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

TL;DR

This paper provides a theoretical analysis of how pretraining and post-training methods like SFT and RL interact with dataset size and quality in transformer models, revealing conditions for optimal data use.

Contribution

It introduces a theoretical framework analyzing transformers on an in-context weight prediction task, explaining the effects of data size and quality on different training strategies.

Findings

Balanced pretraining data can enable latent capabilities for post-training.

Small, challenging datasets improve SFT effectiveness, while large datasets may dilute signals.

RL benefits most from large-scale, manageable data for pretrained models.

Abstract

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.