段落边界不是空白：压缩深度作为层级结构的标志
Paragraph Boundaries Are Not White Space:Compression Depth as the Signature of Hierarchical Structure
AI总结：
本研究提出使用层级旋转位置编码（hRoPE）区分真实段落结构与随机标签，发现压缩深度而非位置是层级结构的可靠标志，且现有语料库特征无法完全解释其跨语料库变化。
AI中文摘要：
标准位置编码将位置表示为一维阅读顺序坐标，但阅读顺序本身并不决定文本的层级结构。我们使用一种层级旋转位置编码（hRoPE），将段落、句子和标记索引表示为独立的通道，保持标记序列固定，对段落坐标p1进行干预，并使用标记距离精确估计器测量跨段落注意力。在所有语料库中，注意力相对于标记距离匹配的基线被压缩，但仅凭压缩本身并不能诊断真实结构：一个架构相同但标签密度匹配的随机标签通道也被压缩，且压缩更浅。区分真实结构的是压缩深度，它更大且依赖于语料库，而对照组的压缩深度则不如此。比较八个仅基于语料库的量在三种构造（词汇持续性、段落长度、基于嵌入的连贯性）上的表现，没有一种能完全重现跨语料库的深度排序，尽管基于嵌入的连贯性最为接近。压缩深度，而非其位置，是我们设置中真实段落结构的可重现标志。
英文摘要：
Standard positional encodings treat position as a one-dimensional reading-order coordinate, but reading order alone does not determine hierarchical textual structure. We use a hierarchical rotary positional encoding (hRoPE) that represents paragraph, sentence, and token indices as separate channels, hold the token sequence fixed, intervene on the paragraph coordinate $p_1$, and measure cross-paragraph attention with a token-distance-exact estimator. Attention is compressed in every corpus, but compression alone is not diagnostic of true structure: an architecturally identical channel with density-matched random labels is compressed too. What distinguishes real structure is the depth of compression: the real-versus-random depth gap is resolvable in two of three corpora and not in the third, and real-structure depth varies more strongly across corpora than the control's. Comparing eight corpus-only quantities across three constructs (lexical persistence, paragraph length, embedding-based coherence), none fully reproduces the cross-corpus ordering of depth, though embedding-based coherence comes closest. At the paragraph level that relation transfers as a common slope, but with the opposite sign to the corpus-level ranking: controlling for length, diversity, and position, paragraphs with more similar neighbors compress less deeply, with no detectable slope difference between any pair of corpora, while length, lexical-diversity, and position effects remain corpus-specific. Compression depth, not its location, is the reproducible signature of genuine paragraph structure in our setting.
