# Theoretical Perspectives on Data Quality and Synergistic Effects in Pre- and Post-Training Reasoning Models

arXiv: https://arxiv.org/abs/2603.01293 · HTML: https://mlsanity.com/paper/2603.01293/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [m1: Unleash the Potential of Test-Time Scaling for Medical Reasoning with Large Language Models](https://mlsanity.com/paper/2504.00869/) (2025)
- [SmallToLarge (S2L): Scalable Data Selection for Fine-tuning Large Language Models by Summarizing Training Trajectories of Small Models](https://mlsanity.com/paper/2403.07384/) (2024)
- [Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought](https://mlsanity.com/paper/2502.21212/) (2025)
- [Front-Loading Reasoning: The Synergy between Pretraining and Post-Training Data](https://mlsanity.com/paper/2510.03264/) (2025)
- [Logarithmic Regret for Online KL-Regularized Reinforcement Learning](https://mlsanity.com/paper/2502.07460/) (2025)
- [Mini-batch Coresets for Memory-efficient Language Model Training on Data Mixtures](https://mlsanity.com/paper/2407.19580/) (2024)
- [KL-Regularized RLHF with Multiple Reference Models: Exact Solutions and Sample Complexity](https://mlsanity.com/paper/2502.01203/) (2025)
- [Understanding the Role of Training Data in Test-Time Scaling](https://mlsanity.com/paper/2510.03605/) (2025)

## Built on by (most cited first, 3 of 3)

- [InfoSFT: Learn More and Forget Less with Information-Aware Token Weighting](https://mlsanity.com/paper/2605.14967/) (2026)
- [Reasoning Quality Emerges Early: Data Curation for Reasoning Models](https://mlsanity.com/paper/2606.26797/) (2026)
- [An Asymptotic Theory of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2606.03217/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are pretrained on massive datasets and later instruction-tuned via supervised fine-tuning (SFT) or reinforcement learning (RL). Best practices emphasize large, diverse pretraining data, whereas post-training operates differently: SFT relies on smaller, high-quality datasets, while RL benefits more from scale, with larger amounts of feedback often outweighing label quality. Yet it remains unclear why pretraining and RL require large datasets, why SFT excels on smaller ones, and what defines high-quality SFT data. In this work, we theoretically analyze transformers trained on an in-context weight prediction task for linear regression. Our analysis reveals several key findings: (i) balanced pretraining data can induce latent capabilities later activated during post-training, and (ii) SFT learns best from a small set of examples challenging for the pretrained model, while excessively large SFT datasets may dilute informative pretraining signals. In contrast, RL is most effective on large-scale data that is not overly difficult for the pretrained model. We validate these theoretical insights with experiments on large nonlinear transformer architectures.