Elamur Research⌕
☰
home / papers / 2024 / Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models

Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models

Paper · 2024 · Wenhao Shi, Zhiqiang Hu, Yi Bin et al.

Summary

Open-source multimodal LLMs such as LLaVA-1.5 handle general VQA well but struggle with math problems that depend on diagrams, charts, or tables. The authors argue that existing instruction-tuning sets offer too few questions per image to make full use of the visual content. They built MathV360K. First, they pooled 24 public QA datasets covering five task types: FQA, GPS, MWP, TQA and VQA. They then kept about 40K images using two ViT classifiers that rate image clarity and comprehension complexity, and balanced the selection across difficulty levels. Next, a vision-language model generated 320K additional question-answer pairs for these images. The new items include fresh questions about each image, harder multi-step questions, rephrased questions, and deliberately underspecified ones. Fine-tuning LLaVA-1.5-13B on this data produced Math-LLaVA. The model gains 19 points on the MathVista minitest split, approaches GPT-4V, and leads open models on Math-V and MathVerse. It also improves on MMMU. The work shows that careful data selection and synthesis can substantially boost visual math reasoning in open models.

Key points

  • MathV360K data: about 40K images with 360K QA pairs, made up of 40K selected seed pairs and 320K synthesized pairs.
    • The clarity and complexity classifiers were ViTs trained on 10K images labeled by GPT-4V.
    • Complexity levels 0–3 were sampled in a 2:3:4:1 ratio.
  • Augmentation strategies: AskImg (new questions mined from the image), CompQ (more complex questions), RephQ (rephrasing for logical consistency) and SimpQ (simplified, underspecified questions).
  • Ablation on MathVista: fine-tuning on 40K random samples scores 35.6%. Using selected data plus all augmentations reaches 46.6%, roughly an 11-point improvement. Training on the selected 40K alone (Math-LLaVA-DS) already adds 10.6%.
  • MMMU: Math-LLaVA scores 38.3, compared with 36.4 for LLaVA-1.5-13B, which indicates broader generalization.
  • Limitations and availability: the data has no intermediate reasoning steps. The code, data and model are released at github.com/HZQ950419/Math-LLaVA.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓National University of SingaporeSingapore · Singapore84 works · 32,204 citations🎓Singapore University of Technology and DesignSingapore · Singapore33 works · 10,760 citations🎓Tongji UniversityShanghai · China4 works · 2,022 citations🎓University of Electronic Science and Technology of ChinaChengdu · China8 works · 1,738 citations

📚 Shelves 6 Computer Science · 9,086 works Artificial Intelligence · 8,889 works Arts and Humanities · 9,296 works Language and Linguistics · 9,206 works Computer Vision and Pattern Recognition · 1,282 works Computational Theory and Mathematics · 116 works

🧭 Topics 3 Language models & pretraining · 1,343 works Reasoning · 510 works Vision & language · 269 works

Cite

Cite as Wenhao Shi, Zhiqiang Hu, Yi Bin, Junhua Liu, Yang Yang, See-Kiong Ng, Lidong Bing and Roy Ka-Wei Lee. 2024. Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models. Findings of the Association for Computational Linguistics: EMNLP 2024.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2024.findings-emnlp.268

@inproceedings{shi2024math,
  title = {{Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models}},
  author = {Wenhao Shi, Zhiqiang Hu, Yi Bin, Junhua Liu, Yang Yang, See-Kiong Ng, Lidong Bing and Roy Ka-Wei Lee},
  booktitle = {Findings of the Association for Computational Linguistics: EMNLP 2024},
  year = {2024},
  doi = {10.18653/v1/2024.findings-emnlp.268},
  url = {https://doi.org/10.18653/v1/2024.findings-emnlp.268}
}

