A New Framework for Trustworthy AI Deductive Reasoning

Authors: (1) Zhan Ling, UC San Diego and equal contribution; (2) Yunhao Fang, UC San Diego and equal contribution; (3) Xuanlin Li, UC San Diego; (4) Zhiao Huang, UC San Diego; (5) Mingu Lee, Qualcomm AI Research and Qualcomm AI Research (6) Roland Memisevic, Qualcomm AI Research; (7) Hao Su, UC San Diego. Table of Links Abstract and Introduction Related work Motivation and Problem Formulation Deductively Verifiable Chain-of-Thought Reasoning Experiments Limitations Conclusion, Acknowledgements and References A Deductive Verification with Vicuna Models B More Discussion on Improvements of Deductive Verification Accuracy Versus Improvements on Final Answer Correctness C More Details on Answer Extraction D Prompts E More Deductive Verification Examples 7 Conclusion In this paper, we aim to enable Large Language Models (LLMs) to perform explicit and rigorous deductive reasoning while ensuring the trustworthiness of their reasoning processes through self-verification. To this end, we have proposed a novel framework based on “Natural Program”, a natural language-based deductive reasoning format that facilitates reasoning verification and can be easily generated through in-context learning. Within this framework, we decompose the verification process of complex reasoning chains into step-by-step subprocesses that focus solely on necessary context and premises, allowing us to significantly enhance the accuracy of verification. Additionally, we introduce a Unanimity-Plurality Voting strategy to further improve verification accuracy. Experimentally, we demonstrate the superiority of our framework in improving the rigor, trustworthiness, and interpretability of reasoning steps and answers. Broader Impact. While our deductive verification approach can mitigate hallucinations and reasoning errors of Large Language Models (LLMs), it does not completely eliminate these phenomena. LLMs can still produce harmful and biased content, make incorrect claims, and produce wrongful advice. This issue becomes particularly significant when LLMs engage in complex reasoning chains, increasing the risk of misleading users. Consequently, it is still crucial for users to exercise great caution when interacting with, deploying, or developing LLM-based applications. Acknowledgements We would like to express our sincere gratitude to Tongzhou Mu and Caiwei Xiao from UC San Diego, Kairong Luo from Tsinghua University, and Pulkit Madan, Reza Pourreza, Sunny Panchal, and Apratim Bhattacharyya from Qualcomm for their valuable discussions and feedback. References [1] Kushal Arora, Layla El Asri, Hareesh Bahuleyan, and Jackie Chi Kit Cheung. Why exposure bias matters: An imitation learning perspective of error accumulation in language generation. arXiv preprint arXiv:2204.01171, 2022. [2] Kaj Bostrom, Zayne Sprague, Swarat Chaudhuri, and Greg Durrett. 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Authors: (1) Zhan Ling, UC San Diego and equal contribution; (2) Yunhao Fang, UC San Diego and equal contribution; (3) Xuanlin Li, UC San Diego; (4) Zhiao Huang, UC San Diego; (5) Mingu Lee, Qualcomm AI Research and Qualcomm AI Research (6) Roland Memisevic, Qualcomm AI Research; (7) Hao Su, UC San Diego. Authors: Authors: (1) Zhan Ling, UC San Diego and equal contribution; (2) Yunhao Fang, UC San Diego and equal contribution; (3) Xuanlin Li, UC San Diego; (4) Zhiao Huang, UC San Diego; (5) Mingu Lee, Qualcomm AI Research and Qualcomm AI Research (6) Roland Memisevic, Qualcomm AI Research; (7) Hao Su, UC San Diego. Table of Links Abstract and Introduction Abstract and Introduction Related work Related work Motivation and Problem Formulation Motivation and Problem Formulation Deductively Verifiable Chain-of-Thought Reasoning Deductively Verifiable Chain-of-Thought Reasoning Experiments Experiments Limitations Limitations Conclusion, Acknowledgements and References Conclusion, Acknowledgements and References A Deductive Verification with Vicuna Models A Deductive Verification with Vicuna Models B More Discussion on Improvements of Deductive Verification Accuracy Versus Improvements on Final Answer Correctness B More Discussion on Improvements of Deductive Verification Accuracy Versus Improvements on Final Answer Correctness C More Details on Answer Extraction C More Details on Answer Extraction D Prompts D Prompts E More Deductive Verification Examples E More Deductive Verification Examples 7 Conclusion In this paper, we aim to enable Large Language Models (LLMs) to perform explicit and rigorous deductive reasoning while ensuring the trustworthiness of their reasoning processes through self-verification. To this end, we have proposed a novel framework based on “Natural Program”, a natural language-based deductive reasoning format that facilitates reasoning verification and can be easily generated through in-context learning. Within this framework, we decompose the verification process of complex reasoning chains into step-by-step subprocesses that focus solely on necessary context and premises, allowing us to significantly enhance the accuracy of verification. Additionally, we introduce a Unanimity-Plurality Voting strategy to further improve verification accuracy. Experimentally, we demonstrate the superiority of our framework in improving the rigor, trustworthiness, and interpretability of reasoning steps and answers. Broader Impact. While our deductive verification approach can mitigate hallucinations and reasoning errors of Large Language Models (LLMs), it does not completely eliminate these phenomena. LLMs can still produce harmful and biased content, make incorrect claims, and produce