The two clocks and the innovation window: When and how generative models learn rules
Generative models trained on finite data face a fundamental tension: their score-matching or next-token objective converges to the empirical training distribution rather than the population distribution we seek to learn. Using rule-valid synthetic tasks, we trace this tension across two training timescales: $τ_{\mathrm{rule}}$, the step at which generations first become rule-valid, and $τ_{\mathrm{mem}}$, the step at which models begin reproducing training samples. Focusing on parity and extending to other binary rules and combinatorial puzzles, we characterize how these two clocks, $τ_{\mathrm{rule}}$ and $τ_{\mathrm{mem}}$, depend on key aspects of the learning setup. Specifically, we s...
| Authors | Binxu Wang, Emma Lucia Byrnes Finn, Bingbin Liu |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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