IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning

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 twoaxis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-bystep guidance (horizontal axis). We design a composite reward combining correctness, stepwise 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 lowresource and bilingual settings, alongside modest improvements in high-resource languages. Our code and dataset will be publicly available at https://github.com/avinanand/ IRIS-Interleaved-Reinforcement- .