mlsanityData to 14 Oct 2026

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

arXiv 2604.24114 ↗First posted 27 Apr 2026cs.CLcited by 0

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 22 of its 41 references that are in the map. First posted on arXiv 27 Apr 2026.

Builds on

22 of 41 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024Generative Verifiers: Reward Modeling as Next-Token Prediction27 Aug
  2. 2023Let's Verify Step by Step31 May

Other references · 20

  1. 2022Training language models to follow instructions with human feedbackcited by 15,971
  2. 2024The Llama 3 Herd of Modelscited by 14,715
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  4. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  5. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  6. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedbackcited by 3,720
  9. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  10. 2023Multimodal Chain-of-Thought Reasoning in Language Modelscited by 752
  11. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 735
  12. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 625
8 more
  1. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 313
  2. 2024InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoningcited by 119
  3. 2023M3Exam: A Multilingual, Multimodal, Multilevel Benchmark for Examining Large Language Modelscited by 110
  4. 2024Multilingual Instruction Tuning With Just a Pinch of Multilingualitycited by 73
  5. 2025Self-rewarding correction for mathematical reasoningcited by 70
  6. 2024SOS-1K: A Fine-grained Suicide Risk Classification Dataset for Chinese Social Media Analysiscited by 1
  7. 2024Logic Contrastive Reasoning with Lightweight Large Language Model for Math Word Problemscited by 1
  8. 2025XL-Suite: Cross-Lingual Synthetic Training and Evaluation Data for Open-Ended Generationcited by 1

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Not cited yet.

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Close in wording, no citation either way

  1. 2025Beyond English-Centric Training: How Reinforcement Learning Improves Cross-Lingual Reasoning in LLMs
  2. 2025Reasoning Curriculum: Bootstrapping Broad LLM Reasoning from Math
  3. 2025VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models
  4. 2025Nemotron-CrossThink: Scaling Self-Learning beyond Math Reasoning
  5. 2025Efficient Reinforcement Finetuning via Adaptive Curriculum Learning
  6. 2026LANG: Reinforcement Learning for Multilingual Reasoning with Language-Adaptive Hint Guidance
  7. 2026Crosslingual On-Policy Self-Distillation for Multilingual Reasoning
  8. 2026On-Policy Delta Distillation for Multilingual Math Reasoning