[Paper Review] Strong Model Collapse

Elvis Dohmatob, Yunzhen Feng+2 more|arXiv (Cornell University)|Oct 7, 2024

Complex Systems and Time Series AnalysisEconomics, Econometrics and Finance3 citations

TL;DR

This paper establishes 'strong model collapse'—a critical performance degradation in machine learning models even with minimal synthetic data (as low as 1%) in training sets. Using linear regression and random projection models, it proves that larger models can exacerbate collapse unless they exceed the interpolation threshold, where robustness may improve, though collapse persists asymptotically unless synthetic data fraction vanishes.

ABSTRACT

Within the scaling laws paradigm, which underpins the training of large neural networks like ChatGPT and Llama, we consider a supervised regression setting and establish the existance of a strong form of the model collapse phenomenon, a critical performance degradation due to synthetic data in the training corpus. Our results show that even the smallest fraction of synthetic data (e.g., as little as 1\% of the total training dataset) can still lead to model collapse: larger and larger training sets do not enhance performance. We further investigate whether increasing model size, an approach aligned with current trends in training large language models, exacerbates or mitigates model collapse. In a simplified regime where neural networks are approximated via random projections of tunable size, we both theoretically and empirically show that larger models can amplify model collapse. Interestingly, our theory also indicates that, beyond the interpolation threshold (which can be extremely high for very large datasets), larger models may mitigate the collapse, although they do not entirely prevent it. Our theoretical findings are empirically verified through experiments on language models and feed-forward neural networks for images.

Motivation & Objective

• To investigate whether model collapse is inevitable when training data contains even a small fraction of synthetic data.
• To determine whether increasing model size mitigates or amplifies model collapse under synthetic data contamination.
• To establish a theoretical foundation for model collapse within the neural scaling laws paradigm, focusing on generalization failure under data distribution shift.
• To analyze the role of model capacity and data mixtures in determining long-term model performance degradation.
• To verify theoretical predictions through empirical evaluation on language models and image-classification networks.

Proposed method

• Analyzes a supervised regression setup with synthetic and real data, modeling the data-generating distribution and the model's learned distribution.
• Uses random projections to approximate neural network behavior, treating model capacity via the parametrization rate $\psi = m/n$.
• Derives fixed-point equations for key quantities (e.g., $\tau$, $e$, $\chi$, $\kappa$) in the limit of small regularization ($\lambda \to 0^+$) to study generalization error.
• Applies tools from random matrix theory and linear algebra to characterize the test error as a function of model size and synthetic data ratio.
• Derives analytic expressions for the limiting behavior of model parameters and generalization error under varying synthetic data proportions and model capacities.
• Empirically validates theoretical findings using feed-forward networks on image data and fine-tuned LLMs, measuring test error under synthetic data contamination.

Experimental results

Research questions

• RQ1 Is model collapse inevitable when even a small fraction of training data is synthetic, and can it be mitigated by data weighting or mixing strategies?
• RQ2 How does model size affect susceptibility to model collapse under synthetic data contamination?
• RQ3 Does the interpolation threshold (where model capacity matches data size) mark a regime shift in model robustness to synthetic data?
• RQ4 Can theoretical predictions on generalization error be empirically verified in real-world models like LLMs and CNNs?
• RQ5 What is the asymptotic behavior of model performance as training data size grows, when synthetic data is present in a non-vanishing fraction?

Key findings

• Even 1% synthetic data in the training set leads to strong model collapse, where increasing training data size fails to improve performance.
• Larger models amplify model collapse when the synthetic data distribution deviates significantly from the real data distribution.
• Beyond the interpolation threshold, larger models may mitigate collapse due to improved generalization, though they do not fully prevent it.
• Theoretical analysis shows that model collapse persists unless the fraction of synthetic data asymptotically approaches zero.
• Empirical results on image and language models confirm that test error increases with synthetic data ratio and model size, aligning with theoretical predictions.
• The unregularized limit reveals that generalization error depends critically on the parametrization rate $\psi = m/n$ and the deviation between synthetic and real data distributions.