Large language models have shown great potential in complex reasoning tasks, yet their performance is often hampered by the scarcity of high-quality and reasoning-focused training datasets. Addressing this challenge, we propose Key-PointDriven Data Synthesis (KPDDS), a novel data synthesis framework that synthesizes question-answer pairs by leveraging key points and exemplar practices from authentic data sources. KPDDS ensures the generation of novel questions with rigorous quality control and substantial scalability. As a result, we present KPMath, an extensive synthetic dataset tailored for mathematical reasoning, comprising over 800K questionanswer pairs. Utilizing KPMath and augmenting it with additional reasoning-intensive corpora, we create the comprehensive KPMath-Plus dataset. Our experiments demonstrate that this dataset can enhance the mathematical reasoning performance of models across various architectures and sizes. The Qwen1.5-72B model, fine-tuned on KPMath-Plus, achieves 87.0% accuracy on GSM8K and 58.3% on MATH, surpassing competitors in the 7B to 72B range and best commercial models like GPT-4 across multiple math reasoning datasets.

Lean is an advanced proof assistant designed to facilitate formal theorem proving by providing a variety of interactive feedback. In this paper, we explore methodologies to leverage proof assistant feedback to augment the capabilities of large language models in constructing formal proofs. First, we deploy online reinforcement learning using Lean verification outcomes as the reward signal to improve the proof completion policy. This straightforward approach shows great promise in enhancing the model's alignment with the formal verification system. In addition, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. The tree structure is organized to represent the transitions of intermediate tactic states, extracted from the compilation messages given by Lean's tactic mode. The intrinsic reward is constructed to incentivize the discovery of novel tactic states, which helps to to mitigate the sparse-reward problem inherent in proof search. These techniques lead to a more efficient planning scheme for formal proof generation, achieving new state-of-the-art results on both miniF2F and ProofNet benchmarks.

Yubo Ma, Zhibin Gou, Junheng Hao, Ruochen Xu, Shuohang Wang, Liangming Pan, Yujiu Yang, Yixin Cao, Aixin Sun. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Recent developments in large language models (LLMs) have been impressive. However, these models sometimes show inconsistencies and problematic behavior, such as hallucinating facts, generating flawed code, or creating offensive and toxic content. Unlike these models, humans typically utilize external tools to cross-check and refine their initial content, like using a search engine for fact-checking, or a code interpreter for debugging. Inspired by this observation, we introduce a framework called CRITIC that allows LLMs, which are essentially “black boxes” to validate and progressively amend their own outputs in a manner similar to human interaction with tools. More specifically, starting with an initial output, CRITIC interacts with appropriate tools to evaluate certain aspects of the text, and then revises the output based on the feedback obtained during this validation process. Comprehensive evaluations involving free-form question answering, mathematical program synthesis, and toxicity reduction demonstrate that CRITIC consistently enhances the performance of LLMs. Meanwhile, our research highlights the crucial importance of external feedback in promoting the ongoing self-improvement of LLMs.

Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging mathematical problems by seamlessly integrating natural language reasoning with the utilization of external tools (e.g., computation libraries and symbolic solvers), thereby amalgamating the analytical prowess of language and the computational efficiency of tools. To train ToRA, we curate interactive tool-use trajectories on mathematical datasets, apply imitation learning on the annotations, and propose output space shaping to further refine models' reasoning behavior. As a result, ToRA models significantly outperform open-source models on 10 mathematical reasoning datasets across all scales with 13%-19% absolute improvements on average. Notably, ToRA-7B reaches 44.6% on the competition-level dataset MATH, surpassing the best open-source model WizardMath-70B by 22% absolute. ToRA-34B is also the first open-source model that achieves an accuracy exceeding 50% on MATH, which significantly outperforms GPT-4's CoT result, and is competitive with GPT-4 solving problems with programs. Additionally, we conduct a comprehensive analysis of the benefits and remaining challenges of tool interaction for mathematical reasoning, providing valuable insights for future research.

Previous language model pre-training methods have uniformly applied a next-token prediction loss to all training tokens. Challenging this norm, we posit that ''Not all tokens in a corpus are equally important for language model training''. Our initial analysis examines token-level training dynamics of language model, revealing distinct loss patterns for different tokens. Leveraging these insights, we introduce a new language model called Rho-1. Unlike traditional LMs that learn to predict every next token in a corpus, Rho-1 employs Selective Language Modeling (SLM), which selectively trains on useful tokens that aligned with the desired distribution. This approach involves scoring training tokens using a reference model, and then training the language model with a focused loss on tokens with higher scores. When continual continual pretraining on 15B OpenWebMath corpus, Rho-1 yields an absolute improvement in few-shot accuracy of up to 30% in 9 math tasks. After fine-tuning, Rho-1-1B and 7B achieved state-of-the-art results of 40.6% and 51.8% on MATH dataset, respectively - matching DeepSeekMath with only 3% of the pretraining tokens. Furthermore, when continual pretraining on 80B general tokens, Rho-1 achieves 6.8% average enhancement across 15 diverse tasks, increasing both data efficiency and performance of the language model pre-training.

Generative methods greatly promote aspectbased sentiment analysis via generating a sequence of sentiment elements in a specified format.However, existing studies usually predict sentiment elements in a fixed order, which ignores the effect of the interdependence of the elements in a sentiment tuple and the diversity of language expression on the results.In this work, we propose Multi-view Prompting (MVP) that aggregates sentiment elements generated in different orders, leveraging the intuition of human-like problem-solving processes from different views.Specifically, MVP introduces element order prompts to guide the language model to generate multiple sentiment tuples, each with a different element order, and then selects the most reasonable tuples by voting.MVP can naturally model multi-view and multi-task as permutations and combinations of elements, respectively, outperforming previous task-specific designed methods on multiple ABSA tasks with a single model.Extensive experiments show that MVP significantly advances the state-of-the-art performance on 10 datasets of 4 benchmark tasks, and performs quite effectively in low-resource settings.Detailed evaluation verified the effectiveness, flexibility, and cross-task transferability of MVP. 1 * Equal contribution.