Document retrieval is a critical challenge in information retrieval systems, where the goal is to efficiently retrieve relevant documents in response to a given query. Dense retrieval methods, which utilize vector embeddings to represent semantic information, require effective indexing to ensure fast and accurate retrieval. Existing methods, such as MEVI, have attempted to address this by using hierarchical K-Means for clustering, but they often face limitations in computational efficiency and retrieval accuracy. In this paper, we introduce the Hildoc Index, a novel document indexing approach that leverages the Hilbert Curve to map document embeddings onto a one-dimensional space. This innovative representation facilitates efficient clustering using a 1D quantile-based algorithm, ensuring uniform partition sizes and preserving the inherent structure of the data. As a result, Hildoc Index not only reduces training complexity but also enhances retrieval accuracy and speed during inference. Our method can be seamlessly integrated into both dense retrieval systems and hybrid ensemble systems. Through comprehensive experiments on standard benchmarks like MSMARCO Passage and Natural Questions, we demonstrate that the Hildoc Index significantly outperforms the current state-of-the-art MEVI in terms of both retrieval speed and recall. These results underscore the Hildoc Index as a solution for fast and accurate dense document retrieval.

The effectiveness of the bidirectional encoder representations from transformers (BERT) model for multiple linguistic tasks is well documented. However, its potential for a narrow and specific domain, such as legal, has not been fully explored. In this study, we examine the use of BERT in the Arabic legal domain and customize this language model for several downstream tasks using different domain-relevant training and test datasets to train BERT from scratch. We introduce AraLegal-BERT, a bidirectional encoder transformer-based model that has been thoroughly tested and carefully optimized with the goal of amplifying the impact of natural language processing-driven solutions on jurisprudence, legal documents, and legal practice. We fine-tuned AraLegal-BERT and evaluated it against three BERT variants for the Arabic language in three natural language understanding tasks. The results showed that the base version of AraLegal-BERT achieved better accuracy than the typical and original BERT model concerning legal texts.