Bidirectional Curriculum Generation: A Multi-Agent Framework for Data-Efficient Mathematical Reasoning

TL;DR

This paper introduces a bidirectional multi-agent curriculum framework that adaptively generates training data by either increasing or decreasing problem complexity, significantly improving data efficiency in mathematical reasoning tasks for large language models.

Contribution

It proposes a novel bidirectional curriculum generation method with a multi-agent system that adaptively adjusts problem difficulty, outperforming traditional unidirectional approaches.

Findings

Outperforms baseline methods in reasoning accuracy.

Reduces the number of instruction samples needed for training.

Grounded in the Optimal Pacing Theorem for effective learning trajectories.

Abstract

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.