We open-source a state-of-the-art 4B-parameter generative model series for Vietnamese, which includes the base pre-trained monolingual model PhoGPT-4B and its chat variant, PhoGPT-4B-Chat. The base model, PhoGPT-4B, with exactly 3.7B parameters, is pre-trained from scratch on a Vietnamese corpus of 102B tokens, with an 8192 context length, employing a vocabulary of 20480 token types. The chat variant, PhoGPT-4B-Chat, is the modeling output obtained by fine-tuning PhoGPT-4B on a dataset of 70K instructional prompts and their responses, along with an additional 290K conversations. We demonstrate its strong performance compared to previous closed-source and open-source 7B-parameter models. Our PhoGPT models are available at: https://github.com/VinAIResearch/PhoGPT

We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive. Furthermore, we provide the relevant rules for the computation of the neighbours of a model. The latter are more efficient than the same operations in the model inclusion lattice, and are then exploited to achieve a more efficient exploration of the search space. These results can be applied to improve the efficiency of both greedy and Bayesian model search procedures. Here we implement a stepwise backward elimination procedure and evaluate its performance by means of simulations. Finally, the procedure is applied to learn a brain network from fMRI data where the two groups correspond to the left and right hemispheres, respectively.