References

73 references, 32 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Boyang Li, Pascale N Fung, and Steven Hoi. 2024. Instructblip: Towards general-purpose vision-language models with instruction tuning. Advances in Neural Information Processing Systems, 36.
  2. AI Anthropic. 2024. The claude 3 model family: Opus, sonnet, haiku. Claude-3 Model Card. find
  3. Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. 2015. Vqa: Visual question answering. In Proceedings of the IEEE international conference on computer vision, pages 2425–2433. find
  4. Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. 2023. Qwen-vl: A frontier large vision-language model with versatile abilities. CoRR, abs/2308.12966.
  5. Yi Bin, Mengqun Han, Wenhao Shi, Lei Wang, Yang Yang, See-Kiong Ng, and Heng Tao Shen. 2023. Non-autoregressive math word problem solver with unified tree structure. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 3290–3301. find
  6. Yi Bin, Wenhao Shi, Yujuan Ding, Zhiqiang Hu, Zheng Wang, Yang Yang, See-Kiong Ng, and Heng Tao Shen. 2024. Gallerygpt: Analyzing paintings with large multimodal models. In ACM Multimedia 2024. find
  7. Jie Cao and Jing Xiao. 2022. An augmented benchmark dataset for geometric question answering through dual parallel text encoding. In Proceedings of the 29th International Conference on Computational Linguistics, pages 1511–1520. find
  8. Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. 2021. An image is worth 16x16 words: Transformers for image recognition at scale. In 9th In…
  9. Jiahui Gao, Renjie Pi, Jipeng Zhang, Jiacheng Ye, Wanjun Zhong, Yufei Wang, Lanqing Hong, Jianhua Han, Hang Xu, Zhenguo Li, et al. 2023a. G-llava: Solving geometric problem with multi-modal large language model. arXiv preprint arXiv:2312.11370. find
  10. Peng Gao, Jiaming Han, Renrui Zhang, Ziyi Lin, Shijie Geng, Aojun Zhou, Wei Zhang, Pan Lu, Conghui He, Xiangyu Yue, et al. 2023b. Llama-adapter v2: Parameter-efficient visual instruction model. arXiv preprint arXiv:2304.15010. find
  11. Google. Gemini. https://gemini.google.com. ↗
  12. Zhibin Gou, Zhihong Shao, Yeyun Gong, Yelong Shen, Yujiu Yang, Minlie Huang, Nan Duan, and Weizhu Chen. 2023. Tora: A tool-integrated reasoning agent for mathematical problem solving. CoRR, abs/2309.17452.
  13. Shuaichen Chang, David Palzer, Jialin Li, Eric Fosler-Lussier, and Ningchuan Xiao. 2022. Mapqa: A dataset for question answering on choropleth maps. arXiv preprint arXiv:2211.08545. — [arXiv:2211.08545](https://arxiv.org/abs/2211.08545) find
  14. Yash Goyal, Tejas Khot, Douglas Summers-Stay, Dhruv Batra, and Devi Parikh. 2017. Making the v in vqa matter: Elevating the role of image understanding in visual question answering. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6904–6913.
  15. Feng Chen and Yujian Feng. 2023. Chain-of-thought prompt distillation for multimodal named entity and multimodal relation extraction. arXiv preprint arXiv:2306.14122. find
  16. Yanyang Guo, Fangkai Jiao, Zhiqi Shen, Liqiang Nie, and Mohan S. Kankanhalli. 2023. UNK-VQA: A dataset and A probe into multi-modal large models’ abstention ability. CoRR, abs/2310.10942. — [arXiv:2310.10942](https://arxiv.org/abs/2310.10942) find
  17. Jiaqi Chen, Tong Li, Jinghui Qin, Pan Lu, Liang Lin, Chongyu Chen, and Xiaodan Liang. 2022. UniGeo: Unifying geometry logical reasoning via reformulating mathematical expression. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 3313–3323.
  18. Danna Gurari, Qing Li, Abigale J Stangl, Anhong Guo, Chi Lin, Kristen Grauman, Jiebo Luo, and Jeffrey P Bigham. 2018. Vizwiz grand challenge: Answering visual questions from blind people. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3608–3617. find
  19. Jiaxing Chen, Yuxuan Liu, Dehu Li, Xiang An, Ziyong Feng, Yongle Zhao, and Yin Xie. 2024a. Plug-and-play grounding of reasoning in multimodal large language models. arXiv preprint arXiv:2403.19322. — [arXiv:2403.19322](https://arxiv.org/abs/2403.19322) find
