As described in 3, the MemRecall is the process to extract the key blocks. We also need "strides" as BM25 is a famous TF-IDF-like information retrieval method. Each block is scored based on the common words with query or textual label. However, the semantic relevance are neglected. Glove is a group of pretrained word representation.

Table 10: Retrieval results on the KIL T test set(s). Reporting page-level R-precision (higher is better). Results are taken from the eval.ai Table 11: KIL T scores on the KIL T test set(s). Results are taken from the eval.ai

B.2 Hierarchical k -means for semantic identifier The pseudo code of hierarchical k -means is detailed in in Algorithm 1. Algorithm 1: Hierarchical k -means.

Identifying/retrieving relevant statutes and prior cases/precedents for a given legal situation are common tasks exercised by law practitioners. Researchers to date have addressed the two tasks independently, thus developing completely different datasets and models for each task; however, both retrieval tasks are inherently related, e.g., similar cases tend to cite similar statutes (due to similar factual situation). In this paper, we address this gap. We propose IL-PCR (Indian Legal corpus for Prior Case and Statute Retrieval), which is a unique corpus that provides a common testbed for developing models for both the tasks (Statute Retrieval and Precedent Retrieval) that can exploit the dependence between the two. We experiment extensively with several baseline models on the tasks, including lexical models, semantic models and ensemble based on GNNs. Further, to exploit the dependence between the two tasks, we develop an LLM-based re-ranking approach that gives the best performance.

We study retrieval design for code-focused generation tasks under realistic compute budgets. Using two complementary tasks from Long Code Arena -- code completion and bug localization -- we systematically compare retrieval configurations across various context window sizes along three axes: (i) chunking strategy, (ii) similarity scoring, and (iii) splitting granularity. (1) For PL-PL, sparse BM25 with word-level splitting is the most effective and practical, significantly outperforming dense alternatives while being an order of magnitude faster. (2) For NL-PL, proprietary dense encoders (Voyager-3 family) consistently beat sparse retrievers, however requiring 100x larger latency. (3) Optimal chunk size scales with available context: 32-64 line chunks work best at small budgets, and whole-file retrieval becomes competitive at 16000 tokens. (4) Simple line-based chunking matches syntax-aware splitting across budgets. (5) Retrieval latency varies by up to 200x across configurations; BPE-based splitting is needlessly slow, and BM25 + word splitting offers the best quality-latency trade-off. Thus, we provide evidence-based recommendations for implementing effective code-oriented RAG systems based on task requirements, model constraints, and computational efficiency.

Text embedding models play a cornerstone role in AI applications, such as retrieval-augmented generation (RAG). While general-purpose text embedding models demonstrate strong performance on generic retrieval benchmarks, their effectiveness diminishes when applied to private datasets (e.g., company-specific proprietary data), which often contain specialized terminology and lingo. In this work, we introduce BMEmbed, a novel method for adapting general-purpose text embedding models to private datasets. By leveraging the well-established keyword-based retrieval technique (BM25), we construct supervisory signals from the ranking of keyword-based retrieval results to facilitate model adaptation. We evaluate BMEmbed across a range of domains, datasets, and models, showing consistent improvements in retrieval performance. Moreover, we provide empirical insights into how BM25-based signals contribute to improving embeddings by fostering alignment and uniformity, highlighting the value of this approach in adapting models to domain-specific data. We release the source code available at https://github.com/BaileyWei/BMEmbed for the research community.

B.2 Hierarchical k -means for semantic identifier The pseudo code of hierarchical k -means is detailed in in Algorithm 1. Algorithm 1: Hierarchical k -means.

Multi-agent systems (MAS), leveraging the remarkable capabilities of Large Language Models (LLMs), show great potential in addressing complex tasks. In this context, integrating MAS with legal tasks is a crucial step. While previous studies have developed legal benchmarks for LLM agents, none are specifically designed to consider the unique advantages of MAS, such as task decomposition, agent specialization, and flexible training. In fact, the lack of evaluation methods limits the potential of MAS in the legal domain. To address this gap, we propose MASLegalBench, a legal benchmark tailored for MAS and designed with a deductive reasoning approach. Our benchmark uses GDPR as the application scenario, encompassing extensive background knowledge and covering complex reasoning processes that effectively reflect the intricacies of real-world legal situations. Furthermore, we manually design various role-based MAS and conduct extensive experiments using different state-of-the-art LLMs. Our results highlight the strengths, limitations, and potential areas for improvement of existing models and MAS architectures.

Table 10: Retrieval results on the KIL T test set(s). Reporting page-level R-precision (higher is better). Results are taken from the eval.ai Table 11: KIL T scores on the KIL T test set(s). Results are taken from the eval.ai

As described in 3, the MemRecall is the process to extract the key blocks. We also need "strides" as BM25 is a famous TF-IDF-like information retrieval method. Each block is scored based on the common words with query or textual label. However, the semantic relevance are neglected. Glove is a group of pretrained word representation.