Rank-Aware Hyperbolic Alignment for Vision-Language Dataset Distillation

Dataset distillation compresses large training sets into compact synthetic datasets while preserving downstream performance. As modern systems increasingly operate on paired vision-language inputs, multimodal distillation must preserve representation quality and cross-modal alignment under tight compute and memory budgets, yet prior methods often require heavy computes and overlook their correlations. To address this, we present Multimodal Distribution Matching (MDM), a geometry-aware framework for efficient and generalizable multimodal distillation. Specifically, MDM integrates complementary components at the data, model, and loss levels. At the data level, it initializes synthetic image-text pairs by sampling from clusters in the joint embedding space. At the model level, it forms a mixed teacher by interpolating independently fine-tuned models in weight space according to their angular deviation from the pretrained anchor. At the loss level, it matches joint distributions on the unit hypersphere using a geometry-aware matching objective that exploits the joint features in the cross-modal agreement and discrepancy directions along with symmetric contrastive learning. Across image-text retrieval benchmarks with cross-architecture evaluation, MDM yields compact synthetic sets that preserve multimodal semantics, substantially reduce distillation cost, and remain robust across architectures.

Vision-language models have shown strong performance, but they often generalize poorly to specialized domains. While semi-supervised vision-language learning mitigates this limitation by leveraging a small set of labeled image-text pairs together with abundant unlabeled images, existing methods remain fundamentally pairwise and fail to model the global structure of multimodal representation manifolds. Existing topology-based alignment methods rely on persistence diagram matching, which neither guarantees geometric alignment nor utilizes the image-text pairing information central to vision-language learning. We propose Topology-Aware Multimodal Representation Alignment (ToMA), a framework that uses persistent homology to identify topologically salient edges and aligns them across modalities through available cross-modal correspondences. ToMA leverages both H_0-death edges and lightweight H_1-birth edges, allowing it to capture both connectivity and cycle structure without constructing 2-simplices. Experiments show that ToMA yields stable gains, with clear improvements on remote sensing and modest but consistent benefits on fashion retrieval. Additional analysis shows that ToMA is more stable than alternative topology-based objectives and that lightweight H_1-birth edges provide useful higher-order structural signals.

Large Language Models (LLMs) possess broad conceptual knowledge acquired through large-scale text pretraining, yet their potential to supervise models in other modalities remains underexplored. In this work, we propose LaViD--Language-to-Visual Knowledge Distillation--a simple and effective framework for transferring high-level semantic knowledge from a language-only teacher to a vision-only student model. Instead of relying on paired multimodal data, LaViD elicits conceptual signals from an LLM by prompting it to generate multiple-choice questions (MCQs) that probe semantic distinctions between visual classes. Each class is mapped to a soft label distribution over these MCQs, forming a rich conceptual signature that guides the student through an auxiliary distillation loss. Notably, despite using a language-only teacher without access to image data, LaViD consistently outperforms recent methods like MaKD that distill from vision-language models across multiple fine-grained benchmarks. It also achieves competitive or superior performance compared to state-of-the-art visual distillation methods such as DKD and MLKD, with further gains when combined with logit standardization. On the Waterbirds dataset, LaViD substantially improves worst-group accuracy, demonstrating enhanced robustness to spurious correlations with distillation. Code is available at https://github.com/lliangthomas/lavid.