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 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.