Rarity Determines Minimax Rates of Semantic Entropy From Weak Pairwise Judgments With a Known Channel
The semantic entropy of a language model is the entropy of the meanings of its sampled answers. The meanings are never observed, and the entropy is estimated from the verdicts of a pairwise equivalence judge. Given the meanings of $n$ answers, a known channel declares each pair equivalent independently, with probability $q+Δ$ within a meaning and $q$ across meanings. At most $K$ meanings occur, and $q$ is bounded away from $0$ and $1$. For a weak judge, with $nΔ^2\to0$, the global minimax rate is set by distributions near a vertex of the simplex and overstates the difficulty elsewhere. We show that the difficulty is set by how many meanings can be rare. Over distributions with at most $s$...
| Authors | Xiaoli Yu, Jiamiao Liu |
|---|---|
| Primary category | cs.IT |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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