Emergent Lorentzian Structure in Wick-Rotated Euclidean Embeddings
Year: 2026
Type: article
Abstract: First version of rewritten and re-researched paper. I fixed a few things that I felt were problematic and have been researching the literature more. This is not a finished version; just the first update of the working paper after taking it back off hold. I apply Wick rotation to the static Euclidean geometry of trained word embeddings, projectinginto a low-dimensional subspace and systematically testing all principal-component axes ascandidate timelike directions. I continue the analysis to positional embeddings and the residual stream, then an overall matrix survey. 2.8 added more in-depth gravitational properties verifications. v2.9 added RoPE section and related appendix A v3.0 added DistilBERT analysis whose results were in line with predictions. Also changed the semantic pairs testing to include 500 pairs and re-tested GPT2 with them as well as the DistilBERT analysis. v3.1 added analysis of Mamba and comparison with other models v3.2 fixed a number of errors throught the document. Mostly minor and irrelevant to the results but errors none the less. Version 3.9f resolved everything wrong with the paper due to my mistaking an older version for the current one at some point. It containd all the latest results, all of the intended sections and corrects all errors and inconsistancies, including those stemming from said confusion. The entire document has been double-checked and should be free from any errors or inconsistancies. Version (3.9f) is the preliminary final version of this paper and includes all of the intended sections, tests and results. There will be one more version (v4f) that will be the finished, final version; it should be identical to this version if no errors are found during the final proofread/consistancy check/result verification. I lied. Version 3.9f got reformatted and submitted to PRXIntelligence Version 4.0 reflects additional findings made after submission to PRXIntelligence, which probably means I shouldn't have submitted the paper yet, but what are you going to do? Includes analysis of OPT-125m, GPT-Neo-125m and Pythia-160m as well as format change to conform to PRXIntelligene submission guidelines. Not likely to be the final version. version (4.01) updated an incorrect bibliography entry. This version (5.01) is the first version from after I put the paper on hold to go do more research. Removed some claims, changed the focus a little bit; ultimately the paper should be a little more grounded as well as accurate. v5.01
Author: Kyle, Ronald
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7149024582
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