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.

One way to enhance the reasoning capability of Large Language Models (LLMs) is to conduct Supervised Fine-Tuning (SFT) using Chain-of-Thought (CoT) annotations. This approach does not show sufficiently strong generalization ability, however, because the training only relies on the given CoT data. In math problem-solving, for example, there is usually only one annotated reasoning path for each question in the training data. Intuitively, it would be better for the algorithm to learn from multiple annotated reasoning paths given a question. To address this issue, we propose a simple yet effective approach called Reinforced Fine-Tuning (ReFT) to enhance the generalizability of learning LLMs for reasoning, with math problem-solving as an example. ReFT first warmups the model with SFT, and then employs on-line reinforcement learning, specifically the PPO algorithm in this paper, to further fine-tune the model, where an abundance of reasoning paths are automatically sampled given the question and the rewards are naturally derived from the ground-truth answers. Extensive experiments on GSM8K, MathQA, and SVAMP datasets show that ReFT significantly outperforms SFT, and the performance can be potentially further boosted by combining inference-time strategies such as majority voting and re-ranking. Note that ReFT obtains the improvement by learning from the same training questions as SFT, without relying on extra or augmented training questions. This indicates a superior generalization ability for ReFT.

Large Language Models (LLMs) have demonstrated impressive capabilities across various domains, garnering significant attention from both academia and industry. However, enhancing the performance of LLMs typically requires scaling up model sizes or fine-tuning with additional datasets, which results in substantial computational costs. This paper poses an intriguing question: Can we improve the performance of LLMs without additional training? Drawing inspiration from signal processing principles, which suggest that noise often resides in high-frequency components while low-frequency components carry the essence of signals, we propose uncovering untapped potential in LLMs from a frequency perspective. We hypothesize that the high-frequency components in the weight matrices of LLMs’ linear layers may conceal noise that interferes with predictive accuracy. Therefore, we propose conducting spectral modulation in the parameter space of LLMs, which can seamlessly integrate with various models in a plug-and-play manner. Extensive experiments have demonstrated the superiority of our approach, with spectral modulation yielding an average performance improvement of up to 10.12%.

This paper proposes EmojiCloud, an open-source Python-based emoji cloud visualization tool, to generate a quick and straightforward understanding of emojis from the perspective of frequency and importance. EmojiCloud is flexible enough to support diverse drawing shapes, such as rectangles, ellipses, and image masked canvases. We also follow inclusive and personalized design principles to cover the unique emoji designs from seven emoji vendors (e.g., Twitter, Apple, and Windows) and allow users to customize plotted emojis and background colors. We hope EmojiCloud can benefit the whole emoji community due to its flexibility, inclusiveness, and customizability.