# Growing and Transferring Pathways for LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2610.16489 · HTML: https://mlsanity.com/paper/2610.16489/

## 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 29 of its 33 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [LLaMA Pro: Progressive LLaMA with Block Expansion](https://mlsanity.com/paper/2401.02415/) (2024)
- [Tina: Tiny Reasoning Models via LoRA](https://mlsanity.com/paper/2504.15777/) (2025)
- [Tiny-Attention Adapter: Contexts Are More Important Than the Number of Parameters](https://mlsanity.com/paper/2211.01979/) (2022)

## Abstract (arXiv)

Reinforcement learning (RL) can substantially improve the reasoning capabilities of large language models, but an effective training run requires considerable resources. Reusing the computation acquired through RL across models would extend the value of that training. We propose GrowRL, an RL method that organizes learned updates into compact computational pathways through structural growth. GrowRL freezes the pretrained backbone and adds an independent causal attention branch and a feed-forward network branch at each Transformer layer. Zero-initialized output projections preserve the pretrained policy at initialization, and RL updates only the added pathways. The learned pathways remain explicit after training, allowing transfer to structurally compatible target models and subsequent adaptation with the target backbone frozen. The architecture also supports sequential transfer of additional pathways. By keeping the learned attention and feed-forward computation separate from the pretrained weights, GrowRL provides an explicit structure for preserving and reusing the outcome of an RL run. Experiments across five backbones show competitive mathematical reasoning and out-of-distribution performance with a small number of trainable parameters. Learned pathways provide immediate gains across all three transfer directions, with performance after only 10 target-side updates already close to that after 100 updates in every case. These results support computational pathways as parameter-efficient and reusable units of reinforcement learning adaptation.