Rank-Aware Hyperbolic Alignment for Vision–Language Dataset Distillation

Vision-language dataset distillation (VLDD) compresses alarge image-text paired dataset into a small set of synthetic pairs thatcan efficiently train contrastive vision-language models under strict dataand compute budgets. Most existing methods match expert trajectoriesor cross-modal statistics, yet still enforce full-dimensional alignment in aEuclidean embedding space. This is often overly restrictive due to rank-deficient image–text correlation, with shared semantics concentrated in alow-dimensional range and remaining variation spread across a weaklycorrelated residual subspace. LoRS relaxes alignment at the similaritylevel by low-rank factorization, but does not explicitly control domi-nant alignment capacity and structure in the representation space. Wethus propose a rank-aware hyperbolic alignment (RAHA) that combineshierarchical geometry with explicit alignment-capacity control. RAHAlifts multimodal representations to hyperbolic space and optimizes dis-tilled pairs with asymmetric objectives that enforce geodesic alignmentin the shared range while regularizing the residual subspace to preservemodality-private diversity and improve transfer robustness. Experimentson benchmarks show that RAHA demonstrates competitive cross-modalretrieval and improved transfer indicators under fixed budgets.