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

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves the efficiency of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets demonstrate that AdaRFT improves convergence efficiency and reasoning performance. Given problem-level difficulty annotations, AdaRFT reduces RFT training time by up to 2 times across data distributions and model scales, offering a more scalable and effective RFT framework.

Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited. We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi. Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages.

Reinforcement Learning with Verifiable Rewards (RLVR) has shown remarkable success in improving the mathematical reasoning of large language models. Yet problems beyond the model's current capability, where rollouts uniformly fail and no learning signal is produced, are structurally wasted despite marking the most informative training frontier. We show that these otherwise-inert problems can be unlocked via teacher-guided curriculum learning: partial reasoning traces from a stronger model create a graded difficulty landscape, and a backward-chaining curriculum progressively withdraws guidance until the model solves problems unaided. Training on only 128 unsolvable problems matches or exceeds GRPO trained on a full 2,000-problem corpus (~16x data efficiency) on the nine-benchmark average for both base models, while substantially expanding the reasoning boundary measured by pass@k at large k. Furthermore, we identify a distribution-shift cost that is particularly acute in the unsolvable-only regime and propose Monotone Frontier Curriculum (MFC), a method that monotonically drives training toward unguided solving, consistently outperforming existing curriculum methods.