IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911625640935424 |
|---|---|
| author | Gupta, Navya Vyalla, Rishitej Reddy Anand, Avinash Kirtani, Chhavi Cambria, Erik Zhang, Zhengchen Wang, Zhengkui Liu, Timothy Ng, Aik Beng See, Simon Shah, Rajiv Ratn |
| author_facet | Gupta, Navya Vyalla, Rishitej Reddy Anand, Avinash Kirtani, Chhavi Cambria, Erik Zhang, Zhengchen Wang, Zhengkui Liu, Timothy Ng, Aik Beng See, Simon Shah, Rajiv Ratn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24114 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning Gupta, Navya Vyalla, Rishitej Reddy Anand, Avinash Kirtani, Chhavi Cambria, Erik Zhang, Zhengchen Wang, Zhengkui Liu, Timothy Ng, Aik Beng See, Simon Shah, Rajiv Ratn Computation and Language 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. |
| title | IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2604.24114 |