G. Tang

Y. Du, G. Wu, G. Tang et al.

Synthetic data generated by large language models has become integral to modern NLP training pipelines, from bootstrapping reasoning capabilities to augmenting instruction-following datasets. While recent work demonstrates successful applications maintaining high external data ratios, systematic understanding of how synthetic data proportion affects model behavior across different scales remains limited. This paper presents a controlled empirical study examining model performance, calibration, and output characteristics when trained on varying synthetic-to-external data ratios. Using the Pythia model suite (410M-12B parameters) across five diverse tasks, we evaluate models after one to three training iterations with synthetic data proportions ranging from 0-50\%. Our key findings include: models maintain stable performance with up to 20\% synthetic data, but degradation accelerates beyond 30\%; larger models (6.9B-12B) show greater robustness to synthetic data than smaller models (410M-1.4B); calibration degradation precedes accuracy loss, providing an early warning signal; and task characteristics matter, with reasoning tasks degrading faster than retrieval tasks under synthetic data training. Importantly, we find that current best practices, such as those employed in STaR and Self-Instruct systems that maintain greater than 80\% external data, operate well within safe regimes identified by our experiments. We provide practical guidance for practitioners on synthetic data budgets based on model scale and task requirements, alongside detailed comparison with concurrent work including Shumailov et al.'s model collapse findings.

Y. Du, C. Guo, W. Wang et al.

Large Language Models (LLMs) face a fundamental challenge in deciding when to rely on rapid, intuitive responses versus engaging in slower, more deliberate reasoning. Inspired by Daniel Kahneman's dual-process theory and his insights on human cognitive biases, we propose a novel Cognitive Decision Routing (CDR) framework that dynamically determines the appropriate reasoning strategy based on query characteristics. Our approach addresses the current limitations where models either apply uniform reasoning depth or rely on computationally expensive methods for all queries. We introduce a meta-cognitive layer that analyzes query complexity through multiple dimensions: correlation strength between given information and required conclusions, domain boundary crossings, stakeholder multiplicity, and uncertainty levels. Through extensive experiments on diverse reasoning tasks, we demonstrate that CDR achieves superior performance while reducing computational costs by 34\% compared to uniform deep reasoning approaches. Our framework shows particular strength in professional judgment tasks, achieving 23\% improvement in consistency and 18\% better accuracy on expert-level evaluations. This work bridges cognitive science principles with practical AI system design, offering a principled approach to adaptive reasoning in LLMs.