Adaptive Geometry Routing for Vision-Language Understanding

Vision-language models face a fundamental geometry trade-off: Euclidean representations excel at instance-level discrimination, while hyperbolic representations naturally encode semantic hierarchies. Hybrid training is challenging because one geometry may dominate early, leaving the other under-trained—a failure mode we term geometry dominance. We introduce Adaptive Geometry Routing (AGR), a framework that addresses this via a novel four-phase training curriculum: (1) Isolation—hyperbolic-only training stabilizes hierarchical structure; (2) Shadow—router learns mixing patterns using only hyperbolic signals; (3) Soft Launch—Euclidean scores gradually become visible; (4) Adaptive—full dual-geometry routing. This phased coordination of router activation (α) and Euclidean visibility (β) prevents early dominance while enabling data-driven geometry selection. Built on a shared backbone with lightweight LoRA-adapted heads and bounded residual corrections, AGR discovers that hyperbolic geometry is preferred by default (85% weight), with routing adapting semantically—abstract queries route more hyperbolic, attribute-rich queries shift toward Euclidean. On ViT-B, AGR achieves 38.8% COCO T2I R@5 (+6.5pp over MERU), 64.7% Flickr30K I2T R@5 (+11.3pp), and 32.6% ImageNet accuracy (+9.3pp), demonstrating that phased curriculum training enables stable hybrid geometry learning for vision-language understanding.