Natural language chain-of-thought (N-CoT) and Program chain-of-thought (P-CoT) have emerged as two primary paradigms for large language models (LLMs) to solve mathematical reasoning problems. Current research typically endeavors to achieve unidirectional enhancement: P-CoT enhanced N-CoT or N-CoT enhanced P-CoT. In this paper, we seek to fully unleash the two paradigms’ strengths for mutual enhancement and ultimately achieve simultaneous improvements. We conduct a detailed analysis of the error types across two paradigms, based on which we propose Parrot, a novel training pipeline for mathematical problems: 1) Three target-designed subtasks integrate sequential P-CoT and N-CoT generation. 2) A subtask hybrid training strategy to facilitate natural language semantic transferability. 3) The converted N-CoT auxiliary reward is designed to alleviate the sparse rewards in P-CoT optimization. Extensive experiments demonstrate that Parrot significantly enhances both the performance of N-CoT and P-CoT, especially on N-CoT. Using Parrot SFT, the LLaMA2’s and CodeLLaMA’s N-CoT performance achieve gains of +21.87 and +21.48 on MathQA over the RL baseline, which is resource-intensive.

Reinforcement Learning from Human Feedback (RLHF) is a crucial approach to aligning language models with human values and intentions. A fundamental challenge in this method lies in ensuring that the reward model accurately understands and evaluates human preferences. Current methods rely on ranking losses to teach the reward model to assess preferences, but they are susceptible to noise and ambiguous data, often failing to deeply understand human intentions. To address this issue, we introduce contrastive learning into the reward modeling process. In addition to supervised ranking loss, we introduce an unsupervised contrastive loss to enable the reward model to fully capture the distinctions in contrastive data. Experimental results demonstrate that the proposed contrastive learning-based reward modeling method effectively enhances the generalization of the reward model, stabilizes the reinforcement learning training process, and improves the final alignment with human preferences.

To enhance the multi-step reasoning capabilities of large language models, researchers have extensively explored prompting methods, notably the Chain-of-Thought (CoT) method which explicitly elicits human-like rationales. However, they have inadvertently overlooked the potential of enhancing model reasoning performance by formulating higher-quality problems. In this work, we start from the problem side and propose Self-Polish (SP), a novel method that facilitates the model’s reasoning by guiding it to progressively refine the given problems to be more comprehensible and solvable. We also explore several automatic prompting varients and propose the Self-Polish prompt bank for the community. SP is orthogonal to all other prompting methods of answer/reasoning side like CoT, allowing for seamless integration with state-of-the-art techniques for further improvement. Thorough experiments show that the proposed method attains notable and consistent effectiveness on five reasoning benchmarks across different models. Furthermore, our method also showcases impressive performance on robustness evaluation. Codes and prompts are available at https://github.com/WooooDyy/Self-Polish.