# Data Mixing Can Induce Phase Transitions in Knowledge Acquisition

arXiv: https://arxiv.org/abs/2505.18091 · HTML: https://mlsanity.com/paper/2505.18091/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 69 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 30 of 49)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [How Much Knowledge Can You Pack Into the Parameters of a Language Model?](https://mlsanity.com/paper/2002.08910/) (2020)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [The Stack: 3 TB of permissively licensed source code](https://mlsanity.com/paper/2211.15533/) (2022)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models](https://mlsanity.com/paper/2205.10770/) (2022)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Head-to-Tail: How Knowledgeable are Large Language Models (LLMs)? A.K.A. Will LLMs Replace Knowledge Graphs?](https://mlsanity.com/paper/2308.10168/) (2023)
- [Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Dataset](https://mlsanity.com/paper/2412.02595/) (2024)

## Built on by (most cited first, 16 of 16)

- [Kimi-Dev: Agentless Training as Skill Prior for SWE-Agents](https://mlsanity.com/paper/2509.23045/) (2025)
- [Can Small Training Runs Reliably Guide Data Curation? Rethinking Proxy-Model Practice](https://mlsanity.com/paper/2512.24503/) (2025)
- [Cram Less to Fit More: Training Data Pruning Improves Memorization of Facts](https://mlsanity.com/paper/2604.08519/) (2026)
- [Understanding Data Temporality Impact on Large Language Models Pre-training](https://mlsanity.com/paper/2605.22769/) (2026)
- [Structure Before Collapse: Transient semantic geometry in next-token prediction](https://mlsanity.com/paper/2606.26749/) (2026)
- [Scaling Domain Data Repetition in LLM Pretraining](https://mlsanity.com/paper/2608.14071/) (2026)
- [Capacity-Aware Mixture Law Enables Efficient LLM Data Optimization](https://mlsanity.com/paper/2603.08022/) (2026)
- [The Future of Facts: Tracing the Factual Generation-Verification Gap](https://mlsanity.com/paper/2605.27564/) (2026)
- [Explaining Data Mixing Scaling Laws](https://mlsanity.com/paper/2606.08167/) (2026)
- [SPA: A Simple but Tough-to-Beat Baseline for Knowledge Injection](https://mlsanity.com/paper/2603.22213/) (2026)
- [The Kinetics of Training: A Driven-Nucleation Rate Law for Emergence, Plasticity Loss, and Circuit Control in Language Models](https://mlsanity.com/paper/2607.27281/) (2026)
- [Harnessing the Potential of Optimizing Data Mixtures via Bayesian Domain Reweighting](https://mlsanity.com/paper/2607.27928/) (2026)
- [Small Models Scout Bottleneck Order for Large-Model Data Control](https://mlsanity.com/paper/2608.14936/) (2026)
- [The Free-Recipe Limit: Every Recipe Effect Measures Which Premise of an Idealised Learner Broke](https://mlsanity.com/paper/2609.26160/) (2026)
- [Generalization Dynamics of LM Pre-training](https://mlsanity.com/paper/2609.33150/) (2026)
- [Conflicting Supervision Moves Commitment, Not Capability: A 12.29σ arrangement effect that is exactly zero under a convention-agnostic score](https://mlsanity.com/paper/2610.00234/) (2026)

## Abstract (arXiv)

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.