Vector Gravity Training and Geometric Phase Transitions in Language Models

Recent studies on large language models (LLMs) increasingly suggest that internal computation is governed less by probabilistic reasoning and more by geometric structure in high-dimensional latent spaces. In this work, we present Vector Gravity Training (VGT), a minimalist training framework that introduces explicit directional constraints on hidden states during learning. Unlike prior work on Logical Difference Vectors (LDVs) and causal intervention, which primarily operate at inference time or via weight-space surgery, our method applies geometric force directly during training dynamics. Using a non-Transformer, attention-free recurrent architecture trained on character-level Shakespeare data, we demonstrate that explicit vector-directional constraints ($\alpha=25.0$) induce clear lexical, syntactic, and stylistic phase transitions. These transitions—exemplified by the spontaneous "crystallization" of specific character personas like CORIOLANUS at iteration 4650—provide strong evidence that logical structure emerges as a consequence of geometric state evolution rather than architectural specificity. This supports a unifying view of intelligence as a dimensionality transduction engine evolving on a semantic manifold.