Gaussian Mean-Chasing Language Models: A Mathematical Proposal with Phase I Toy-Scale Checks

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.