Vector Gravity Training under Geometric Constraints: An Empirical Comparison with Pure Transformers

Recent studies suggest that introducing explicit geometric constraints into neural network training can influence learning dynamics and downstream behavior. In this work, we report a modest empirical comparison between a baseline Transformer model and a variant augmented with Vector Gravity Training (VGT), evaluated on a controlled arithmetic generalization task. Under identical training budgets (20,000 optimization steps), the VGT-augmented model exhibits a higher rate of exact numerical correctness than the baseline Transformer, though errors and failure cases remain present. We interpret these results cautiously, framing VGT not as a replacement for standard optimization, but as an auxiliary geometric bias that may affect internal representation dynamics. No claims are made regarding optimality, universality, or causal sufficiency.