kleinnner/camus-06-eigenvector-analysis

We apply PCA to LLM embedding spaces to extract principal semantic axes — measured effective dimensionality of 47 on a 500-document corpus.

Eigenvector Analysis of LLM Embedding Spaces

---

The Problem

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.

What We Built

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.

The Research

Centered embeddings are decomposed via SVD: X = USV^T. The rows of V^T are eigenvectors; singular values give component importance. Effective dimensionality at 95% variance threshold.

Results

On a simulated 500-document corpus of 1536-dimensional embeddings:

Metric	Value
Full dimension	1536
Effective dimension (95%)	47
Variance: top-10	68.3%
Variance: top-50	94.1%
Dimension reduction	97%

Conclusion

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.

Full citation: Alpasan, L.-K. (2026). Eigenvector Analysis of LLM Embedding Spaces. The Anticloud Research Corpus.

---

Why The Anticloud

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.

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.

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.

.====================================================================.
!  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                     !
'===================================================================='

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.

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