Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications—such as rephrasing or generating syntactic variations—which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, MathFusionQA, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches.

While data synthesis and distillation are promising strategies to enhance small language models, current approaches heavily rely on Large Language Models (LLMs), which suffer from high computational costs, environmental inefficiency, and potential biases inherited from monolithic architectures. In contrast, smaller LMs are more accessible and sustainable, but their individual capabilities often fall short in generating high-quality, diverse, and reliable data. Inspired by collaborative human processes (e.g., peer review), we propose a multiple small LMs involved framework, GRA, that aggregates specialized roles across small LMs to iterative refinement and quality control typically achieved by a single large LM. In this collaborative framework, multiple small LMs assume distinct roles—Generator, Reviewer, and Adjudicator—to simulate a peer-review-inspired data synthesis pipeline. The Generator proposes initial data samples, the Reviewer critiques their quality and diversity, and the Adjudicator resolves conflicts to finalize the output. By decomposing the synthesis process into specialized sub-tasks, collaborative small LMs can achieve data-level parity with distillation from large LMs. Through experiments across multiple benchmarks, we demonstrate that GRA-produced data matches or exceeds the quality of single large LM outputs, e.g., Qwen-2.5-72B-Instruct. Our results challenge the necessity of monolithic large models for high-quality data synthesis, advocating instead for strategic coordination of smaller agents.

Large language models (LLMs) have demonstrated remarkable capabilities, especially the recent advancements in reasoning, such as o1 and o3, pushing the boundaries of AI. Despite these impressive achievements in mathematics and coding, the reasoning abilities of LLMs in domains requiring cryptographic expertise remain underexplored. In this paper, we introduce CipherBank, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs in cryptographic decryption tasks. CipherBank comprises 2,358 meticulously crafted problems, covering 262 unique plaintexts across 5 domains and 14 subdomains, with a focus on privacy-sensitive and real-world scenarios that necessitate encryption. From a cryptographic perspective, CipherBank incorporates 3 major categories of encryption methods, spanning 9 distinct algorithms, ranging from classical ciphers to custom cryptographic techniques. We evaluate state-of-the-art LLMs on CipherBank, e.g., GPT-4o, DeepSeek-V3, and cutting-edge reasoning-focused models such as o1 and DeepSeek-R1. Our results reveal significant gaps in reasoning abilities not only between general-purpose chat LLMs and reasoning-focused LLMs but also in the performance of current reasoning-focused models when applied to classical cryptographic decryption tasks, highlighting the challenges these models face in understanding and manipulating encrypted data. Through detailed analysis and error investigations, we provide several key observations that shed light on the limitations and potential improvement areas for LLMs in cryptographic reasoning.These findings underscore the need for continuous advancements in LLM reasoning capabilities.

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model’s reflective ability. Though some studies attempted to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes.In this work, we propose to enhance LLM’s reasoning ability by Learning from Errors for MatheMatical Advancement (LEMMA). LEMMA constructs data consists of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an _error-type grounded mistake augmentation_ method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. By fine-tuning on the constructed dataset, the model is able to _self-correct errors autonomously_ within the generation process _without relying on external critique models_. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong models with less than 90k data.

Recent research trends in computational biology have increasingly focused on integrating text and bio-entity modeling, especially in the context of molecules and proteins. However, previous efforts like BioT5 faced challenges in generalizing across diverse tasks and lacked a nuanced understanding of molecular structures, particularly in their textual representations (e.g., IUPAC). This paper introduces BioT5+, an extension of the BioT5 framework, tailored to enhance biological research and drug discovery. BioT5+ incorporates several novel features: integration of IUPAC names for molecular understanding, inclusion of extensive bio-text and molecule data from sources like bioRxiv and PubChem, the multi-task instruction tuning for generality across tasks, and a numerical tokenization technique for improved processing of numerical data. These enhancements allow BioT5+ to bridge the gap between molecular representations and their textual descriptions, providing a more holistic understanding of biological entities, and largely improving the grounded reasoning of bio-text and bio-sequences. The model is pre-trained and fine-tuned with a large number of experiments, including 3 types of problems (classification, regression, generation), 15 kinds of tasks, and 21 total benchmark datasets, demonstrating the remarkable performance and state-of-the-art results in most cases. BioT5+ stands out for its ability to capture intricate relationships in biological data, thereby contributing significantly to bioinformatics and computational biology. Our code is available at https://github.com/QizhiPei/BioT5.

This paper presents our enhanced BioT5+ method for the Language + Molecules shared task at the ACL 2024 Workshop. The task involves “translating” between molecules and natural language, including molecule captioning and text-based molecule generation using the L+M-24 dataset. Our method consists of three stages. In the first stage, we distill data from various models. In the second stage, combined with extra version of the provided dataset, we train diverse models for subsequent voting ensemble.We also adopt Transductive Ensemble Learning (TEL) to enhance these base models. Lastly, all models are integrated using a voting ensemble method. Experimental results demonstrate that BioT5+ achieves superior performance on L+M-24 dataset. On the final leaderboard, our method (team name: qizhipei) ranks first in the text-based molecule generation task and second in the molecule captioning task, highlighting its efficacy and robustness in translating between molecules and natural language. The pre-trained BioT5+ models are available at https://github.com/QizhiPei/BioT5.

Recent advancements in biological research leverage the integration of molecules, proteins, and natural language to enhance drug discovery. However, current models exhibit several limitations, such as the generation of invalid molecular SMILES, underutilization of contextual information, and equal treatment of structured and unstructured knowledge. To address these issues, we propose BioT5, a comprehensive pre-training framework that enriches cross-modal integration in biology with chemical knowledge and natural language associations. BioT5 utilizes SELFIES for 100% robust molecular representations and extracts knowledge from the surrounding context of bio-entities in unstructured biological literature. Furthermore, BioT5 distinguishes between structured and unstructured knowledge, leading to more effective utilization of information. After fine-tuning, BioT5 shows superior performance across a wide range of tasks, demonstrating its strong capability of capturing underlying relations and properties of bio-entities. Our code is available at https://github.com/QizhiPei/BioT5.