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

TL;DR

IRIS introduces a dual-axis curriculum learning framework combining supervised fine-tuning and reinforcement learning to enhance multilingual mathematical reasoning, especially in low-resource languages.

Contribution

It proposes a novel interleaved reinforcement and staged curriculum approach, along with a new dataset, to improve cross-lingual math reasoning performance.

Findings

IRIS outperforms baseline models on multilingual math reasoning benchmarks.

The approach yields significant gains in low-resource language settings.

The CL-Math dataset contains 29,000 problems with step-level annotations in English, Hindi, and Marathi.

Abstract

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.