesia G, Wang R, et al. Solving Math Word Problems by Combining Language Models With Symbolic Solvers[C]//The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'23. 2023.
[89] Chen W, Ma X, Wang X, et al. Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks[J]. Transactions on Machine Learning Research, 2023.
[90] Chen M, Tworek J, Jun H, et al. Evaluating large language models trained on code[J]. arXiv preprint arXiv:2107.03374, 2021.
[91] Bin Y, SHI W, Ding Y, et al. Solving Math Word Problems with Reexamination[C]//The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'23. 2023.
[ 92 ] Zhu X, Wang J, Zhang L, et al. Solving Math Word Problems via Cooperative Reasoning induced Language Models[C]//Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023: 4471-4485.
[93] Wu Y, Jia F, Zhang S, et al. An empirical study on challenging math problem solving with gpt-4[J]. arXiv preprint arXiv:2306.01337, 2023.
[94] Peng R, Yang C, Huang L, et al. A Numeracy-Enhanced Decoding for Solving Math Word Problem[C]//CCF International Conference on Natural Language Processing and Chinese Computing. Cham: Springer Nature Switzerland, 2023: 111-122.
[95] Yao J, Zhou Z, Wang Q. Solving math word problem with problem type classification[C]//CCF International Conference on Natural Language Processing and Chinese Computing. Cham: Springer Nature Switzerland, 2023: 123-134.
[96] Jiang X, Zheng Z, Lyu C, et al. Treebert: A tree-based pre-trained model for programming language[C]//Uncertainty in artificial intelligence. PMLR, 2021: 54-63.
[97] Huang W, Xiao J. A New Encoder Using Character and Word Feature Fusion for Chinese Math Word Problem Solving[C]//CCF International Conference on Natural Language Processing and Chinese Computing. Cham: Springer Nature Switzerland, 2023: 313-324.
[98]Imani S, Du L, Shrivastava H. MathPrompter: Mathematical Reasoning using Large Language Models[C]//ICLR 2023 Workshop on Trustworthy and Reliable Large-Scale Machine Learning Models. 2023.
[99] Fu Y, Peng H, Sabharwal A, et al. Complexity-based prompting for multi-step reasoning[C]//The Eleventh International Conference on Learning Representations. 2022.
[100] Roy S, Roth D. Solving General Arithmetic Word Problems[C]//Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing. 2015: 1743-1752.
[101] Kojima T, Gu S S, Reid M, et al. Large Language Models are Zero-Shot Reasoners[C]//ICML 2022 Workshop on KnowledgeRetrieval and Language Models. 2022.
[102] Zhang Z, Zhang A, Li M, et al. Automatic Chain of Thought Prompting in Large Language Models[C]//The Eleventh International Conference on Learning Representations. 2022.
[103]Wan X, Sun R, Dai H, et al. Better Zero-Shot Reasoning with Self-Adaptive Prompting[C]//Findings of the Association for Computational Linguistics: ACL 2023. 2023: 3493-3514.
[104]Wang L, Xu W, Lan Y, et al. Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models[C]//Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023: 2609-2634.
[105] Liu P, Yuan W, Fu J, et al. Pre-train, prompt, and predict: A systematic survey of prompting methods in natural language processing[J]. ACM Computing Surveys, 2023, 55(9): 1-35.
[106 ]Shao Z, Gong Y, Shen Y, et al. Synthetic prompting: generating chain-of-thought demonstrations for large language models[C]//Proceedings of the 40th International Conference on Machine Learning. 2023: 30706-30775.
[107] KaShun S, Diao S, Zhang T. Automatic Prompt Augmentation and Selection with Chain-of-Thought from Labeled Data[C]//The 2023 Conference on Empirical Methods in Natural Language Processing. 2023.
[108] Wang X, Wei J, Schuurmans D, et al. Self-Consistency Improves Chain of Thought Reasoning in Language Models[C]//The Eleventh International Conference on Learning Representations. 2022.
[109] Hu H, Lu H, Zhang H, et al. Chain-of-symbol prompting elicits planning in large langauge models[J]. arXiv preprint arXiv:2305.10276, 2023.
[110] Yao S, Yu D, Zhao J, et al. Tree of Thoughts: Deliberate Problem Solving with Large Language Models[C]//Thirty-seventh Conference on Neural Information Processing Systems. 2023.
[111] Mo S, Xin M. Tree of uncertain thoughts reasoning for large language models[C]//ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2024: 12742-12746.
[112]Ning X, Lin Z, Zhou Z, et al. Skeleton-of-Thought: Large Language Models Can Do Parallel Decoding[C]//The Twelfth International Conference on Learning Representations. 2023.
[113]Besta M, Blach N, Kubicek A, et al. Graph of thoughts: Solving elaborate problems with large language models[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024, 38(16): 17682-17690.
[114] Lei B, Liao C, Ding C. Boosting logical reasoning in large language models through a new framework: The graph of thought[J]. arXiv preprint arXiv:2308.08614, 2023.
[115] 刘明, 吴忠明, 廖剑, 等. 大语言模型的教育应用: 原理, 现状与挑战*——从轻量级 BERT 到对话式 ChatGPT[J]. Modern Educational Technology, 2023, 33(8).
[116] Baidoo-Anu D, Ansah L O. Education in the era of generative artificial intelligence (AI): Understanding the potential benefits of ChatGPT in promoting teaching and learning[J]. Journal of AI, 2023, 7(1): 52-62.
[117] 刘宝存, 苟鸣瀚. ChatGPT 等新一代人工智能工具对教育科研的影响及对策[J]. Journal of Soochow University Educational Science Edition, 2023, 11(3).
[118] Wang C, Liu X, Awadallah A H. Cost-Effective Hyperparameter Optimization for Large Language Model Generation Inference[C]//AutoML Conference 2023. 2023.
[119] Cai T, Li Y, Geng Z, et al. Medusa: Simple llm inference acceleration framework with multiple decoding heads[J]. arXiv preprint arXiv:2401.10774, 2024.
[120] Wang Y, Rossi R A, Park N, et al. Large Generative Graph Models[J]. arXiv e-prints, 2024: arXiv: 2406.05109.
[121] Zhao H, Chen H, Yang F, et al. Explainability for large language models: A survey[J]. ACM Transactions on Intelligent Systems and Technology, 2024, 15(2): 1-38.
[122] Staab R, Vero M, Balunovic M, et al. Beyond Memorization: Violating Privacy via Inference with Large Language Models[C]//The Twelfth International Conference on Learning Representations. 2023.

选择文件类型/文献管理软件名称

选择包含的内容