Daily Papers

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

This paper addresses the challenges translating case law under Hong Kong's bilingual legal system. It highlights the initial success of translating all written statutes into Chinese before the 1997 handover, a task mandated by the Basic Law. The effort involved significant collaboration among legal, linguistic, and translation experts, resulting in a comprehensive and culturally appropriate bilingual legal system. However, translating case law remains a significant challenge due to the sheer volume and continuous growth of judicial decisions. The paper critiques the governments and judiciarys sporadic and uncoordinated efforts to translate case law, contrasting it with the thorough approach previously taken for statute translation. Although the government acknowledges the importance of legal bilingualism, it lacks a sustainable strategy for translating case law. The Judiciarys position that translating all judgments is unnecessary, unrealistic, and not cost-effectiveis analyzed and critiqued for its impact on legal transparency and public trust. A proposed solution involves leveraging machine translation technology through a human-machine interactive translation platform, which undergoes two major transitions. Initially based on a neural model, the platform transitions to using a large language model for improved translation accuracy. Furthermore, it evolves from a single-agent system to a multi-agent system, incorporating Translator, Annotator, and Proofreader agents. This multi-agent approach, supported by a grant, aims to facilitate efficient, high-quality translation of judicial judgments by integrating advanced artificial intelligence and continuous feedback mechanisms, thus better meeting the needs of a bilingual legal system.

Language barriers in scientific documents hinder the diffusion and development of science and technologies. However, prior efforts in translating such documents largely overlooked the information in layouts. To bridge the gap, we introduce PDFMathTranslate, the world's first open-source software for translating scientific documents while preserving layouts. Leveraging the most recent advances in large language models and precise layout detection, we contribute to the community with key improvements in precision, flexibility, and efficiency. The work has been open-sourced at https://github.com/byaidu/pdfmathtranslate with more than 222k downloads.