Learn-to-Distance: Distance Learning for Detecting LLM-Generated Text

Modern large language models (LLMs) such as GPT, Claude, and Gemini have transformed the way we learn, work, and communicate. Y et, their ability to produce highly human-like text raises serious concerns about misinformation and academic integrity, making it an urgent need for reliable algorithms to detect LLMgenerated content. In this paper, we start by presenting a geometric approach to demystify rewrite-based detection algorithms, revealing their underlying rationale and demonstrating their generalization ability. Building on this insight, we introduce a novel rewrite-based detection algorithm that adaptively learns the distance between the original and rewritten text. Theoretically, we demonstrate that employing an adaptively learned distance function is more effective for detection than using a fixed distance. Empirically, we conduct extensive experiments with over 100 settings, and find that our approach demonstrates superior performance over baseline algorithms in the majority of scenarios. In particular, it achieves relative improvements from 57.8% to 80.6% over the strongest baseline across different target LLMs (e.g., GPT, Claude, and Gemini). The past few years have witnessed the emergence and rapid development of large language models (LLMs) such as GPT (Hurst et al., 2024), DeepSeek (Liu et al., 2024), Claude (Anthropic, 2024), Gemini (Comanici et al., 2025), Grok (xAI, 2025) and Qwen (Y ang et al., 2025). Their impact is everywhere, from education, academia and software development to healthcare and everyday life (Arora & Arora, 2023; Chan & Hu, 2023; Hou et al., 2024). On one side of the coin, LLMs can support users with conversational question answering, help students learn more effectively, draft emails, write computer code, prepare presentation slides and more. On the other side, their ability to closely mimic human-written text also raises serious concerns, including the generation of biased or harmful content, the spread of misinformation in the news ecosystem, and the challenges related to authorship attribution and intellectual property (Dave et al., 2023; Fang et al., 2024; Messeri & Crockett, 2024; Mahajan et al., 2025; Laurito et al., 2025). Addressing these concerns requires effective algorithms to distinguish between human-written and LLM-generated text, which has become an active and popular research direction in recent literature (see Crothers et al., 2023; Wu et al., 2025, for reviews).