We introduce HyperCLOVA X, a family of large language models (LLMs) tailored to the Korean language and culture, along with competitive capabilities in English, math, and coding. HyperCLOVA X was trained on a balanced mix of Korean, English, and code data, followed by instruction-tuning with high-quality human-annotated datasets while abiding by strict safety guidelines reflecting our commitment to responsible AI. The model is evaluated across various benchmarks, including comprehensive reasoning, knowledge, commonsense, factuality, coding, math, chatting, instruction-following, and harmlessness, in both Korean and English. HyperCLOVA X exhibits strong reasoning capabilities in Korean backed by a deep understanding of the language and cultural nuances. Further analysis of the inherent bilingual nature and its extension to multilingualism highlights the model's cross-lingual proficiency and strong generalization ability to untargeted languages, including machine translation between several language pairs and cross-lingual inference tasks. We believe that HyperCLOVA X can provide helpful guidance for regions or countries in developing their sovereign LLMs.

L1-Graph has been proven to be effective in data clustering, which partitions the data space by using the sparse representation of the data as the similarity measure. However, the sparse representation is performed for each datum separately without taking into account the geometric structure of the data. Motivated by L1-Graph and manifold leaning, we propose Laplacian Regularized L1-Graph (LRℓ1-Graph) for data clustering. The sparse representations of LRℓ1-Graph are regularized by the geometric information of the data so that they vary smoothly along the geodesics of the data manifold by the graph Laplacian according to the manifold assumption. Moreover, we propose an iterative regularization scheme, where the sparse representation obtained from the previous iteration is used to build the graph Laplacian for the current iteration of regularization. The experimental results on real data sets demonstrate the superiority of our algorithm compared to L1-Graph and other competing clustering methods.