The Double-Ellipsoid Geometry of CLIP

TL;DR

This paper reveals that CLIP embeddings form ellipsoid shells rather than centered spheres, and introduces a conformity measure to better understand and improve contrastive training by accounting for data uncertainty.

Contribution

It uncovers the geometric structure of CLIP embeddings as ellipsoids and proposes a new conformity measure to enhance contrastive learning based on this geometry.

Findings

Text and image embeddings lie on linearly separable ellipsoid shells.

Conformity can be estimated by cosine similarity to the mean vector.

CLIP's modality gap aligns conformity distributions of images and texts.

Abstract

Contrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood. We examine the raw unnormalized embedding and show that text and image reside on linearly separable ellipsoid shells, not centered at the origin. We explain the benefits of having this structure, allowing to better embed instances according to their uncertainty during contrastive training. Frequent concepts in the dataset yield more false negatives, inducing greater uncertainty. A new notion of conformity is introduced, which measures the average cosine similarity of an instance to any other instance within a representative data set. We show this measure can be accurately estimated by simply computing the cosine similarity to the modality mean vector. Furthermore, we find that CLIP's modality gap optimizes the matching of the conformity distributions of image and text.