  20. Shengding Hu, Yuge Tu, Xu Han, Chaoqun He, Ganqu Cui, Xiang Long, Zhi Zheng, Yewei Fang, Yuxiang Huang, Weilin Zhao, et al. 2024. Minicpm: Unveiling the potential of small language models with scalable training strategies. arXiv preprint arXiv:2404.06395.
  21. Lin Chen, Jinsong Li, Xiaoyi Dong, Pan Zhang, Yuhang Zang, Zehui Chen, Haodong Duan, Jiaqi Wang, Yu Qiao, Dahua Lin, et al. 2024b. Are we on the right way for evaluating large vision-language models? arXiv preprint arXiv:2403.20330.
  22. Wenliang Dai, Junnan Li, Dongxu Li, Anthony Meng Huat Tiong, Junqi Zhao, Weisheng Wang, Yushi Hu, Otilia Stretcu, Chun-Ta Lu, Krishnamurthy Viswanathan, Kenji Hata, Enming Luo, Ranjay Krishna, and Ariel Fuxman. 2023a. Visual program distillation: Distilling tools and programmatic reasoning into visi… — [arXiv:2312.03052](https://arxiv.org/abs/2312.03052) find
  23. Yushi Hu, Otilia Stretcu, Chun-Ta Lu, Krishnamurthy Viswanathan, Kenji Hata, Enming Luo, Ranjay Krishna, and Ariel Fuxman. 2023b. Visual program distillation: Distilling tools and programmatic reasoning into vision-language models. CoRR, abs/2312.03052. — [arXiv:2312.03052](https://arxiv.org/abs/2312.03052) find
  24. Hongzhan Lin, Ziyang Luo, Jing Ma, and Long Chen. 2023a. Beneath the surface: Unveiling harmful memes with multimodal reasoning distilled from large language models. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 9114–9128. find
  25. Kushal Kafle, Brian Price, Scott Cohen, and Christopher Kanan. 2018. Dvqa: Understanding data visualizations via question answering. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5648–5656. find
  26. Ziyi Lin, Chris Liu, Renrui Zhang, Peng Gao, Longtian Qiu, Han Xiao, Han Qiu, Chen Lin, Wenqi Shao, Keqin Chen, et al. 2023b. Sphinx: The joint mixing of weights, tasks, and visual embeddings for multi-modal large language models. arXiv preprint arXiv:2311.07575. — [arXiv:2311.07575](https://arxiv.org/abs/2311.07575) find
  27. Samira Ebrahimi Kahou, Vincent Michalski, Adam Atkinson, Ákos Kádár, Adam Trischler, and Yoshua Bengio. 2017. Figureqa: An annotated figure dataset for visual reasoning. arXiv preprint arXiv:1710.07300. find
  28. Aniruddha Kembhavi, Mike Salvato, Eric Kolve, Minjoon Seo, Hannaneh Hajishirzi, and Ali Farhadi. 2016. A diagram is worth a dozen images. In Computer Vision–ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11–14, 2016, Proceedings, Part IV 14, pages 235– 251.
  29. Aniruddha Kembhavi, Minjoon Seo, Dustin Schwenk, Jonghyun Choi, Ali Farhadi, and Hannaneh Hajishirzi. 2017. Are you smarter than a sixth grader? textbook question answering for multimodal machine comprehension. In Proceedings of the IEEE Conference on Computer Vision and Pattern recognition, pages 4… find
  30. Jason J Lau, Soumya Gayen, Asma Ben Abacha, and Dina Demner-Fushman. 2018. A dataset of clinically generated visual questions and answers about radiology images. Scientific data, 5(1):1–10. find
  31. Haoxuan Li, Zhengmao Yang, Yunshan Ma, Yi Bin, Yang Yang, and Tat-Seng Chua. 2024a. Mm-forecast: A multimodal approach to temporal event forecasting with large language models. In ACM Multimedia 2024. find
  32. Junnan Li, Dongxu Li, Caiming Xiong, and Steven Hoi. 2022. Blip: Bootstrapping language-image pre-training for unified vision-language understanding and generation. In International conference on machine learning, pages 12888–12900.
  33. Lei Li, Yuqi Wang, Runxin Xu, Peiyi Wang, Xiachong Feng, Lingpeng Kong, and Qi Liu. 2024b. Multimodal ArXiv: A dataset for improving scientific comprehension of large vision-language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics, pages 14369–14387…
  34. Zhuowan Li, Xingrui Wang, Elias Stengel-Eskin, Adam Kortylewski, Wufei Ma, Benjamin Van Durme, and Alan L Yuille. 2023. Super-clevr: A virtual benchmark to diagnose domain robustness in visual reasoning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1496… find
  35. Adam Dahlgren Lindström and Savitha Sam Abraham. 2022. Clevr-math: A dataset for compositional language, visual and mathematical reasoning. arXiv preprint arXiv:2208.05358. — [arXiv:2208.05358](https://arxiv.org/abs/2208.05358) find
