Weighted Point Set Embedding for Multimodal Contrastive Learning Toward Optimal Similarity Metric

TL;DR

This paper introduces weighted point set representations for multimodal contrastive learning, providing theoretical insights and demonstrating improved similarity metrics and downstream task performance.

Contribution

It proposes a novel weighted point set representation for contrastive learning, with theoretical analysis and empirical validation showing its superiority over traditional methods.

Findings

Weighted point sets achieve optimal similarity metrics.

Theoretical analysis links optimal similarity to pointwise mutual information.

Empirical results show improved downstream classification performance.

Abstract

In typical multimodal contrastive learning, such as CLIP, encoders produce one point in the latent representation space for each input. However, one-point representation has difficulty in capturing the relationship and the similarity structure of a huge amount of instances in the real world. For richer classes of the similarity, we propose the use of weighted point sets, namely, sets of pairs of weight and vector, as representations of instances. In this work, we theoretically show the benefit of our proposed method through a new understanding of the contrastive loss of CLIP, which we call symmetric InfoNCE. We clarify that the optimal similarity that minimizes symmetric InfoNCE is the pointwise mutual information, and show an upper bound of excess risk on downstream classification tasks of representations that achieve the optimal similarity. In addition, we show that our proposed similarity based on weighted point sets consistently achieves the optimal similarity. To verify the effectiveness of our proposed method, we demonstrate pretraining of text-image representation models and classification tasks on common benchmarks.