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We study (differentially) private federated learning (FL) of language models. The language models in cross-device FL are relatively small, which can be trained with meaningful formal user-level differential privacy (DP) guarantees when massive parallelism in training is enabled by the participation of a moderate size of users. Recently, public data has been used to improve privacy-utility trade-offs for both large and small language models. In this work, we provide a systematic study of using large-scale public data and LLMs to help differentially private training of on-device FL models, and further improve the privacy-utility tradeoff by techniques of distillation. Moreover, we propose a novel distribution matching algorithm with theoretical grounding to sample public data close to private data distribution, which significantly improves the sample efficiency of (pre-) training on public data. The proposed method is efficient and effective for training private models by taking advantage of public data, especially for customized on-device architectures that do not have ready-touse pre-trained models. 

Abstract Atmospheric warming heats lakes, but the causes of variation among basins are poorly understood. Here, multi-decadal profiles of water temperatures, trophic state, and local climate from 345 temperate lakes are combined with data on lake geomorphology and watershed characteristics to identify controls of the relative rates of temperature change in water (WT) and air (AT) during summer. We show that differences in local climate (AT, wind speed, humidity, irradiance), land cover (forest, urban, agriculture), geomorphology (elevation, area/depth ratio), and water transparency explain >30% of the difference in rate of lake heating compared to that of the atmosphere. Importantly, the rate of lake heating slows as air warms (P < 0.001). Clear, cold, and deep lakes, especially at high elevation and in undisturbed catchments, are particularly responsive to changes in atmospheric temperature. We suggest that rates of surface water warming may decline relative to the atmosphere in a warmer future, particularly in sites already experiencing terrestrial development or eutrophication.