Teaching Vision-Language Models to Use the Scale They Are Given: Label-Free Equivariance Training for Metric Physical Reasoning
EquiSD is a label-free training method that teaches vision-language models to respect physical scaling laws, specifically the homogeneity relation. By exploiting this exact symmetry—where scaling world quantities by alpha scales the answer by alpha—EquiSD improves metric grounding without needing any ground-truth annotations. This technique significantly boosts performance across different scales and generalizes well from simulated data to real videos.