Gaussian Mean-Chasing Language Models: A Mathematical Proposal with Phase I Toy-Scale Checks
Abstract
This deposit contains a mathematical proposal and Phase I toy-scale checks for Gaussian Mean-Chasing (GMC) dynamics in language-model-style embedding spaces. The work analyzes Gaussian mixture densities, fixed points, iteration trajectories, and a stability regularizer. Included are the PDF and a separate reproducibility archive containing toy code, instructions, metadata, and figures.
Scope and limitations: these are analytic and toy-scale demonstrations, not evidence that a language model was trained or that language-model performance improved. The stability plots are illustrative, and the regularized optimum remains below the estimated stability edge.
AI assistance: extensive assistance from ChatGPT and Sarvam AI was used in drafting, coding, analysis, and figure preparation. The author reviewed and is responsible for the deposited work.
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BibTeX
@misc{kanth2026gaussian,
title = {{Gaussian Mean-Chasing Language Models: A Mathematical Proposal with Phase I Toy-Scale Checks}},
author = {Chaman Prakash Kanth},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23620974},
url = {https://zenodo.org/records/23620974},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gaussian Mean-Chasing Language Models: A Mathematical Proposal with Phase I Toy-Scale Checks
AU - Chaman Prakash Kanth
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23620974
UR - https://zenodo.org/records/23620974
AB - This deposit contains a mathematical proposal and Phase I toy-scale checks for Gaussian Mean-Chasing (GMC) dynamics in language-model-style embedding spaces. The work analyzes Gaussian mixture densities, fixed points, iteration trajectories, and a stability regularizer. Included are the PDF and a separate reproducibility archive containing toy code, instructions, metadata, and figures. Scope and limitations: these are analytic and toy-scale demonstrations, not evidence that a language model was trained or that language-model performance improved. The stability plots are illustrative, and the regularized optimum remains below the estimated stability edge. AI assistance: extensive assistance from ChatGPT and Sarvam AI was used in drafting, coding, analysis, and figure preparation. The author reviewed and is responsible for the deposited work.
ER -