wrongful advice. This issue becomes particularly significant when LLMs engage in complex reasoning chains, increasing the risk of misleading users. Consequently, it is still crucial for users to exercise great caution when interacting with, deploying, or developing LLM-based applications. Broader Impact. Acknowledgements We would like to express our sincere gratitude to Tongzhou Mu and Caiwei Xiao from UC San Diego, Kairong Luo from Tsinghua University, and Pulkit Madan, Reza Pourreza, Sunny Panchal, and Apratim Bhattacharyya from Qualcomm for their valuable discussions and feedback. References [1] Kushal Arora, Layla El Asri, Hareesh Bahuleyan, and Jackie Chi Kit Cheung. Why exposure bias matters: An imitation learning perspective of error accumulation in language generation. arXiv preprint arXiv:2204.01171, 2022. [2] Kaj Bostrom, Zayne Sprague, Swarat Chaudhuri, and Greg Durrett. Natural language deduction through search over statement compositions. arXiv preprint arXiv:2201.06028, 2022. [3] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in neural information processing systems, 33:1877–1901, 2020. [4] Sébastien Bubeck, Varun Chandrasekaran, Ronen Eldan, Johannes Gehrke, Eric Horvitz, Ece Kamar, Peter Lee, Yin Tat Lee, Yuanzhi Li, Scott Lundberg, et al. Sparks of artificial general intelligence: Early experiments with gpt-4. arXiv preprint arXiv:2303.12712, 2023. [5] Wenhu Chen, Xueguang Ma, Xinyi Wang, and William W Cohen. Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks. arXiv preprint arXiv:2211.12588, 2022. [6] Xinyun Chen, Maxwell Lin, Nathanael Schärli, and Denny Zhou. Teaching large language models to self-debug. arXiv preprint arXiv:2304.05128, 2023. [7] Wei-Lin Chiang, Zhuohan Li, Zi Lin, Ying Sheng, Zhanghao Wu, Hao Zhang, Lianmin Zheng, Siyuan Zhuang, Yonghao Zhuang, Joseph E. Gonzalez, Ion Stoica, and Eric P. Xing. Vicuna: An open-source chatbot impressing gpt-4 with 90%* chatgpt quality, March 2023. [8] Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al. Palm: Scaling language modeling with pathways. arXiv preprint arXiv:2204.02311, 2022. [9] Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Eric Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, et al. Scaling instruction-finetuned language models. arXiv preprint arXiv:2210.11416, 2022. [10] Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021. [11] Antonia Creswell and Murray Shanahan. Faithful reasoning using large language models. arXiv preprint arXiv:2208.14271, 2022. [12] Antonia Creswell, Murray Shanahan, and Irina Higgins. Selection-inference: Exploiting large language models for interpretable logical reasoning. In The Eleventh International Conference on Learning Representations, 2023. [13] Danny Driess, Fei Xia, Mehdi SM Sajjadi, Corey Lynch, Aakanksha Chowdhery, Brian Ichter, Ayzaan Wahid, Jonathan Tompson, Quan Vuong, Tianhe Yu, et al. Palm-e: An embodied multimodal language model. arXiv preprint arXiv:2303.03378, 2023. [14] Andrew Drozdov, Nathanael Schärli, Ekin Akyürek, Nathan Scales, Xinying Song, Xinyun Chen, Olivier Bousquet, and Denny Zhou. Compositional semantic parsing with large language models. arXiv preprint arXiv:2209.15003, 2022. [15] Olga Golovneva, Moya Peng Chen, Spencer Poff, Martin Corredor, Luke Zettlemoyer, Maryam FazelZarandi, and Asli Celikyilmaz. Roscoe: A suite of metrics for scoring step-by-step reasoning. In The Eleventh International Conference on Learning Representations, 2022. [16] Nuno M Guerreiro, Duarte Alves, Jonas Waldendorf, Barry Haddow, Alexandra Birch, Pierre Colombo, and André FT Martins. Hallucinations in large multilingual translation models. arXiv preprint arXiv:2303.16104, 2023. [17] Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874, 2021. [18] Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, et al. Training compute-optimal large language models. arXiv preprint arXiv:2203.15556, 2022. [19] Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, and Nate Kushman. Learning to solve arithmetic word problems with verb categorization. In EMNLP, pages 523–533, 2014. [20] Ziwei Ji, Nayeon Lee, Rita Frieske, Tiezheng Yu, Dan Su, Yan Xu, Etsuko Ishii, Ye Jin Bang, Andrea Madotto, and Pascale Fung. Survey of hallucination in natural language generation. ACM Computing Surveys, 55(12):1–38, 2023. [21] Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa. Large language models are zero-shot reasoners. arXiv preprint arXiv:2205.11916, 2022. [22] Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay. Learning to automatically solve algebra word problems. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 271–281, Baltimore, Maryland, June 2014. Association for Computational Linguistics. 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Learn to explain: Multimodal reasoning via thought chains for science question answering. Advances in Neural Information Processing Systems, 35:2507–2521, 2022. [27] Qing Lyu, Shreya Havaldar, Adam Stein, Li Zhang, Delip Rao, Eric Wong, Marianna Apidianaki, and Chris Callison-Burch. Faithful chain-of-thought reasoning. arXiv preprint arXiv:2301.13379, 2023. [28] Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye, Yiming Yang, et al. Self-refine: Iterative refinement with self-feedback. arXiv preprint arXiv:2303.17651, 2023. [29] Ana Marasovic, Iz Beltagy, Doug Downey, and Matthew E. Peters. Few-shot self-rationalization with ´ natural language prompts, 2022. [30] Joshua Maynez, Shashi Narayan, Bernd Bohnet, and Ryan McDonald. On faithfulness and factuality in abstractive summarization. arXiv preprint arXiv:2005.00661, 2020. [31] OpenAI. Gpt-4 technical report, 2023. 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