用几何分解方法揭示小说续作的创作规律
Story Operators: Decomposing the Original $\to$ Sequel Transformation in Embedding Space
- 将小说视为嵌入空间中的点，通过向量差分析原作到续作的转换路径
- 发现续作变化可分为公式化、集中型和组合型三类，其中《汤姆·索亚》到《哈克贝利·费恩》以结构转变为主
- 揭示作者意图与文本演变的对应关系，支持可复现的定量分析
本文将小说视为句子嵌入空间中的一个点，将文学创作视为点之间的操作。给定一部原著及其续作，探讨从第一本到第二本在几何上所需的变化。基于PG19语料库预计算的all-mpnet-base-v2段落嵌入，计算出位移向量d = x_seq - x_orig，并通过主成分分析（PCA）在两本书段落上构建内容基底，对位移进行贪婪分解。每个分量对应一个可解释的轴，其两端锚定真实文本片段。在13组已验证的作者对中，分解结果揭示了续作的微型分类：公式化（极小且低秩变化，如道尔的福尔摩斯系列，‖d‖=0.12）、集中型（单一主导轴，如奥尔科特《小妇人》→《小男人》，75%集中在一条轴上）和组合型（多个小轴，如马克·吐温、巴勒斯的巴索姆系列）。以经典案例《汤姆·索亚历险记》→《哈克贝利·费恩历险记》为例，主导轴为结构性转变——庇护性的家庭生活塌陷为流浪式冒险旅程，而非广为人知的方言或奴隶制主题，后者出现在后续较小轴上；转换路径经由冒险旅程空间，而非趋向通用现实主义。通过对比马克·吐温1875–76年致豪威尔斯的信件，证实其早先即提出第一人称流浪叙事构想，量化了其声明意图所覆盖的实际文本演变程度。所有计算均可通过公开脚本与数据复现。
原文摘要 · Abstract (English)
I treat a book as a point in a sentence-embedding space and a literary transformation as an operation on points. Given an original novel and its sequel, I ask what it takes, geometrically, to turn the first into the second. Using all-mpnet-base-v2 paragraph embeddings drawn from a precomputed index of the PG19 corpus, I form the displacement $d=\bar{x}_{\rm seq}-\bar{x}_{\rm orig}$ and greedily decompose it along a content basis obtained by PCA over the two books' own paragraphs. Each component is an interpretable axis anchored by real passages at its poles. Across thirteen verified author pairs from Project Gutenberg, the decomposition reveals a small taxonomy of sequels: formulaic (a tiny, low-rank change: Doyle's Holmes collections, $\|d\|=0.12$), concentrated (one dominant axis: Alcott's Little Women $\to$ Little Men, 75% on a single move), and compositional (many small axes: Twain, Burroughs's Barsoom, Nesbit). For the canonical case, Tom Sawyer $\to$ Huckleberry Finn, the dominant recovered axis is structural -- the collapse of sheltering domesticity into a picaresque road -- rather than the famous surface themes of vernacular voice or slavery, which ride later, smaller axes; and the transformation routes through adventure-journey space rather than diluting toward generic realism. I corroborate the recovered geometry against Twain's documented authorial intent (his 1875--76 letters to Howells), which names the first-person picaresque move years in advance, and I quantify, with an explicit representation caveat, how much of the realized transformation his stated intentions span. All computations are reproducible from the released scripts and data.
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