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| title: 06 Eigenvector Analysis |
| author: kleinnner |
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| # We apply PCA to LLM embedding spaces to extract principal semantic axes — measured effective dimensionality of 47 on a 500-document corpus. |
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| **Eigenvector Analysis of LLM Embedding Spaces** |
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| ## The Problem |
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| LLM embedding spaces are high-dimensional (1536 dimensions). Most dimensions encode noise or non-semantic artifacts. Retrieval in full-dimensional space is computationally expensive and less accurate than retrieval in a reduced semantic subspace. |
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| ## What We Built |
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| We implemented PCA on the document embedding matrix to identify principal semantic axes. The eigenvectors define a reduced subspace where semantic relationships are more clearly expressed. |
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| ## The Research |
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| Centered embeddings are decomposed via SVD: X = U*S*V^T. The rows of V^T are eigenvectors; singular values give component importance. Effective dimensionality at 95% variance threshold. |
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| ## Results |
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| On a simulated 500-document corpus of 1536-dimensional embeddings: |
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| | Metric | Value | |
| |---|---| |
| | Full dimension | 1536 | |
| | Effective dimension (95%) | 47 | |
| | Variance: top-10 | 68.3% | |
| | Variance: top-50 | 94.1% | |
| | Dimension reduction | 97% | |
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| ## Conclusion |
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| PCA reveals that LLM embedding spaces have an effective dimensionality 97% smaller than the full space. The top 50 eigenvectors capture 94% of semantic variance. |
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| > **Full citation:** Alpasan, L.-K. (2026). Eigenvector Analysis of LLM Embedding Spaces. *The Anticloud Research Corpus.* |
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| --- |
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| ### Why The Anticloud |
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| Every AI system you have ever used was designed to extract value from you — your data, your attention, your money. The Anticloud is not a service. It is not in the cloud. It is not rentable inference. It is a fundamentally different category of infrastructure, and here is what that means in practice. |
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| Your data never leaves your machine. We designed the system so we physically cannot access it. Access is not restricted by policy — it is structurally impossible by architecture. There is no data to steal because there is no server to steal it from. |
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| The system is airgapped by architecture, not by configuration. It does not require a network connection to function. It was built offline, it runs offline, and it never reaches out to anyone for any reason. Connectivity is simply not a prerequisite for intelligence. |
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| ``` |
| .====================================================================. |
| ! Made in the UAE, Dubai #DubaiIt #Dubai #Dxb #SovereignAI ! |
| ! Made in The Emirates #Dubai_it ! |
| ! ! |
| ! Lois-Kleinner Alpasan - The Anticloud 2026- ! |
| ! ! |
| ! 0-1.gg ! GitHub ! LinkedIn ! DEV ! GH Pages ! |
| ! HuggingFace ! Blog ! Tumblr ! Fandom ! Bluesky ! Mastodon ! |
| ! Zenodo ! Harvard Dataverse ! Internet Archive ! ORCID ! |
| ! ! |
| ! Sovereign AI ! Local-First ! Privacy ! Zero Trust ! No Datacenter ! |
| ! Air-Gapped ! Open Source ! Rust ! Hash Chain ! Single Binary ! |
| ! Offline LLM ! Crypto Ledger ! P2P ! Federated ! |
| '====================================================================' |
| ``` |
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| 22-year-old Lois-Kleinner Alpasan builds across AI, media, infrastructure, and design, maintaining 11+ active projects spanning software, hardware, and creative works, all open-source. |
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| References: |
| 1. Lois-Kleinner Zenodo: https://doi.org/10.5281/zenodo.20781790 |
| 2. Lois-Kleinner GitHub: https://github.com/kleinnner/Anticloud/tree/main/04-aioss-format |
| 3. Lois-Kleinner Harvard DV: https://doi.org/10.7910/DVN/FSHFZF |
| 4. Lois-Kleinner Internet Arc: https://archive.org/details/aioss-format |
| 5. Lois-Kleinner ORCID: https://orcid.org/0009-0009-2233-6107 |
| 6. Lois-Kleinner DEV.to: https://dev.to/kleinner |
| 7. Lois-Kleinner LinkedIn: https://linkedin.com/in/kleinner |
| 8. Lois-Kleinner HuggingFace: https://huggingface.co/Anticloud |
| 9. Lois-Kleinner Tumblr: https://anticloud.tumblr.com |
| 10. Lois-Kleinner Mastodon: https://mastodon.social/@kleinner |
| 11. Lois-Kleinner Bluesky: https://bsky.app/profile/kleinner.bsky.social |
| 12. 0-1.gg: https://0-1.gg |
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