# One Sample to Rule Them All: Extreme Data Efficiency in Multidiscipline Reasoning with Reinforcement Learning

arXiv: https://arxiv.org/abs/2601.03111 · HTML: https://mlsanity.com/paper/2601.03111/

## 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 47 of its 85 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 47)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [SRPO: A Cross-Domain Implementation of Large-Scale Reinforcement Learning on LLM](https://mlsanity.com/paper/2504.14286/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)

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

- [Prompt replay: speeding up grpo with on-policy reuse of high-signal prompts](https://mlsanity.com/paper/2603.21177/) (2026)
- [Single-Rollout Hidden-State Dynamics for Training-Free RLVR Data Selection](https://mlsanity.com/paper/2605.28631/) (2026)

## Abstract (arXiv)

The reasoning ability of large language models (LLMs) can be unleashed with reinforcement learning (RL) (OpenAI, 2024; DeepSeek-AI et al., 2025a; Zeng et al., 2025). The success of existing RL attempts in LLMs usually rely on high-quality samples of large volumes. In this paper, we challenge conventional assumptions about data requirements in RL for LLMs by demonstrating the effectiveness of one-shot reinforcement learning. Specifically, we introduce polymath learning, a framework for designing one training sample that elicits multidisciplinary reasoning improvement. We present three key findings: (1) A single, strategically selected math reasoning sample can produce significant performance improvements across multiple domains, including physics, chemistry, and biology; (2) Analysis of salient mathematical skills provides insight into the characteristics associated with effective polymath samples; and (3) An engineered synthetic sample that integrates multidisciplinary elements and broader skill coverage achieves stronger performance than naturally occurring individual samples. Across various reasoning benchmarks, polymath learning achieves stronger performance than larger datasets, demonstrating that reasoning structure and skills in samples, rather than quantity, may be the key to unlock enhanced reasoning capabilities in language models. Our results suggest a shift, dubbed as sample engineering, toward precision engineering of samples that complements simply increasing data volume.