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

ACL ARR 2026 January Submission9717 Authors

Keywords: curriculum learning, reinforcement learning, mathematical reasoning, multilingual NLP, low-resource languages, question answering

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.

Paper Type: Long

Research Area: Machine Learning for NLP

Research Area Keywords: multilingualism, cross-lingual transfer, multilingual benchmarks, less-resourced languages, mathematical reasoning, math QA

Contribution Types: NLP engineering experiment, Approaches to low-resource settings, Data resources

Languages Studied: English, Hindi, Marathi

Submission Number: 9717