Official PyTorch implementation of the paper Hyperbolic Geometry in Computer Vision: A Novel Framework for Convolutional Neural Networks.

By Ahmad Bdeir, Kristian Schwethelm, Niels Landwehr

TL; DR. In this work, we propose HCNN, a generalization of the convolutional neural network that learns latent feature representations in hyperbolic spaces in every layer, fully leveraging the benefits of hyperbolic geometry. This leads to better image representations and performance.

Abstract. Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current HNNs in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, the first fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression. Experimentation on standard vision tasks demonstrates the superiority of our HCNN framework and the Lorentz model in both hybrid and fully hyperbolic settings. Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data.

This repository. In this repository, we provide implementations of the main experiments from our paper. Additionally, we set up a library with many network components for HNNs in the Lorentz model. The following components are included:

Lorentz model:

• [file link] Our ResNet blocks
• [file link] Our 1D and 2D (transposed) convolutional layers
• [file link] Our 1D and 2D batch normalizations
• [file link] Our multinomial logistic regression (MLR) classifier
• [file link] Our non-linear activation and global average pooling
• [file link] Modified fully-connected layer of Chen et al. (2022)
• [file link] Modified wrapped normal distribution of Nagano et al. (2019)
• [file link] Extension of Geoopt's Lorentz manifold with new methods like flattening/reshaping, centroid, etc.

Poincaré ball:

• [file link] MLR of Shimizu et al. (2019)
• [file link] Wrapped normal distribution of Mathieu et al. (2019)

Additional features:

• [file link] Visualization in Lorentz model and Poincaré ball using Umap

Note. The curvature K of the Lorentz model is defined differently in our paper and in Geoopt -> geoopt.K = -1/K.

This code is released under the MIT License.

If you find our work useful for your research, please cite our paper as follows:

@misc{bdeir2023hyperbolic,
      title={Hyperbolic Geometry in Computer Vision: A Novel Framework for Convolutional Neural Networks}, 
      author={Ahmad Bdeir and Kristian Schwethelm and Niels Landwehr},
      year={2023},
      eprint={2303.15919},
      archivePrefix={arXiv},
      primaryClass={cs.CV}
}

In this section, we provide our experimental results and configuration files for reproduction.

In this experiment, we evaluate the performance of HNNs on standard image classification tasks using ResNet-18 and three benchmark datasets: CIFAR-10, CIFAR-100, and Tiny-ImageNet. For this, we employ the training procedure of DeVries and Taylor (2017).

Table 1: Main results (Accuracy (%), estimated average and standard deviation from 5 runs).

In this experiment, we evaluate the performance of HNNs on image generation tasks using vanilla VAEs and three benchmark datasets: CIFAR-10, CIFAR-100, and CelebA.

Table 2: Main results (FID, estimated average and standard deviation from 5 runs).

• Python>=3.8

  We recommend using Anaconda:

  conda create -n HCNN python=3.8 pip 
  conda activate HCNN

• PyTorch, torchvision

  Get the correct command from here. For example, for Linux systems with CUDA version 11.7:

  conda install pytorch torchvision pytorch-cuda=11.7 -c pytorch -c nvidia

• Additional requirements:

  pip install -r requirements.txt

We employ CIFAR-10/100 and CelebA implementations from torchvision. Tiny-ImageNet must be downloaded from here and organized as follows

HyperbolicCV/
└── code/
    └── classification/
        └── data/
            └── tiny-imagenet-200/
                └── train/
                    └── images/
                        └── n01443537/
                            └── n01443537_0.JPEG
                            └── ...
                        └── ...
                └── val/
                    └── images/
                        └── n01443537/
                            └── val_68.JPEG
                            └── ...
                        └── ...
                    └── val_annotations.txt

You can follow the following steps to download and organize the Tiny-ImageNet dataset automatically.

1. Download dataset

   cd code/classification
   bash get_tinyimagenet.sh

2. Organize dataset

   cd code/classification
   python org_tinyimagenet.py

• For classification, choose a config file and adapt the following command.

  python code/classification/train.py -c classification/config/L-ResNet18.txt

  You can also add additional arguments without changing the config file. For example:

  python code/classification/train.py -c classification/config/L-ResNet18.txt\
     --output_dir classification/output --device cuda:1 --dataset CIFAR-10

• For generation, choose a config file and adapt the following command.

  python code/generation/train.py -c generation/config/L-VAE/L-VAE-CIFAR.txt

  You can also add additional arguments without changing the config file. For example:

  python code/generation/train.py -c generation/config/L-VAE/L-VAE-CIFAR.txt\
     --output_dir generation/output --device cuda:1 --dataset CIFAR-100

• For classification, we provide a test script with the following options.

  • Test accuracy of a model. For example:

    python code/classification/test.py -c classification/config/L-ResNet18.txt\
      --mode test_accuracy --load_checkpoint PATH/TO/WEIGHTS.pth

  • Visualize embeddings of a model. For example:

    python code/classification/test.py -c classification/config/L-ResNet18.txt\
      --mode visualize_embeddings --load_checkpoint PATH/TO/WEIGHTS.pth --output_dir classification/output

  • Adversarial attacks (FGSM and PGD). For example:

    python code/classification/test.py -c classification/config/L-ResNet18.txt\
      --mode fgsm --load_checkpoint PATH/TO/WEIGHTS.pth

    python code/classification/test.py -c classification/config/L-ResNet18.txt\
      --mode pgd --load_checkpoint PATH/TO/WEIGHTS.pth

• For generation, we provide a similar test script with the following options.

  • Test FID of a model. For example:

    python code/generation/test.py -c generation/config/L-VAE/L-VAE-CIFAR.txt\
      --mode test_FID --load_checkpoint PATH/TO/WEIGHTS.pth

  • Visualize latent embeddings of a model. For example:

    python code/generation/test.py -c generation/config/L-VAE/L-VAE-MNIST.txt\
      --mode visualize_embeddings --load_checkpoint PATH/TO/WEIGHTS.pth --output_dir generation/output

  • Visualize sample generations/reconstructions of a model. For example:

    python code/generation/test.py -c generation/config/L-VAE/L-VAE-CIFAR.txt\
      --mode generate --load_checkpoint PATH/TO/WEIGHTS.pth --output_dir generation/output

    python code/generation/test.py -c generation/config/L-VAE/L-VAE-CIFAR.txt\
      --mode reconstruct --load_checkpoint PATH/TO/WEIGHTS.pth --output_dir generation/output