# Sub-Scaling Laws: On the Role of Data Density and Training Strategies in LLMs

arXiv: https://arxiv.org/abs/2507.10613 · HTML: https://mlsanity.com/paper/2507.10613/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## Builds on (most cited first, 27 of 27)

- [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)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Model](https://mlsanity.com/paper/2201.11990/) (2022)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Scaling Laws and Interpretability of Learning from Repeated Data](https://mlsanity.com/paper/2205.10487/) (2022)
- [Scaling Laws for Neural Machine Translation](https://mlsanity.com/paper/2109.07740/) (2021)
- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [Pareto Self-Supervised Training for Few-Shot Learning](https://mlsanity.com/paper/2104.07841/) (2021)
- [One Epoch Is All You Need](https://mlsanity.com/paper/1906.06669/) (2019)
- [Effective pruning of web-scale datasets based on complexity of concept clusters](https://mlsanity.com/paper/2401.04578/) (2024)
- [Predicting Emergent Abilities with Infinite Resolution Evaluation](https://mlsanity.com/paper/2310.03262/) (2023)
- [SimPER: A Minimalist Approach to Preference Alignment without Hyperparameters](https://mlsanity.com/paper/2502.00883/) (2025)
- [On a Connection Between Imitation Learning and RLHF](https://mlsanity.com/paper/2503.05079/) (2025)
- [From Mathematical Reasoning to Code: Generalization of Process Reward Models in Test-Time Scaling](https://mlsanity.com/paper/2506.00027/) (2025)
- [The Fine Line: Navigating Large Language Model Pretraining with Down-streaming Capability Analysis](https://mlsanity.com/paper/2404.01204/) (2024)

## Built on by (most cited first, 2 of 2)

- [InfoLaw: Information Scaling Laws for Large Language Models with Quality-Weighted Mixture Data and Repetition](https://mlsanity.com/paper/2605.02364/) (2026)
- [Principled Synthetic Data Enables the First Scaling Laws for LLMs in Recommendation](https://mlsanity.com/paper/2602.07298/) (2026)

## Abstract (arXiv)

Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance improvements decelerate, which is a phenomenon known as sub-scaling. This paper revisits these scaling laws by examining the impact of data quality and training strategies on model performance. Through extensive empirical analysis of over 400 models, we identify high data density and non-optimal resource allocation as key factors contributing to sub-scaling. High data density leads to diminishing returns due to redundant information, while optimal resource allocation is crucial for sustained performance improvements. We propose a sub-optimal scaling law that better predicts performance in sub-scaling regimes, highlighting the importance of data quality and diversity.