Bidirectional Curriculum Generation: A Multi-Agent Framework for Data-Efficient Mathematical Reasoning
This work tackles the problem of data inefficiency in mathematical reasoning for Large Language Models, offering an adaptive pedagogical approach to optimize learning trajectories.
This paper addresses the data inefficiency in training Large Language Models for mathematical reasoning by introducing a Bidirectional Curriculum Generation framework. This framework dynamically generates training data, either complicating problems to challenge the model or simplifying them to address specific reasoning failures, resulting in superior reasoning performance with substantially fewer instruction samples compared to baselines.
Enhancing mathematical reasoning in Large Language Models typically demands massive datasets, yet data efficiency remains a critical bottleneck. While Curriculum Learning attempts to structure this process, standard unidirectional approaches (simple-to-complex) suffer from inefficient sample utilization: they blindly escalate complexity even when foundational gaps persist, leading to wasted computation on unsolvable problems. To maximize the instructional value of every training sample, we introduce a novel Bidirectional Curriculum Generation framework. Unlike rigid trajectories, our multi-agent ecosystem mimics adaptive pedagogy to establish a closed feedback loop. It dynamically generates data by either complicating problems to challenge the model or, crucially, simplying them to repair specific reasoning failures. This mechanism ensures that the model consumes only the most effective data at any given stage. Grounded in the Optimal Pacing Theorem, our approach optimizes the learning trajectory, significantly outperforming baselines while achieving superior reasoning performance with substantially fewer instruction samples.