  36. Haotian Liu, Chunyuan Li, Yuheng Li, and Yong Jae Lee. 2024. Improved baselines with visual instruction tuning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 26296–26306.
  37. Haotian Liu, Chunyuan Li, Qingyang Wu, and Yong Jae Lee. 2023. Visual instruction tuning. In Advances in Neural Information Processing Systems.
  38. Pan Lu, Hritik Bansal, Tony Xia, Jiacheng Liu, Chunyuan Li, Hannaneh Hajishirzi, Hao Cheng, Kai-Wei Chang, Michel Galley, and Jianfeng Gao. 2023. Mathvista: Evaluating math reasoning in visual contexts with gpt-4v, bard, and other large multimodal models. CoRR, abs/2310.02255.
  39. Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, and Song-Chun Zhu. 2021a. Inter-GPS: Interpretable geometry problem solving with formal language and symbolic reasoning. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th In…
  40. Pan Lu, Swaroop Mishra, Tanglin Xia, Liang Qiu, Kai-Wei Chang, Song-Chun Zhu, Oyvind Tafjord, Peter Clark, and Ashwin Kalyan. 2022a. Learn to explain: Multimodal reasoning via thought chains for science question answering. Advances in Neural Information Processing Systems, 35:2507–2521. find
  41. Pan Lu, Liang Qiu, Kai-Wei Chang, Ying Nian Wu, Song-Chun Zhu, Tanmay Rajpurohit, Peter Clark, and Ashwin Kalyan. 2022b. Dynamic prompt learning via policy gradient for semi-structured mathematical reasoning. arXiv preprint arXiv:2209.14610.
  42. Pan Lu, Liang Qiu, Jiaqi Chen, Tony Xia, Yizhou Zhao, Wei Zhang, Zhou Yu, Xiaodan Liang, and Song-Chun Zhu. 2021b. Iconqa: A new benchmark for abstract diagram understanding and visual language reasoning. arXiv preprint arXiv:2110.13214. find
  43. Haipeng Luo, Qingfeng Sun, Can Xu, Pu Zhao, Jian-guang Lou, Chongyang Tao, Xiubo Geng, Qingwei Lin, Shifeng Chen, and Dongmei Zhang. 2023. Wizardmath: Empowering mathematical reasoning for large language models via reinforced evol-instruct. CoRR, abs/2308.09583.
  44. Ahmed Masry, Xuan Long Do, Jia Qing Tan, Shafiq Joty, and Enamul Hoque. 2022. ChartQA: A benchmark for question answering about charts with visual and logical reasoning. In Findings of the Association for Computational Linguistics: ACL 2022, pages 2263– 2279.
  45. Minesh Mathew, Viraj Bagal, Rubèn Tito, Dimosthenis Karatzas, Ernest Valveny, and CV Jawahar. 2022. Infographicvqa. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 1697–1706. find
  46. Nitesh Methani, Pritha Ganguly, Mitesh M Khapra, and Pratyush Kumar. 2020. Plotqa: Reasoning over scientific plots. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 1527–1536. find
  47. OpenAI. Gpt-4v(ision). https://openai.com/ research/gpt-4v-system-card. ↗
  48. OpenBMB. 2024. Large multi-modal models for strong performance and efficient deployment. https://github.com/OpenBMB/OmniLMM. ↗
  49. Sandro Pezzelle. 2023. Dealing with semantic underspecification in multimodal nlp. arXiv preprint arXiv:2306.05240. find
  50. Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. 2021. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748–8763.
  51. Dustin Schwenk, Apoorv Khandelwal, Christopher Clark, Kenneth Marino, and Roozbeh Mottaghi. 2022. A-okvqa: A benchmark for visual question answering using world knowledge. In European Conference on Computer Vision, pages 146–162.
  52. Minjoon Seo, Hannaneh Hajishirzi, Ali Farhadi, Oren Etzioni, and Clint Malcolm. 2015. Solving geometry problems: Combining text and diagram interpretation. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1466–1476.
  53. Amanpreet Singh, Vivek Natarajan, Meet Shah, Yu Jiang, Xinlei Chen, Dhruv Batra, Devi Parikh, and Marcus Rohrbach. 2019. Towards vqa models that can read. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8317–8326. find
  54. Sergio Tascon-Morales, Pablo Márquez-Neila, and Raphael Sznitman. 2023. Logical implications for visual question answering consistency. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6725–6735. find
  55. Gemini Team, Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, et al. 2023. Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805.
