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The Double-Ellipsoid Geometry of CLIP
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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.
Forward citations
Cited by 3 Pith papers
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On the modality gap and the contrastive loss in multi-modal representation learning
InfoNCE with independent encoders actively creates a modality gap at low temperature; mixing intra- and inter-modality negatives (xNCE) removes the gap while improving zero-shot transfer.
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The Hyperspherical Geometry of CLIP Latent Space: A Semantic Mixture Model
CLIP embeddings are modeled as a mixture of von Mises-Fisher distributions on the unit sphere, improving out-of-distribution detection and semantic decomposition over single-Gaussian baselines.
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On the rankability of visual embeddings
Visual embeddings from CLIP and other vision encoders encode ordinal attributes along linear directions, recoverable from as few as two extreme reference images, without full supervision.
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