大型语言模型是否遵循六度分隔理论？测量长上下文流形中的拓扑压缩
Do Large Language Models Play Six Degrees of Separation? Measuring Topological Compression in Long-Context Manifolds
- BRAC University（BRAC大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过分析LLM隐藏状态流形的几何结构，发现深度推理层的语义锚点遵循六度分隔理论，该拓扑特性可用于RAG的零样本幻觉检测，为评估事实可靠性提供了几何指标。
AI中文摘要：
大型语言模型（LLMs）在长上下文场景下展现出卓越的多跳推理能力，但支撑这些远距离认知跳跃的内部机制仍鲜为人知。传统基于注意力的可解释性方法常因注意力汇等路由伪影无法捕捉真实语义邻近性。本文绕过注意力权重，直接分析隐藏状态流形的动态几何，证明深度LLM的潜在空间天然组织为小世界网络。我们将长上下文表示的连续相似矩阵稀疏化为无权重图，追踪两种不同架构中高度不相交语义锚点间的连通性。研究发现存在显著的拓扑相变：早期句法层完全呈破碎状态，而深度推理层突然将巨大的概念距离压缩为严格受限于“六度分隔”（≤6个语义跳）的高度可导航路径。此外，我们将该框架应用于检索增强生成（RAG）中基于RAGognize数据集的零样本幻觉检测，验证其实际效用：事实依据充分的生成内容与源上下文保持结构完整性（约3跳），而幻觉会引发严重的拓扑崩溃。最终，本研究从数学上形式化了Transformer执行抽象推理的方式，并提供了一种新颖的、严格几何形式的事实可靠性评估指标。
英文摘要：
Large Language Models (LLMs) demonstrate remarkable multi-hop reasoning capabilities over long contexts, yet the internal mechanisms enabling these distant cognitive leaps remain poorly understood. Traditional attention-based interpretability often fails to capture true semantic proximity due to routing artifacts like attention sinks. In this paper, we bypass attention weights to directly analyze the dynamic geometry of the hidden state manifold, proving that deep LLM latent spaces natively organize into Small-World networks. By sparsifying the continuous similarity matrices of long-context representations into unweighted graphs, we trace the connectivity between highly disjoint semantic anchors across two distinct architectures. Our findings reveal a sharp topological phase transition: while early syntactic layers remain entirely fractured, deep reasoning layers abruptly compress massive conceptual distances into highly navigable pathways strictly bounded by the "Six Degrees of Separation" limit (=< 6 semantic hops). Furthermore, we demonstrate the practical efficacy of this framework by applying it to zero-shot hallucination detection within Retrieval-Augmented Generation (RAG) using the RAGognize dataset. We show that factually grounded generations maintain structural integrity with their source context (approximately 3 hops), whereas hallucinations induce severe topological collapse. Ultimately, this work mathematically formalizes how transformers execute abstract reasoning and provides a novel, strictly geometric signature for evaluating factual reliability.
