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Collapse or Thrive: Perils and Promises of Synthetic Data in a Self-Generating World
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Tests three data-usage workflows (replace, accumulate, accumulate-subsample) for model collapse across multivariate Gaussian, KDE, linear regression, and language model fine-tuning/pretraining settings, finding collapse only under replace.
Problem
Whether model collapse from training generative models on synthetic data is unavoidable, or can be contained by how real and synthetic data are accumulated and used in training; prior work disagrees on definitions and assumed workflows.
Approach
Disentangle collapse by explicitly comparing three training-workflows (replace, accumulate, and a fixed-compute accumulate-subsample) across several task-settings, with theoretical results for Gaussian and KDE cases, and an empirical study of real vs synthetic data proportions in SFT.
Key results
- Under replace, test loss on real data diverges across generations in all studied settings, while accumulate keeps test loss bounded across the three new settings (MGM, KDE, SFT).
- Accumulate-subsample shows slower, gradual degradation: its test loss lies between accumulate and replace across five task-settings, often plateauing at a higher level than accumulate.
- In SFT with Gemma 2 2B, when real data are at most 1024 points, a small amount of synthetic data (near 1024 points) lowers test loss; with more than 1024 real points, adding synthetic data generally increases test loss.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace prior data with each generation's synthetic data | Iterative generative modeling · Multivariate Gaussian modeling, KDE, and supervised fine-tuning | test loss | Hurt |
| Retain real and synthetic data across generations instead of replacing prior data | Iterative generative modeling · Multivariate Gaussian modeling, KDE, and supervised fine-tuning | test loss | Helped |
| Use fixed-size subsamples from the accumulated pool instead of training on all accumulated data | Iterative generative modeling · Five generative-model task-settings | test loss | Hurt |
| Accumulate real and synthetic data rather than replacing prior data | Kernel density estimation · Blobs, circles, moons, and Swiss roll | negative log-likelihood | Mixed |
| Add a small amount of synthetic data when real data are scarce | Gemma 2 2B fine-tuning · HelpSteer2, 1024 or fewer real datapoints | test loss | Helped |
| Add synthetic data while holding plentiful real data constant | Gemma 2 2B fine-tuning · HelpSteer2, more than 1024 real datapoints | test loss | Hurt |
| Use transformed real-data cardinality as a predictor of test loss | Gemma 2 2B fine-tuning · HelpSteer2, mixed real and synthetic data | R²: 0.59 | Helped |
| Use real-data proportion as a predictor of test loss | Gemma 2 2B fine-tuning · HelpSteer2, mixed real and synthetic data | R²: 0.34 | Helped |
| Adjust the KDE bandwidth at each generation to c·(tn)^−1/5 (ablation) | Accumulating KDE · Kernel density estimation | asymptotic variance | Helped |
Surprising findings
- Accumulating real and synthetic data can yield lower held-out real-data NLL than training on real data alone in KDE experiments.
- Removing all synthetic data can yield better SFT test loss than doubling the amount of real data.
Limitations
- Experiments ignore data quality and filtering, which practitioners use heavily.
- Accumulate-subsample still shows degradation, and KDE with out-of-the-box bandwidth may diverge slowly even under accumulate.
Experimental setup
Datasets: NVIDIA HelpSteer2 sklearn synthetic datasets (blobs, circles, moons, swiss roll) TinyStories
Benchmarks: sklearn synthetic datasets (NLL on held-out real data) HelpSteer2 test loss TinyStories test loss
Metrics: test loss negative log likelihood squared error of fitted mean Wasserstein-2 distance R^2 F-statistic
Baselines: replace workflow accumulate workflow
Builds on: Gerstgrasser et al. accumulate vs replace model collapse analysis Shumailov et al. model collapse
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