Your LLM Has a Curved Space of Paragraphs
Large Language ModelsYour LLM Has a Curved Space of ParagraphsInside a transformer, token index is a coordinate. Paragraph structure is what turns it into a metric.Shuyang XiangSeptember 26, 20268 min readImage by Brett Jordan (CC BY 4.0)Image by Brett JordanI spent years studying general relativity theory since the beginning of my PhD student life. One of the things that make GR different from classic mechanics is:Coordinates are not distances.In GR, you write down coordinates for events.
- ▪Large Language ModelsYour LLM Has a Curved Space of ParagraphsInside a transformer, token index is a coordinate.
- ▪Paragraph structure is what turns it into a metric.Shuyang XiangSeptember 26, 20268 min readImage by Brett Jordan (CC BY 4.0)Image by Brett JordanI spent years studying general relativity theory since the beginning of my PhD student life.
- ▪One of the things that make GR different from classic mechanics is:Coordinates are not distances.In GR, you write down coordinates for events.
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| Original publisher | Towards Data Science |
| Canonical URL | https://towardsdatascience.com/your-llm-has-a-curved-space-of-paragraphs/ |
| Publication time | Sat, 26 Sep 2026 12:00:01 GMT |
| Retrieval time | 2026-09-26T12:01:00.618Z |
| Last seen | 2026-09-26T12:01:00.618Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | j4eCBbTJT51Y · 1 stories |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
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Large Language ModelsYour LLM Has a Curved Space of ParagraphsInside a transformer, token index is a coordinate. Paragraph structure is what turns it into a metric.Shuyang XiangSeptember 26, 20268 min readImage by Brett Jordan (CC BY 4.0)Image by Brett JordanI spent years studying general relativity theory since the beginning of my PhD student life. One of the things that make GR different from classic mechanics is:Coordinates are not distances.In GR, you write down coordinates for events. But the distance between two events isn't a function of their coordinates alone. Instead, it might depend on the metric, which varies from place to place. This post is about an experiment I designed to look for that distinction inside a language model.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Towards Data Science.
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