Inspired by Federated Learning, in this paper, we propose personal large models that are distilled from traditional large language models but more adaptive to local users' personal information such as education background and hobbies. We classify the large language models into three levels: the personal level, expert level and traditional level. The personal level models are adaptive to users' personal information. They encrypt the users' input and protect their privacy. The expert level models focus on merging specific knowledge such as finance, IT and art. The traditional models focus on the universal knowledge discovery and upgrading the expert models. In such classifications, the personal models directly interact with the user. For the whole system, the personal models have users' (encrypted) personal information. Moreover, such models must be small enough to be performed on personal computers or mobile devices. Finally, they also have to response in real-time for better user experience and produce high quality results. The proposed personal large models can be applied in a wide range of applications such as language and vision tasks.

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a byproduct, we propose an algorithmic approach that also leads to a significant reduction of space complexity. Our method is based on careful recycling of Gaussian vectors into structured matrices that share properties of fully random matrices. The quality of the proposed structured approach follows from combinatorial properties of the graphs encoding correlations between rows of these structured matrices. Our framework covers as special cases already known structured approaches such as the Fast Johnson-Lindenstrauss Transform, but is much more general since it can be applied also to highly nonlinear embeddings. We provide strong concentration results showing the quality of the presented paradigm.