# Data Value in the Age of Scaling: Understanding LLM Scaling Dynamics Under Real-Synthetic Data Mixtures

arXiv: https://arxiv.org/abs/2511.13640 · HTML: https://mlsanity.com/paper/2511.13640/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in LLM synthetic data generation, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 41 of its 61 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [LLM synthetic data generation](https://mlsanity.com/synth/llm-synthetic-data-generation/)

## Builds on (most cited first, 30 of 41)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [FinGPT: Open-Source Financial Large Language Models](https://mlsanity.com/paper/2306.06031/) (2023)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions](https://mlsanity.com/paper/2405.13954/) (2024)
- [Model Collapse Demystified: The Case of Regression](https://mlsanity.com/paper/2402.07712/) (2024)
- [How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse](https://mlsanity.com/paper/2404.05090/) (2024)
- [Strong Model Collapse](https://mlsanity.com/paper/2410.04840/) (2024)
- [On the Diversity of Synthetic Data and its Impact on Training Large Language Models](https://mlsanity.com/paper/2410.15226/) (2024)
- [Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamics](https://mlsanity.com/paper/2105.03703/) (2021)

## Built on by (most cited first, 1 of 1)

- [Principled Synthetic Data Enables the First Scaling Laws for LLMs in Recommendation](https://mlsanity.com/paper/2602.07298/) (2026)

## Abstract (arXiv)

The rapid progress of large language models (LLMs) is fueled by the growing reliance on datasets that blend real and synthetic data. While synthetic data offers scalability and cost-efficiency, it often introduces systematic distributional discrepancies, particularly underrepresenting long-tail knowledge due to truncation effects from data generation mechanisms like top-p sampling, temperature scaling, and finite sampling. These discrepancies pose fundamental challenges in characterizing and evaluating the utility of mixed real-synthetic datasets. In this paper, we identify a three-phase scaling behavior characterized by two breakpoints that reflect transitions in model behavior across learning head and tail knowledge. We further derive an LLM generalization bound designed for real and synthetic mixtures, revealing several key factors that govern their generalization performance. Building on our theoretical findings, we propose an effective yet efficient data valuation method that scales to large-scale datasets. Comprehensive experiments across four tasks, including image classification, sentiment classification, instruction following, and complex reasoning, demonstrate that our method surpasses state-of-the-art baselines in data valuation with significantly low computational cost.