A Theory of Contrastive Learning with Natural Images
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| Authors | Antonio Torralba & Yair Weiss |
| Year | 2026 |
| HF Upvotes | 1 |
| arXiv | 2607.07470 |
| Download | |
| HF Page | View on Hugging Face |
Abstract
Why does contrastive learning with simple images and augmentations yield useful representations for downstream tasks? We address this question by analytically computing the optimal representation in terms of a contrastive loss for a range of basic augmentations and any image dataset with stationary statistics. We show that for certain augmentations the optimum can be attained by a CNN whose first layer filters are sinusoids, followed by a pointwise nonlinearity, global average pooling, and a final linear layer that performs partial whitening. We also show that the optimal weights in such CNNs for more complicated augmentations are still sinusoids. The frequencies of the sinusoids and their weights can be computed using a simple waterfilling algorithm given the dataset's expected power spectrum. Experiments with different image datasets and augmentations show that such CNNs trained with SGD empirically learn sinusoids in their first layer and to perform partial whitening
Engineering Breakdown
The Problem
Why does contrastive learning with simple images and augmentations yield useful representations for downstream tasks?
The Approach
We show that for certain augmentations the optimum can be attained by a CNN whose first layer filters are sinusoids, followed by a pointwise nonlinearity, global average pooling, and a final linear layer that performs partial whitening.
Key Results
Experiments with different image datasets and augmentations show that such CNNs trained with SGD empirically learn sinusoids in their first layer and to perform partial whitening
Research Areas
This paper contributes to the following areas of AI/ML engineering:
- Machine learning
- Deep learning
- Neural networks
- Model optimization
- AI systems
- Contrastive
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