# A Tale of Tails: Model Collapse as a Change of Scaling Laws

arXiv: https://arxiv.org/abs/2402.07043 · HTML: https://mlsanity.com/paper/2402.07043/

## Key facts

- Cited by 130 papers in the map (data through 14 Oct 2026).
- Placed in Model collapse from synthetic data, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 48 of its 68 references that are in the map.
- First posted on arXiv 10 Feb 2024.

## Placed in

- Synthetic data and self-improvement for LLMs / [Model collapse from synthetic data](https://mlsanity.com/synth/model-collapse-from-synthetic-data/)

## Builds on (most cited first, 30 of 48)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (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)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Synthetic Data from Diffusion Models Improves ImageNet Classification](https://mlsanity.com/paper/2304.08466/) (2023)
- [Is synthetic data from generative models ready for image recognition?](https://mlsanity.com/paper/2210.07574/) (2022)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Inverse Scaling: When Bigger Isn't Better](https://mlsanity.com/paper/2306.09479/) (2023)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [The Quantization Model of Neural Scaling](https://mlsanity.com/paper/2303.13506/) (2023)
- [Scaling Laws for Generative Mixed-Modal Language Models](https://mlsanity.com/paper/2301.03728/) (2023)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [A Solvable Model of Neural Scaling Laws](https://mlsanity.com/paper/2210.16859/) (2022)
- [A Theory for Emergence of Complex Skills in Language Models](https://mlsanity.com/paper/2307.15936/) (2023)

## Built on by (most cited first, 30 of 130)

- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (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)
- [Scaling Laws in Linear Regression: Compute, Parameters, and Data](https://mlsanity.com/paper/2406.08466/) (2024)
- [Large Language Models Can Self-Improve At Web Agent Tasks](https://mlsanity.com/paper/2405.20309/) (2024)
- [Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World](https://mlsanity.com/paper/2410.16713/) (2024)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Beyond Model Collapse: Scaling Up with Synthesized Data Requires Verification](https://mlsanity.com/paper/2406.07515/) (2024)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Is Synthetic Data all We Need? Benchmarking the Robustness of Models Trained with Synthetic Images](https://mlsanity.com/paper/2405.20469/) (2024)
- [Scaling Optimal LR Across Token Horizons](https://mlsanity.com/paper/2409.19913/) (2024)
- [Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferences](https://mlsanity.com/paper/2407.09499/) (2024)
- [Self-Improving Diffusion Models with Synthetic Data](https://mlsanity.com/paper/2408.16333/) (2024)
- [AI and the Problem of Knowledge Collapse](https://mlsanity.com/paper/2404.03502/) (2024)
- [Position: Model Collapse Does Not Mean What You Think](https://mlsanity.com/paper/2503.03150/) (2025)
- [Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges](https://mlsanity.com/paper/2502.01612/) (2025)
- [Universality of the π2/6 Pathway in Avoiding Model Collapse](https://mlsanity.com/paper/2410.22812/) (2024)
- [Demystifying Synthetic Data in LLM Pre-training: A Systematic Study of Scaling Laws, Benefits, and Pitfalls](https://mlsanity.com/paper/2510.01631/) (2025)
- [How to Synthesize Text Data without Model Collapse?](https://mlsanity.com/paper/2412.14689/) (2024)
- [Rate of Model Collapse in Recursive Training](https://mlsanity.com/paper/2412.17646/) (2024)
- [Researchy Questions: A Dataset of Multi-Perspective, Decompositional Questions for LLM Web Agents](https://mlsanity.com/paper/2402.17896/) (2024)
- [Let's Ask GNN: Empowering Large Language Model for Graph In-Context Learning](https://mlsanity.com/paper/2410.07074/) (2024)
- [A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective](https://mlsanity.com/paper/2509.16499/) (2025)
- [When LLMs Play the Telephone Game: Cultural Attractors as Conceptual Tools to Evaluate LLMs in Multi-turn Settings](https://mlsanity.com/paper/2407.04503/) (2024)
- [Improving the Scaling Laws of Synthetic Data with Deliberate Practice](https://mlsanity.com/paper/2502.15588/) (2025)
- [A Theoretical Perspective: How to Prevent Model Collapse in Self-consuming Training Loops](https://mlsanity.com/paper/2502.18865/) (2025)

## Abstract (arXiv)

As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2.