On the Price of Privacy for Language Identification and Generation

We initiate the study of language generation in the limit, a model recently introduced by Kleinberg and Mullainathan [KM24], under the constraint of differential privacy. We consider the continual release model, where a generator must eventually output a stream of valid strings while protecting the privacy of the entire input sequence. Our first main result is that for countable collections of languages, privacy comes at no qualitative cost: we provide an $\varepsilon$-differentially-private algorithm that generates in the limit from any countable collection. This stands in contrast to many learning settings where privacy renders learnability impossible. However, privacy does impose a quantitative cost: there are finite collections of size $k$ for which uniform private generation requires $Ω(k/\varepsilon)$ samples, whereas just one sample suffices non-privately. We then turn to the harder problem of language identification in the limit. Here, we show that privacy creates fundamental barriers. We prove that no $\varepsilon$-DP algorithm can identify a collection containing two languages with an infinite intersection and a finite set difference, a condition far stronger than the classical non-private characterization of identification. Next, we turn to the stochastic setting where the sample strings are sampled i.i.d. from a distribution (instead of being generated by an adversary). Here, we show that private identification is possible if and only if the collection is identifiable in the adversarial model. Together, our results establish new dimensions along which generation and identification differ and, for identification, a separation between adversarial and stochastic settings induced by privacy constraints.

Differentially private (DP) fine-tuning of large language models (LLMs) requires massive compute and full model access, which rules out state-of-the-art proprietary APIs for general users. Generating DP synthetic data offers a practical workaround. This approach also allows for transparent exploratory data analysis and arbitrary reuse across downstream tasks, sidestepping the rigid constraints of a model's parameter space. Private Evolution (PE) provides a promising API-based framework for generating this data, but its success relies heavily on initialization. If the private data distribution falls too far outside the foundation model's pre-training priors -- a common issue in highly specialized domain -- PE struggles to align with the target data. This misalignment causes poor convergence, degraded utility, and wasted API calls. To solve this initialization bottleneck, we introduce Metadata Augmented Private Language Evolution (MAPLE). MAPLE extracts DP tabular metadata and uses in-context learning to firmly ground the initial synthetic distribution in the target domain. Our evaluations on domain-specific text generation tasks show that MAPLE yields a strictly better privacy-utility trade-off, converges significantly faster, and sharply reduces API costs compared to baseline PE methods.

Large language models (LLMs) are increasingly adapted to proprietary and domain-specific corpora that contain sensitive information, creating a tension between formal privacy guarantees and efficient deployment through model compression. Differential privacy (DP), typically enforced via DP-SGD, provides record-level protection but often incurs substantial utility loss in autoregressive generation, where optimization noise can amplify exposure bias and compounding errors along long rollouts. Existing approaches to private distillation either apply DP-SGD to both teacher and student, worsening computation and the privacy--utility tradeoff, or rely on DP synthetic text generation from a DP-trained teacher, avoiding DP on the student at the cost of DP-optimizing a large teacher and introducing an offline generation pipeline. We propose Differentially Private On-Policy Distillation (DP-OPD), a synthesis-free framework that enforces privacy solely through DP-SGD on the student while leveraging a frozen teacher to provide dense token-level targets on student-generated trajectories. DP-OPD instantiates this idea via private generalized knowledge distillation on continuation tokens. Under a strict privacy budget ($\varepsilon=2.0$), DP-OPD improves perplexity over DP fine-tuning and off-policy DP distillation, and outperforms synthesis-based DP distillation (Yelp: 44.15$\rightarrow$41.68; BigPatent: 32.43$\rightarrow$30.63), while substantially simplifying the training pipeline. In particular, DP-OPD collapses private compression into a single DP student-training loop by eliminating DP teacher training and offline synthetic text generation. Code will be released upon publication at https://github.com/khademfatemeh/dp_opd.