# Hard Examples Are All You Need: Maximizing GRPO Post-Training Under Annotation Budgets

arXiv: https://arxiv.org/abs/2508.14094 · HTML: https://mlsanity.com/paper/2508.14094/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [On The Power of Curriculum Learning in Training Deep Networks](https://mlsanity.com/paper/1904.03626/) (2019)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Improving Data Efficiency for LLM Reinforcement Fine-tuning Through Difficulty-targeted Online Data Selection and Rollout Replay](https://mlsanity.com/paper/2506.05316/) (2025)
- [DeepDistill: Enhancing LLM Reasoning Capabilities via Large-Scale Difficulty-Graded Data Training](https://mlsanity.com/paper/2504.17565/) (2025)
- [SPARQ: Synthetic Problem Generation for Reasoning via Quality-Diversity Algorithms](https://mlsanity.com/paper/2506.06499/) (2025)
- [Understanding Trade offs When Conditioning Synthetic Data](https://mlsanity.com/paper/2507.02217/) (2025)

## Built on by (most cited first, 17 of 17)

- [BOTS: A Unified Framework for Bayesian Online Task Selection in LLM Reinforcement Finetuning](https://mlsanity.com/paper/2510.26374/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptation](https://mlsanity.com/paper/2602.05548/) (2026)
- [Revisiting Generalization Across Difficulty Levels: It's Not So Easy](https://mlsanity.com/paper/2511.21692/) (2025)
- [DeReason: A Difficulty-Aware Curriculum Improves Decoupled SFT-then-RL Training for General Reasoning](https://mlsanity.com/paper/2603.11193/) (2026)
- [LLM Reasoning with Process Rewards for Outcome-Guided Steps](https://mlsanity.com/paper/2604.02341/) (2026)
- [Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery](https://mlsanity.com/paper/2609.19164/) (2026)
- [ToMPO: Training LLM Strategic Decision Making from a Multi-Agent Perspective](https://mlsanity.com/paper/2509.21134/) (2025)
- [Rethinking Reinforcement fine-tuning of LLMs: A Multi-armed Bandit Learning Perspective](https://mlsanity.com/paper/2601.14599/) (2026)
- [Rethinking Easy-to-Hard: Limits of Curriculum Learning in Post-Training for Deductive Reasoning](https://mlsanity.com/paper/2603.27226/) (2026)
- [Adaptive Loss Balancing for Noise-Robust GRPO in Generative Recommendation](https://mlsanity.com/paper/2606.08480/) (2026)
- [Selective Timestep Weighting and Advantage-Based Replay for Sample-Efficient Diffusion RLHF](https://mlsanity.com/paper/2607.07693/) (2026)
- [Selective Left-Shift: Turning Test-Time Compute and Difficulty-based Curation into Training Data for Low-Resource Code Generation](https://mlsanity.com/paper/2607.07748/) (2026)
- [Wnuan: Staged Post-Training for Question Answering over Proprietary Enterprise Knowledge](https://mlsanity.com/paper/2608.01862/) (2026)
- [Unlocking the Unsolvable: Teacher-Guided Curriculum for Data-Efficient RLVR](https://mlsanity.com/paper/2609.13997/) (2026)
- [OmniFysics-Nano-V2 Technical Report: Understanding the Physical World Across Modalities](https://mlsanity.com/paper/2609.25738/) (2026)
- [DART-ES: Difficulty-Aware Reweighting and Targeted Replay for Fine-Tuning LLMs with Evolution Strategies](https://mlsanity.com/paper/2610.06993/) (2026)

## Abstract (arXiv)

Collecting high-quality training examples for language model fine-tuning is expensive, with practical budgets limiting the amount of data that can be procured. We investigate whether example difficulty affects GRPO training effectiveness by comparing selection strategies (easy, medium, hard, random) across multiple models and reasoning tasks. Training on the hardest 10% of examples (those where the base model fails most often) yields dramatic performance gains up to 47%, while easy examples produce minimal improvements of 3-15%. This occurs because GRPO requires outcome variance to generate learning signals; hard examples maintain mixed success/failure outcomes throughout training while easy examples quickly converge to consistent success, eliminating learning opportunities. Moreover, models trained on hard examples show superior out-of-distribution generalization, with only hard-trained models achieving meaningful gains on the AIME2025 benchmark. Our findings provide clear guidance: when budget-constrained, prioritize collecting and annotating examples where your base model struggles, as these drive nearly all learning value in GRPO fine-tuning