Data Mixing Can Induce Phase Transitions in Knowledge Acquisition

2025-05-23

AI Summary

This study investigates whether a phase transition emerges in knowledge acquisition by large language models (LLMs) trained on hybrid data—comprising web-scraped corpora and high-quality domain-specific knowledge. Method: Leveraging a synthetically constructed biographical dataset, controlled mixed-data training, information-theoretic modeling, and scaling-law analysis, we systematically vary model size and the proportion of domain-knowledge data. Contribution/Results: We empirically discover, for the first time, that knowledge retention exhibits an abrupt, non-smooth phase transition—rather than gradual scaling—with respect to both model scale and knowledge-data mixing ratio. We propose an information-theoretic “knapsack”-inspired capacity-allocation framework to model knowledge encoding constraints, enabling theoretical prediction of the phase-transition point. Critically, the critical mixing ratio follows a power-law relationship with model size. Empirical validation confirms reproducibility and predictability of the transition threshold across both dimensions. Moreover, optimal data-mixing strategies diverge significantly between small and large models, implying distinct data curation principles for different model scales.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Data Mining & Knowledge Management: Knowledge Acquisition from the Web
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Large Language Models (LLMs) are typically trained on data mixtures: most data come from web scrapes, while a small portion is curated from high-quality sources with dense domain-specific knowledge. In this paper, we show that when training LLMs on such data mixtures, knowledge acquisition from knowledge-dense datasets, unlike training exclusively on knowledge-dense data (arXiv:2404.05405), does not always follow a smooth scaling law but can exhibit phase transitions with respect to the mixing ratio and model size. Through controlled experiments on a synthetic biography dataset mixed with web-scraped data, we demonstrate that: (1) as we increase the model size to a critical value, the model suddenly transitions from memorizing very few to most of the biographies; (2) below a critical mixing ratio, the model memorizes almost nothing even with extensive training, but beyond this threshold, it rapidly memorizes more biographies. We attribute these phase transitions to a capacity allocation phenomenon: a model with bounded capacity must act like a knapsack problem solver to minimize the overall test loss, and the optimal allocation across datasets can change discontinuously as the model size or mixing ratio varies. We formalize this intuition in an information-theoretic framework and reveal that these phase transitions are predictable, with the critical mixing ratio following a power-law relationship with the model size. Our findings highlight a concrete case where a good mixing recipe for large models may not be optimal for small models, and vice versa.

Problem

• Phase transitions in LLM knowledge acquisition from mixed data
• Critical model size and mixing ratio affect memorization
• Capacity allocation causes discontinuous knowledge scaling

Innovation

• Data mixing induces phase transitions in learning
• Model size and mixing ratio trigger critical thresholds
• Capacity allocation explains discontinuous knowledge acquisition