The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding
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| Format: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901923010969600 |
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| author | McEntire, Jeremy |
| author_facet | McEntire, Jeremy |
| contents | Proves that universal entanglement in transformer representations is a geometric consequence of high-dimensional encoding via the Johnson-Lindenstrauss lemma and concentration of measure. The Entanglement Theorem shows that for any d-dimensional representation with k concept-informative directions, random m-dimensional projections with m > 32k preserve entanglement with probability exceeding 1 - 2exp(-m/128). Experimental validation across GPT-2 to Qwen-7B confirms the theoretical predictions. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18918719 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding McEntire, Jeremy entanglement theorem concentration of measure Johnson-Lindenstrauss geometric proof universal entanglement high-dimensional encoding transformer representations Proves that universal entanglement in transformer representations is a geometric consequence of high-dimensional encoding via the Johnson-Lindenstrauss lemma and concentration of measure. The Entanglement Theorem shows that for any d-dimensional representation with k concept-informative directions, random m-dimensional projections with m > 32k preserve entanglement with probability exceeding 1 - 2exp(-m/128). Experimental validation across GPT-2 to Qwen-7B confirms the theoretical predictions. |
| title | The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding |
| topic | entanglement theorem concentration of measure Johnson-Lindenstrauss geometric proof universal entanglement high-dimensional encoding transformer representations |
| url | https://doi.org/10.5281/zenodo.18918719 |