Private Uniform Language Generation

Di Wang; Peng Ye

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arXiv · 2611.00797

Private Uniform Language Generation

Di Wang·Peng Ye

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Abstract

We study uniform language generation under approximate differential privacy. Given a uniformly bounded number of distinct examples from an unknown target language, a generator must produce infinitely many new examples from that language with probability one while protecting the privacy of its input. We introduce a new combinatorial dimension termed the nested branching dimension and prove that a language class is privately uniformly generatable if and only if both its closure dimension and nested branching dimension are finite. Previous work characterizes non-private uniform generation by the finiteness of the closure dimension alone. Our results therefore identify an additional combinatorial obstruction imposed by privacy.

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BibTeX RIS

Di Wang, Peng Ye. 2026-10-31. Private Uniform Language Generation. https://arxiv.org/abs/2611.00797

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