Fast Differentiable Matrix Sqrt Root and Its Inverse

Geometric Interpretation of Matrix Square Root and Inverse Square Root

This repository constains the official Pytorch implementation of ICLR 22 paper "Fast Differentiable Matrix Square Root" and the expanded T-PAMI journal "Fast Differentiable Matrix Square Root and Inverse Square Root".

You can find the presentation of our work by the slides and poster.

Usages

Check torch_utils.py for the implementation. Minimal exemplery usage is given as follows:

# Import and define function
from torch_utils import *
FastMatSqrt = MPA_Lya.apply
FastInvSqrt = MPA_Lya_Inv.apply

# For any batched matrices, compute their square root or inverse square root:
rand_matrix = torch.randn(5,32,32)
rand_cov = rand_matrix.bmm(rand_matrix.transpose(1,2))
rand_cov_sqrt = FastMatSqrt(rand_cov)
rand_inv_sqrt = FastInvSqrt(rand_cov)

Computer Vision Experiments

All the codes for the following experiments are available:

• Decorrelated Batch Normalization (BN)
• Second-order Vision Transformer (So-ViT)
• Neural Style Transfer by Whitening and Coloring Transform (WCT)
• Temporal-Attentive Covariance Pooling (TACP) for Video Action Recognition
• Global Covariance Pooling for Large-Scale and Fine-grained Visual Recognition

Citation

Please consider citing our paper if you think the code is helpful to your research.

@inproceedings{song2022fast,
  title={Fast Differentiable Matrix Square Root},
  author={Song, Yue and Sebe, Nicu and Wang, Wei},
  booktitle={ICLR},
  year={2022}
}

@article{song2022fast2,
  title={Fast Differentiable Matrix Square Root and Inverse Square Root},
  author={Song, Yue and Sebe, Nicu and Wang, Wei},
  journal={IEEE TPAMI},
  year={2022},
  publisher={IEEE}
}

Contact

If you have any questions or suggestions, please feel free to contact me

yue.song@unitn.it