# The Reasoning Boundary Paradox: How Reinforcement Learning Constrains Language Models

arXiv: https://arxiv.org/abs/2510.02230 · HTML: https://mlsanity.com/paper/2510.02230/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [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)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (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)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (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)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [Transient Non-Stationarity and Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2006.05826/) (2020)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [Ray Interference: a Source of Plateaus in Deep Reinforcement Learning](https://mlsanity.com/paper/1904.11455/) (2019)
- [No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO](https://mlsanity.com/paper/2405.00662/) (2024)
- [A Study of Plasticity Loss in On-Policy Deep Reinforcement Learning](https://mlsanity.com/paper/2405.19153/) (2024)
- [Plasticity Loss in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2411.04832/) (2024)
- [Mitigating Plasticity Loss in Continual Reinforcement Learning by Reducing Churn](https://mlsanity.com/paper/2506.00592/) (2025)
- [Improving Deep Reinforcement Learning by Reducing the Chain Effect of Value and Policy Churn](https://mlsanity.com/paper/2409.04792/) (2024)

## Built on by (most cited first, 18 of 18)

- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [Understanding and Mitigating Premature Confidence for Better LLM Reasoning](https://mlsanity.com/paper/2605.24396/) (2026)
- [CriPO: Enhancing Rubric-based RL via Self-Distillation](https://mlsanity.com/paper/2607.18082/) (2026)
- [GeoRA: Geometry-Aware Low-Rank Adaptation for RLVR](https://mlsanity.com/paper/2601.09361/) (2026)
- [Can RL Improve Generalization of LLM Agents? An Empirical Study](https://mlsanity.com/paper/2603.12011/) (2026)
- [The Unlearnability Phenomenon in RLVR for Language Models](https://mlsanity.com/paper/2605.16787/) (2026)
- [Tail-Likelihood Reinforcement Learning](https://mlsanity.com/paper/2609.02987/) (2026)
- [Asymmetric Advantage Modulation Calibrates Entropy Dynamics in RLVR](https://mlsanity.com/paper/2604.04894/) (2026)
- [Non-vacuous Generalization Bounds for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2607.14506/) (2026)
- [Reachability Is Not Realization: Tracing the Sources of LLM Benchmark Gains](https://mlsanity.com/paper/2608.03219/) (2026)
- [OGER: A Robust Offline-Guided Exploration Reward for Hybrid Reinforcement Learning](https://mlsanity.com/paper/2604.18530/) (2026)
- [Reasoning Fine-Tuning Induces Persistent Latent Policy States](https://mlsanity.com/paper/2607.18532/) (2026)
- [SLPO: Scaling Latent Reasoning via a Surrogate Policy](https://mlsanity.com/paper/2607.19691/) (2026)
- [Locked at the Entrance, Open Inside: Where RLVR Narrows the Solution Space](https://mlsanity.com/paper/2608.29188/) (2026)
- [On-Policy Parameter Update Direction Underlies Generalization in LLM Post-Training](https://mlsanity.com/paper/2609.36659/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key method for improving Large Language Models' reasoning capabilities, yet recent evidence suggests it may paradoxically shrink the reasoning boundary rather than expand it. This paper investigates the shrinkage issue of RLVR by analyzing its learning dynamics and reveals two critical phenomena that explain this failure. First, we expose negative interference in RLVR, where learning to solve certain training problems actively reduces the likelihood of correct solutions for others, leading to the decline of Pass@k performance, or the probability of generating a correct solution within k attempts. Second, we uncover the winner-take-all phenomenon: RLVR disproportionately reinforces problems with high likelihood, correct solutions, under the base model, while suppressing other initially low-likelihood ones. Through extensive theoretical and empirical analysis on multiple mathematical reasoning benchmarks, we show that this effect arises from the inherent on-policy sampling in standard RL objectives, causing the model to converge toward narrow solution strategies. Based on these insights, we propose a simple yet effective data curation algorithm that focuses RLVR learning on low-likelihood problems, achieving notable improvement in Pass@k performance. Our code is available at https://github.com/mail-research/SELF-llm-interference.