Fusing Cross-modal and Uni-modal Representations: A Kronecker Product Approach

Cross-modal embeddings, such as CLIP, BLIP and their variants, have achieved promising results in aligning representations across modalities. However, these embeddings could underperform compared to state-of-the-art single-modality embeddings on modality-specific tasks. On the other hand, single-modality embeddings excel in their domains but lack cross-modal alignment capabilities. In this work, we focus on the problem of unifying cross-modality and single-modality embeddings to achieve the performance of modality-expert embedding within individual modalities while preserving cross-modal alignment. To this end, we propose RP-KrossFuse, a method that leverages a random projection-based Kronecker product to integrate cross-modal embeddings with single-modality embeddings. RP-KrossFuse aims to fuse the sample-pairwise similarity scores of the fused embeddings and operates efficiently in a specified kernel space and supports scalable implementations via random Fourier features for shift-invariant kernels such as the Gaussian kernel. We demonstrate the effectiveness of RP-KrossFuse through several numerical experiments, combining CLIP embeddings with uni-modal image and text embeddings. Our numerical results indicate that RP-KrossFuse achieves competitive modality-specific performance while retaining cross-modal alignment, bridging the gap between cross-modal and single-modality embeddings.