Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Works
Preliminary
Q*: A General, Versatile and Agile Deliberation Framework for LLMs
Experiments
Conclusion and References Related Works Related Works Preliminary Preliminary Q*: A General, Versatile and Agile Deliberation Framework for LLMs Q*: A General, Versatile and Agile Deliberation Framework for LLMs Experiments Experiments Conclusion and References Conclusion and References 5 Experiments 5.1 Experimental Settings 5.1 Experimental Settings Datasets. We evaluate the effectiveness of Q* on two math reasoning and one code generation tasks, where the dataset statistics have been summarized in Table 1. 1) GSM8K [2] is a dataset of Datasets grade school math problems, where the solution is given in a one-line-per-step format with an exact numerical answer in the last line; 2) MATH [3] is a dataset consisting of math problems of high school math competitions, where the solutions are given in a format that mixes latex code and natural language; 3) MBPP [44] is an entry-level Python programming dataset, where the questions are coding challenges along with a test case that defines the function format. The solutions are Python code that is excepted to pass the pre-collected test cases of each question. Implementation Details. The implementation of Q* method mainly includes three steps: 1) Q-value estimation. As discussed in Section 4.1, we propose several ways for estimating Q values and will illustrate the implementation details in the next paragraph; 2) Utility aggregation for each step (cf. Eq. (5)). For GSM8K dataset, we adopt a process reward model (PRM) trained on PRM800K [22] to model RP to provide an intermediate signal for each reasoning step, and use min as the aggregation function; For MATH dataset, we set g(st) = 0 for all passed states {si} t i=1 in each trajectory for fairness, because PRM800K contains data samples constructed from MATH testing set and there is a potential risk of data leakage; For MBPP dataset, we tokenize the code generated so far with function tokenize.generate_tokens and give a penalty of -0.5 if TokenError is raised, which is often the case that there are mismatched delimiters (e.g., parentheses, quotation marks) and invalid indention in the code. We use [−1] as the aggregation function to cancel the previous penalties since the code is generated on-the-fly and mismatched delimiters may be fixed in subsequent steps. 3) A* planning. For GSM8K and MATH datasets, we treat a single line outputted by the LLM as an action, while the action in MBPP is defined as a code snippet with 24 tokens when planning. Besides, in all experiments, we set λ = 1 when computing f-values and expand a state with K = 6 actions at each reasoning step. Finally, following the common practice of Best-of-N, we perform planning to collect N = 6 trajectories for each question, and select the one with the maximum f-value as the final result for evaluation. Implementation Details For Q-value estimation, in our practice, we find that learning from rollout could be the most effective and robust way to collect precise Q-value labels. Specifically, given the prompt of questions, we will firstly perform random rollout to obtain complete trajectories with LLM, denoted as πθ, under the setting of high temperature, e.g., τ = 0.9 for math reasoning and τ = 0.2 for code generation, and split each trajectory into a series of states according to the newline token “\n”. Then, for each state-action pair in a trajectory, denoted as (st, at), we can perform random rollout or MCTS with the same LLM to collect a pool P of trajectories, and then select the best reasoning path with the highest accumulated rewards to construct the corresponding Q-value label of the current state-action pair. Note that the reward R(st, at) is given as 1 only if the obtained math numerical answer is correct or the program passes all test cases, indicating that the Q value of a state-action pair can be 1 only if it has the potential to generate a trajectory containing the correct answer. 