# Parallel Scaling Law: Unveiling Reasoning Generalization through A Cross-Linguistic Perspective

arXiv: https://arxiv.org/abs/2510.02272 · HTML: https://mlsanity.com/paper/2510.02272/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 27 of 27)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [X-Reasoner: Towards Generalizable Reasoning Across Modalities and Domains](https://mlsanity.com/paper/2505.03981/) (2025)
- [Language Mixing in Reasoning Language Models: Patterns, Impact, and Internal Causes](https://mlsanity.com/paper/2505.14815/) (2025)
- [KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning](https://mlsanity.com/paper/2505.16826/) (2025)
- [Look Again, Think Slowly: Enhancing Visual Reflection in Vision-Language Models](https://mlsanity.com/paper/2509.12132/) (2025)
- [When Models Reason in Your Language: Controlling Thinking Language Comes at the Cost of Accuracy](https://mlsanity.com/paper/2505.22888/) (2025)
- [Implicit Cross-Lingual Rewarding for Efficient Multilingual Preference Alignment](https://mlsanity.com/paper/2503.04647/) (2025)
- [ACE-RL: Adaptive Constraint-Enhanced Reward for Long-form Generation Reinforcement Learning](https://mlsanity.com/paper/2509.04903/) (2025)
- [Just Go Parallel: Improving the Multilingual Capabilities of Large Language Models](https://mlsanity.com/paper/2506.13044/) (2025)
- [Does Learning Mathematical Problem-Solving Generalize to Broader Reasoning?](https://mlsanity.com/paper/2507.04391/) (2025)
- [LR^2Bench: Evaluating Long-chain Reflective Reasoning Capabilities of Large Language Models via Constraint Satisfaction Problems](https://mlsanity.com/paper/2502.17848/) (2025)
- [Breaking Barriers: Do Reinforcement Post Training Gains Transfer To Unseen Domains?](https://mlsanity.com/paper/2506.19733/) (2025)

## Built on by (most cited first, 4 of 4)

- [LANG: Reinforcement Learning for Multilingual Reasoning with Language-Adaptive Hint Guidance](https://mlsanity.com/paper/2605.22567/) (2026)
- [Enough is as good as a feast: A Comprehensive Analysis of How Reinforcement Learning Mitigates Task Conflicts in LLMs](https://mlsanity.com/paper/2607.22039/) (2026)
- [Soft Token Alignment for Cross-Lingual Reasoning](https://mlsanity.com/paper/2606.26466/) (2026)
- [Building Multilingual Bridges: Data Mixing as the Pillar of Generalization for In-Language Reasoning](https://mlsanity.com/paper/2609.10445/) (2026)

## Abstract (arXiv)

Recent advancements in Reinforcement Post-Training (RPT) have significantly enhanced the capabilities of Large Reasoning Models (LRMs), sparking increased interest in the generalization of RL-based reasoning. While existing work has primarily focused on investigating its generalization across tasks or modalities, this study proposes a novel cross-linguistic perspective to investigate reasoning generalization. This raises a crucial question: textitDoes the reasoning capability achieved from English RPT effectively transfer to other languages? We address this by systematically evaluating English-centric LRMs on multilingual reasoning benchmarks and introducing a metric to quantify cross-lingual transferability. Our findings reveal that cross-lingual transferability varies significantly across initial model, target language, and training paradigm. Through interventional studies, we find that models with stronger initial English capabilities tend to over-rely on English-specific patterns, leading to diminished cross-lingual generalization. To address this, we conduct a thorough parallel training study. Experimental results yield three key findings: First-Parallel Leap, a substantial leap in performance when transitioning from monolingual to just a single parallel language, and a predictable Parallel Scaling Law, revealing that cross-lingual reasoning transfer follows a power-law with the number of training parallel languages. Moreover, we identify the discrepancy between actual monolingual performance and the power-law prediction as Monolingual Generalization Gap, indicating that English-centric LRMs fail to fully generalize across languages. Our study challenges the assumption that LRM reasoning mirrors human cognition, providing critical insights for the development of more language-agnostic LRMs.