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This paper introduces rank-aware hyperbolic alignment (RAHA) for vision-language dataset distillation (VLDD), addressing the limitations of existing methods that enforce full-dimensional alignment in Euclidean spaces. By leveraging hierarchical geometry and low-rank factorization, RAHA optimizes synthetic image-text pairs to enhance geodesic alignment in shared semantic ranges while maintaining diversity in modality-private representations. Experimental results indicate that RAHA achieves competitive performance in cross-modal retrieval and enhances transfer robustness under strict data and compute constraints.
RAHA achieves superior cross-modal retrieval performance by leveraging hyperbolic geometry to better capture the low-dimensional semantics of image-text pairs.
Vision-language dataset distillation (VLDD) compresses a large image-text paired dataset into a small set of synthetic pairs that can efficiently train contrastive vision-language models under strict data and compute budgets. Most existing methods match expert trajectories or cross-modal statistics, yet still enforce full-dimensional alignment in a Euclidean embedding space. This is often overly restrictive due to rank-deficient image--text correlation, with shared semantics concentrated in a low-dimensional range and remaining variation spread across a weakly correlated residual subspace. LoRS relaxes alignment at the similarity level by low-rank factorization, but does not explicitly control dominant alignment capacity and structure in the representation space. We thus propose a rank-aware hyperbolic alignment (RAHA) that combines hierarchical geometry with explicit alignment-capacity control. RAHA lifts multimodal representations to hyperbolic space and optimizes distilled pairs with asymmetric objectives that enforce geodesic alignment in the shared range while regularizing the residual subspace to preserve modality-private diversity and improve transfer robustness. Experiments on benchmarks show that RAHA demonstrates competitive cross-modal retrieval and improved transfer indicators under fixed budgets.
