Alignment and Uniformity Metrics for Representation Learning

This repository provides a PyTorch implementation of the alignment and uniformity metrics for unsupervised representation learning. These metrics are proposed in Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere.

• arXiv Paper
• Project Page
• Code for ImageNet and ImageNet-100 with a MoCo Variant

These metrics/losses are useful for:

1. (as metrics) quantifying encoder feature distribution properties,
2. (as losses) directly training the encoder.

Requirements:

• PyTorch >= 1.5.0

Documentation

Thanks to their simple forms, these losses are implemented in just a few lines of code in align_uniform/__init__.py:

# bsz : batch size (number of positive pairs)
# d   : latent dim
# x   : Tensor, shape=[bsz, d]
#       latents for one side of positive pairs
# y   : Tensor, shape=[bsz, d]
#       latents for the other side of positive pairs

def align_loss(x, y, alpha=2):
    return (x - y).norm(p=2, dim=1).pow(alpha).mean()

def uniform_loss(x, t=2):
    return torch.pdist(x, p=2).pow(2).mul(-t).exp().mean().log()

After import align_uniform, you can access them with

align_uniform.align_loss(x, y)

align_uniform.uniform_loss(x)

Examples

We provide the following examples to perform unsupervised representation learning using these two losses:

• STL-10
• ImageNet and ImageNet-100 with a MoCo Variant

Citation

Tongzhou Wang, Phillip Isola. "Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere". International Conference on Machine Learning. 2020.

@inproceedings{wang2020hypersphere,
  title={Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere},
  author={Wang, Tongzhou and Isola, Phillip},
  booktitle={International Conference on Machine Learning},
  organization={PMLR},
  pages={9929--9939},
  year={2020}
}

Questions

For questions about the code provided in this repository, please open an GitHub issue.

For questions about the paper, please contact Tongzhou Wang (tongzhou _AT_ mit _DOT_ edu).