# New Skills or Sharper Primitives? A Probabilistic Perspective on the Emergence of Reasoning in RLVR

arXiv: https://arxiv.org/abs/2602.08281 · HTML: https://mlsanity.com/paper/2602.08281/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (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)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones](https://mlsanity.com/paper/2509.25123/) (2025)
- [Rethinking Entropy Regularization in Large Reasoning Models](https://mlsanity.com/paper/2509.25133/) (2025)
- [Atomic Skills are the Prerequisite: When Reinforcement Learning Synthesizes Compositional Reasoning, and When It Only Amplifies](https://mlsanity.com/paper/2512.01970/) (2025)
- [How Does RL Post-training Induce Skill Composition? A Case Study on Countdown](https://mlsanity.com/paper/2512.01775/) (2025)

## Built on by (most cited first, 2 of 2)

- [Predictable GRPO: A Closed-Form Model of Training Dynamics](https://mlsanity.com/paper/2606.30789/) (2026)
- [What Will Post-Training Fix? Per-Problem Gains Are Shared Across Independent RL Runs, and Existing Checkpoints Predict Them Better Than A Priori Signals](https://mlsanity.com/paper/2610.04978/) (2026)

## Abstract (arXiv)

Whether Reinforcement Learning with Verifiable Rewards (RLVR) endows Large Language Models (LLMs) with new capabilities or merely elicits latent traces remains a central debate. In this work, we align with the former view, proposing a probabilistic framework where capability is defined by instance-level solvability. We hypothesize that the emergence of complex reasoning can be driven by sharpening atomic step probabilities, which enables models to overcome the exponential decay of success rates inherent in multi-step reasoning chains. Utilizing the Algebrarium framework, we train models exclusively on single-step operations and evaluate their performance on unseen multi-step tasks. Our empirical results confirm that: (1) RLVR incentivizes the exploration of previously inaccessible solution paths by amplifying the model's existing skills; (2) composite performance is strictly governed by the joint probability of atomic steps, evidenced by high Pearson correlation coefficients (ρ ∈ [0.69, 0.96]); and (3) RLVR, acting as a global optimizer, can cause specific skills to be sacrificed to maximize aggregate reward. Our work offers a novel explanation for emergent abilities in RLVR, suggesting that the iterative optimization of solvable problems enables models to develop the capabilities to tackle previously unsolvable scenarios.