Variance Alignment Score: A Simple But Tough-to-Beat Data Selection Method for Multimodal Contrastive Learning

In recent years, data selection has emerged as a core issue for large-scale visual-language model pretraining, especially on noisy web-curated datasets. One widely adopted strategy assigns quality scores such as CLIP similarity for each sample and retains the data pairs with the highest scores. However, these approaches are agnostic of data distribution and always fail to select the most informative samples. To solve this problem, we propose a simple yet theoretically principled metric named Variance Alignment Score (VAS), which has the form $\langle \Sigma_{\text{test}}, \Sigma_i\rangle$. Here, $\Sigma_{\text{test}}$ represents the target (cross-)covariance matrix we aim to align, potentially based on prior knowledge, while $\Sigma_i$ denotes the tensor product of single or multi-modal representations for the $i$-th sample. We further design a new data selection method that maximizes the total VAS. We provide theoretical analysis in a simplified setting to demonstrate the theoretical advantage of VAS over random or other existing data selection. Experimentally, applying VAS and CLIP scores together can outperform baselines by a margin of $1.3\%$ average on 38 evaluation sets for noisy dataset DataComp and $2.5\%$ on VTAB for high-quality dataset CC12M. Additionally, our ablation study also shows visual features are better than text for calculating VAS, and the related classical experimental design methods may fail under this context.