# RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?

arXiv: https://arxiv.org/abs/2509.21016 · HTML: https://mlsanity.com/paper/2509.21016/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Spider 2.0: Evaluating Language Models on Real-World Enterprise Text-to-SQL Workflows](https://mlsanity.com/paper/2411.07763/) (2024)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [Omnigrok: Grokking Beyond Algorithmic Data](https://mlsanity.com/paper/2210.01117/) (2022)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding](https://mlsanity.com/paper/2503.02951/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?](https://mlsanity.com/paper/2506.11928/) (2025)
- [Unifying Grokking and Double Descent](https://mlsanity.com/paper/2303.06173/) (2023)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Grokfast: Accelerated Grokking by Amplifying Slow Gradients](https://mlsanity.com/paper/2405.20233/) (2024)
- [RLEP: Reinforcement Learning with Experience Replay for LLM Reasoning](https://mlsanity.com/paper/2507.07451/) (2025)
- [Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning](https://mlsanity.com/paper/2502.13834/) (2025)
- [Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers](https://mlsanity.com/paper/2504.20752/) (2025)
- [Ineq-Comp: Benchmarking Human-Intuitive Compositional Reasoning in Automated Theorem Proving on Inequalities](https://mlsanity.com/paper/2505.12680/) (2025)

## Built on by (most cited first, 23 of 23)

- [On the Interplay of Pre-Training, Mid-Training, and RL on Reasoning Language Models](https://mlsanity.com/paper/2512.07783/) (2025)
- [Endless Terminals: Scaling RL Environments for Terminal Agents](https://mlsanity.com/paper/2601.16443/) (2026)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability](https://mlsanity.com/paper/2601.18778/) (2026)
- [Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL](https://mlsanity.com/paper/2602.03773/) (2026)
- [How and Why LLMs Generalize: A Fine-Grained Analysis of LLM Reasoning from Cognitive Behaviors to Low-Level Patterns](https://mlsanity.com/paper/2512.24063/) (2025)
- [Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation](https://mlsanity.com/paper/2605.12741/) (2026)
- [The Tool-Overuse Illusion: Why Does LLM Prefer External Tools over Internal Knowledge?](https://mlsanity.com/paper/2604.19749/) (2026)
- [From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning](https://mlsanity.com/paper/2606.18089/) (2026)
- [Understanding Reasoning from Pretraining to Post-Training](https://mlsanity.com/paper/2607.16097/) (2026)
- [Text Before Vision: Staged Knowledge Injection Matters for Agentic RLVR in Ultra-High-Resolution Remote Sensing Understanding](https://mlsanity.com/paper/2602.14225/) (2026)
- [Cog-DRIFT: Exploration on Adaptively Reformulated Instances Enables Learning from Hard Reasoning Problems](https://mlsanity.com/paper/2604.04767/) (2026)
- [VeriGate: Verifier-Gated Step-Level Supervision for GRPO](https://mlsanity.com/paper/2605.30451/) (2026)
- [Select and Improve: Understanding the Mechanics of Post-Training for Reasoning](https://mlsanity.com/paper/2606.13125/) (2026)
- [CoRPO: Adding a Correctness Bias to GRPO Improves Generalization](https://mlsanity.com/paper/2511.04439/) (2025)
- [Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States](https://mlsanity.com/paper/2603.19987/) (2026)
- [Combinatorial Synthesis: Scaling Code RLVR via Atomic Decomposition and Recombination](https://mlsanity.com/paper/2605.31058/) (2026)
- [Parameter Exploration for RLVR via Variational Learning](https://mlsanity.com/paper/2608.09805/) (2026)
- [Learning to Solve Hard Problems in RL for LLMs by Never Giving Up](https://mlsanity.com/paper/2609.13443/) (2026)
- [TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition](https://mlsanity.com/paper/2606.09883/) (2026)
- [LLM Evolution as an Industry-Scale Ecosystem: A Lifecycle Perspective on Continual Learning](https://mlsanity.com/paper/2606.24901/) (2026)
- [The Generalization Spectrum: A Chromatographic Approach to Evaluating Learning Algorithms](https://mlsanity.com/paper/2606.25450/) (2026)
- [Self-Evolving Algorithm-Design Agents: Escaping In-Context Evolutionary Stagnation via Population-Curated Policy Optimization](https://mlsanity.com/paper/2609.38757/) (2026)

## Abstract (arXiv)

It remains an open question whether LLMs can acquire or generalize genuinely new reasoning strategies, beyond the sharpened skills encoded in their parameters during pre-training or post-training. To attempt to answer this debate, we introduce DELTA-Code -- Distributional Evaluation of Learnability and Transferrability in Algorithmic Coding -- a controlled benchmark of synthetic coding problem families designed to probe two fundamental aspects: learnability -- can LLMs, through reinforcement learning (RL), solve problem families where pretrained models exhibit failure with large enough attempts (pass@K=0)? -- and transferrability -- if learnability happens, can such skills transfer systematically to out-of-distribution (OOD) test sets? Unlike prior public coding datasets, DELTA isolates reasoning skills through templated problem generators and introduces fully OOD problem families that demand novel strategies rather than tool invocation or memorized patterns. Our experiments reveal a striking grokking phase transition: after an extended period with near-zero reward, RL-trained models abruptly climb to near-perfect accuracy. To enable learnability on previously unsolvable problem families, we explore key training ingredients such as staged warm-up with dense rewards, experience replay, curriculum training, and verification-in-the-loop. Beyond learnability, we use DELTA to evaluate transferability or generalization along exploratory, compositional, and transformative axes, as well as cross-family transfer. Results show solid gains within families and for recomposed skills, but persistent weaknesses in transformative cases. DELTA thus offers a clean testbed for probing the limits of RL-driven reasoning and for understanding how models can move beyond existing priors to acquire new algorithmic skills.