Identified-Set Geometry of Distributional Model Extraction under Top-$K$ Censored API Access
Modern LLM APIs often reveal only top-$K$ logit scores and censor the remaining vocabulary. We study the per-position distribution-recovery limits of this access model. For censoring threshold $τ$, the compatible teacher distributions form an identified set whose total-variation diameter is exactly $U_K=(V-K)\exp(τ)/(Z_A+(V-K)\exp(τ))$, where $Z_A$ is the observed partition function. For KL recovery, we give a computable binary-endpoint lower bound and an asymptotically matching small-ambiguity upper bound, with an extension to reference-aware attackers. Experiments on a Qwen3 math-reasoning teacher reveal a layered extraction hierarchy: on-task top-$K$ distillation recovers 12% of privat...
| Authors | Wenhua Nie, ZiCheng Zhu, Jianan Wu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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