5.2 Experimental Results 5.2 Experimental Results GSM8K. For the comparison on GSM8K dataset, we select Llama-2-7b [45] as our base model, whose accuracy can achieve 65.2% after finetuning on MetaMath [5]. Then, we treat Llama-2-7b finetuned on MetaMath as policy πθ, and perform random rollout to collect Q-value labels for training Q-value model (QVM). For utility aggregation, we train a process reward model (PRM) on PRM800K [22] to provide intermediate signal for each reasoning step. With PRM and QVM in hand, traditional methods tend to treat either of them as a verifier to select the Best-of-N trajectory or utilize them to perform PPO training of RLHF. As the results shown in Table 2, we can find that with the same PRM/QVM, using it for verification performs significantly better than using it for alignment. Further, in the comparison of planning-based methods, we can find that with the same QVM, Q* method with constant aggregated utility can still outperform Best-of-N method. With the PRM trained on PRM800K determining whether the intermediate reasoning steps are correct, Q* method that combines PRM and QVM achieves the best performance among all methods based on the same LLM, helping Llama-2-7b surpass the performance of close-sourced ChatGPT-turbo [46] and reaching an accuracy of 80.8%. GSM8K MATH. As the results shown in Table 3, considering the weak performance of Llama-2-7b finetuned with MetaMath for the MATH dataset, we seek for two other stronger LLMs to evaluate the effectiveness of our Q* method. One is Llama-2-7b fine-tuned on Synthetic Data [47], which is constructed following the instruction of scaling up the SFT data, and achieves 41.9% accuracy on MATH dataset, approaching the performance of GPT-4 [48]. The other base model is DeepSeekMath-7b [49], which could be the most powerful open-source 7b model for math reasoning on MATH dataset, achieving 50.8% accuracy in our evaluation. From the results shown in the second and third blocks of Table 3, we can find that Q* can still lead to further performance improvement compared to the Best-of-N method on either of base models. Additionally, it is noteworthy that the performance of DeepSeek-Math-7b enhanced with Q* has already surpassed a series of closed-source models on the leaderboard of MATH dataset[2], such as Gemini Ultra (4-shot), reaching an accuracy of 55.4% . MATH MBPP. As for the comparison on MBPP dataset, we also choose the most powerful open-source LLM in the aspect of code generation, specifically CodeQwen1.5-7b-Chat, as our base model for evaluating the effectiveness of Q*. Following a similar procedure of math reasoning, we train a QVM for Q-value estimation and manually construct the utility function as described in the previous part of implementation details (tokenize the code generated so far with function tokenize.generate_tokens and give a penalty of -0.5 if TokenError is raised). From the results shown in Table 4, we can find that Q* can still outperform Best-of-N method in the aspect of code generation, and help CodeQwen1.5- 7b-Chat to achieve 77.0% accuracy on MBPP dataset, which is also a promising performance in the leaderboard of MPBB[3]. MBPP 6 Conclusion Solving challenging multi-step reasoning problems requires LLMs to perform in-depth deliberation beyond auto-regressive token generation. In this paper, we present Q*, a general, versatile and agile deliberation framework for LLMs. Unlike existing deliberation methods which need extensive expertise to design a utility function for each specific task, Q* relies on ground-truth solely to train value model and can be easily applied to various reasoning tasks without modification. 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[49] Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, YK Li, Y Wu, and Daya Guo. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024. [50] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. GPT-4 technical report. arXiv preprint arXiv:2303.08774, 2023. [51] Gemini Team, Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, et al. Gemini: A family of highly capable multimodal models. arXiv preprint arXiv:2312.11805, 2023. [52] Xinyun Chen, Maxwell Lin, Nathanael Schärli, and Denny Zhou. Teaching large language models to self-debug. arXiv preprint arXiv:2304.05128, 2023. Authors:
(1) Chaojie Wang*, Skywork AI;
(2) Yanchen Deng*, Nanyang Technological University;
(3) Zhiyi Lyu, Nanyang Technological University;
(4) Liang Zeng, Skywork AI;
(5) Jujie He, Skywork AI. Authors: Authors: (1) Chaojie Wang*, Skywork AI; (2) Yanchen Deng*, Nanyang Technological University; (3) Zhiyi Lyu, Nanyang Technological University; (4) Liang Zeng, Skywork AI; (5) Jujie He, Skywork AI. This paper is available on arxiv under CC BY 4.0 license. This paper is available on arxiv under CC BY 4.0 license. available on arxiv available on arxiv [2] https://paperswithcode.com/sota/math-word-problem-solving-on-math [3] https://paperswithcode.com/sota/code-generation-on-mbpp

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