# On the Generalization Gap in Self-Evolving Language Model Reasoning

arXiv: https://arxiv.org/abs/2606.01075 · HTML: https://mlsanity.com/paper/2606.01075/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 53 of its 72 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 30 of 53)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [On Designing Effective RL Reward at Training Time for LLM Reasoning](https://mlsanity.com/paper/2410.15115/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [ResearchRubrics: A Benchmark of Prompts and Rubrics For Evaluating Deep Research Agents](https://mlsanity.com/paper/2511.07685/) (2025)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [Multi-Agent Verification: Scaling Test-Time Compute with Multiple Verifiers](https://mlsanity.com/paper/2502.20379/) (2025)

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

- [SEED: Self-Evolving On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.14777/) (2026)
- [Scaling Large Reasoning Models beyond Human Supervision: A Path toward Superintelligence](https://mlsanity.com/paper/2608.31075/) (2026)
- [Phantom Gains: Auditing Self-Improvement Against a Measured Null](https://mlsanity.com/paper/2608.20290/) (2026)
- [Vestrum: Improving Agent Harnesses by Adapting Their Verification, Structure and Memory](https://mlsanity.com/paper/2609.33822/) (2026)

## Abstract (arXiv)

Recent work suggests that large language models (LLMs) can improve through self-evolution (SE), using supervision signals generated by the model itself. In this work, we ask: under a strict closed-loop setup, where the self-evolution algorithm has access only to an unlabeled prompt set and a base model, how close can internally generated supervision come to oracle-supervised training? We analyze four representative strategies in a unified offline self-evolution framework: single-round verification, multi-turn revision with feedback, iterative training, and curriculum learning. Our primary experiments use Knights and Knaves (KK) logical reasoning tasks, which provide deterministic solutions, controlled difficulty levels, and a clean testbed for easy-to-hard generalization. We first show that self-evolution consistently improves over the base model, but plateaus after excessive training compute is invested, and eventually still leaves a non-trivial gap to oracle supervision. We find that multi-turn critic-revision with large models can reach strong self-evolution performance, with Gemma 12B nearly matching oracle-supervised training. Beyond Knights and Knaves, we also evaluate self-evolution on real-world reasoning benchmarks, where gains are also modest. Overall, our results characterize when closed-loop self-evolution can help and show how internally generated supervision remains insufficient under this minimal formulation.