Learning From Itself.
Generated data is useful when it is checked and mixed with real data; recursive and unchecked, it narrows.
This volume describes the field as of October 2026. Claims are marked established (replicated or long-standing), reported (from a single lab or report, not independently reproduced) or contested (actively disputed). Synthetic data is now a standard ingredient (established): reasoning traces from strong models distilled into small ones (plate XIX.11), generated exercises filtered by verifiers, rewritten web text, and self-play in which a model sets and solves its own problems. Shumailov and colleagues (Nature, 2024) showed the failure mode: models trained recursively on the previous generation’s output lose the tails of the original distribution and converge to a narrowing caricature — model collapse. Later work showed that keeping the real data and adding synthetic data, rather than replacing it, avoids the collapse in their settings (established for those settings).
The workshop repeats the core experiment with word-bigram models of held-out course text: each generation is fitted to words sampled from the previous one, either replacing the data or accumulating it alongside the real text, and it tracks how many of the real text’s rare words survive.
Below: the share of the real text’s rare words still produced, and the cross-entropy of held-out real text, over generations, for replacing and accumulating.
- Describe current uses of synthetic data.
- Explain model collapse.
- Contrast replacing with accumulating data.
- State what keeps self-training healthy.
Check it, and keep the real data
Replacing the data each generation, the word model still produces only 16% of the real text’s rare words after eight generations, and its cross-entropy on held-out real text rises from 6.84 to 7.24 nats — each generation can only resample what the last one happened to produce, and what it misses is gone. Accumulating alongside the real text keeps 54% of the rare words, with held-out cross-entropy 7.00. The real data anchors the distribution; the generated data adds to it.
The successful uses of synthetic data share two features the collapse experiment lacks: verification — generated solutions kept only when checked, as in expert iteration (plate XXVI.6) — and a source of new information outside the model: a stronger teacher, a verifier, an environment, real data mixed in. Self-play systems that invent their own problems (reported in 2025 for code and maths with an executor as the verifier) depend on that external check. Whether self-generated data can carry a frontier model past the limits of human-written data is contested — it is the hope behind several responses to the data wall (next plate).
Terms
- Synthetic data
- Training data generated by models.
- Model collapse
- Degeneration from training recursively on model output.
- Self-play
- A model generating its own problems and learning from solving them.
- Verification
- Checking generated data before training on it.
Sources
- Shumailov et al., “AI models collapse when trained on recursively generated data”, Nature 631, 2024.
- Gerstgrasser et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data”, arXiv:2404.01413, 2024.
- Zhao et al., “Absolute Zero: Reinforced Self-play Reasoning with Zero Data”, arXiv:2505.03335, 2025.
- Abdin et al., “Phi-4 Technical Report”, arXiv:2412.08905, 2024 (synthetic data at scale).