A Conditional No-Hair Theorem for Transformers: How Language Models Forget Their Prompt
We ask how much an autoregressive transformer retains of its prompt after generating $t$ tokens. Consider two different prompts followed by the same continuation text, so that any difference in their hidden states comes from the prompt alone, and we find that the distance between their hidden states decays approximately as a power law $t^{-α}$, where $α=1$ is the rate at which a fixed prompt's share of uniform attention shrinks and smaller values mean longer memory. Trained models forget fast ($α\approx0.55$--$0.7$), untrained ones slowly ($α\approx0.2$--$0.5$). We prove that this offset is $O\big(P(\log t)^{L-1}/t\big)$ for a prompt of length $P$ and depth $L$. The bound holds for finite...
| Authors | Shuyang Xiang |
|---|---|
| Primary category | cs.AI |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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