  56. The Vicuna Team. 2023. Vicuna: An open-source chatbot impressing gpt-4 with 90%* chatgpt quality. https://lmsys.org/blog/2023-03-30-vicuna. ↗
  57. Ke Wang, Junting Pan, Weikang Shi, Zimu Lu, Mingjie Zhan, and Hongsheng Li. 2024a. Measuring multimodal mathematical reasoning with math-vision dataset. arXiv preprint arXiv:2402.14804.
  58. Lei Wang, Yi Hu, Jiabang He, Xing Xu, Ning Liu, Hui Liu, and Heng Tao Shen. 2024b. T-sciq: Teaching multimodal chain-of-thought reasoning via large language model signals for science question answering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 19162–19170. find
  59. Lei Wang, Wanyu Xu, Zhiqiang Hu, Yihuai Lan, Shan Dong, Hao Wang, Roy Ka-Wei Lee, and Ee-Peng Lim. 2024c. All in a single image: Large multimodal models are in-image learners. arXiv preprint arXiv:2402.17971. — [arXiv:2402.17971](https://arxiv.org/abs/2402.17971) find
  60. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V. Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations.
  61. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed H. Chi, Quoc V. Le, and Denny Zhou. 2022. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems.
  62. Qinghao Ye, Haiyang Xu, Guohai Xu, Jiabo Ye, Ming Yan, Yiyang Zhou, Junyang Wang, Anwen Hu, Pengcheng Shi, Yaya Shi, et al. 2023. mplug-owl: Modularization empowers large language models with multimodality. arXiv preprint arXiv:2304.14178.
  63. Haoxuan You, Rui Sun, Zhecan Wang, Long Chen, Gengyu Wang, Hammad A. Ayyubi, Kai-Wei Chang, and Shih-Fu Chang. 2023. Idealgpt: Iteratively decomposing vision and language reasoning via large language models. In Findings of the Association for Computational Linguistics: EMNLP, pages 11289– 11303. find
  64. Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Yuxuan Sun, Cong Wei, Botao Yu, Ruibin Yuan, Renliang Sun, Ming Yin, Boyuan Zheng, Zhenzhu Yang, Yibo Liu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. 2023a. MMMU: A massive multi-dis…
  65. Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. 2023b. Mammoth: Building math generalist models through hybrid instruction tuning. CoRR, abs/2309.05653.
  66. Jipeng Zhang, Lei Wang, Roy Ka-Wei Lee, Yi Bin, Yan Wang, Jie Shao, and Ee-Peng Lim. 2020. Graph-to-tree learning for solving math word problems. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 3928–3937. find
  67. Renrui Zhang, Dongzhi Jiang, Yichi Zhang, Haokun Lin, Ziyu Guo, Pengshuo Qiu, Aojun Zhou, Pan Lu, Kai-Wei Chang, Peng Gao, et al. 2024. Mathverse: Does your multi-modal llm truly see the diagrams in visual math problems? arXiv preprint arXiv:2403.14624.
  68. Xiaoman Zhang, Chaoyi Wu, Ziheng Zhao, Weixiong Lin, Ya Zhang, Yanfeng Wang, and Weidi Xie. 2023a. Pmc-vqa: Visual instruction tuning for medical visual question answering. arXiv preprint arXiv:2305.10415. — [arXiv:2305.10415](https://arxiv.org/abs/2305.10415) find
  69. Yanzhe Zhang, Ruiyi Zhang, Jiuxiang Gu, Yufan Zhou, Nedim Lipka, Diyi Yang, and Tong Sun. 2023b. Llavar: Enhanced visual instruction tuning for text-rich image understanding. arXiv preprint arXiv:2306.17107. find
  70. Zhuosheng Zhang, Aston Zhang, Mu Li, Hai Zhao, George Karypis, and Alex Smola. 2023c. Multimodal chain-of-thought reasoning in language models. arXiv preprint arXiv:2302.00923.
  71. Ge Zheng, Bin Yang, Jiajin Tang, Hong-Yu Zhou, and Sibei Yang. 2023. Ddcot: Duty-distinct chain-of-thought prompting for multimodal reasoning in language models. Advances in Neural Information Processing Systems, 36:5168–5191. find
  72. Denny Zhou, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, Quoc V. Le, and Ed H. Chi. 2023. Least-to-most prompting enables complex reasoning in large language models. In The Eleventh International Conference on Learning Representatio…
  73. Deyao Zhu, Jun Chen, Xiaoqian Shen, Xiang Li, and Mohamed Elhoseiny. 2023. Minigpt-4: Enhancing vision-language understanding with advanced large language models. CoRR, abs/2304.10592.

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/shi-2024-math-llava-bootstrapping-mathematical-reasoning/