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Differentiable Sorting Networks

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# Felix-Petersen/diffsort

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# diffsort - Differentiable Sorting Networks

Official implementation for our ICLR 2022 Paper "Monotonic Differentiable Sorting Networks" and our ICML 2021 Paper "Differentiable Sorting Networks for Scalable Sorting and Ranking Supervision". In this work, we leverage classic sorting networks and relax them to propose a new differentiable sorting function: diffsort. This allows propagating gradients through (an approximation of) the sorting / ranking function / operation. Herein, diffsort outperforms existing differentiable sorting functions on the four-digit MNIST and the SVHN sorting tasks. In this repo, we present the PyTorch implementation of differentiable sorting networks.

## 💻 Installation

diffsort can be installed via pip from PyPI with

pip install diffsort

Or from source, e.g., in a virtual environment like

virtualenv -p python3 .env1
. .env1/bin/activate
pip install .

## 👩‍💻 Usage

import torch
from diffsort import DiffSortNet

vector_length = 2**4
vectors = torch.randperm(vector_length, dtype=torch.float32, device='cpu', requires_grad=True).view(1, -1)
vectors = vectors - 5.

# sort using a bitonic-sorting-network
sorter = DiffSortNet('bitonic', vector_length, steepness=5)
sorted_vectors, permutation_matrices = sorter(vectors)
print(sorted_vectors)

Math vs. Code Convention

In the code, we follow the convention that allows sort(x) = x @ P where P is the permutation matrix (P = sorter(x)[1]). In contrast, in typical mathematical (written) notation, we would multipy as $\mathrm{sort}(x) = P \cdot x$. Accordingly, P = $P^\top$, i.e., there is a transpose between typical mathematical permutation notation (which is also used in the papers) and the permutation matrices returned by the code.

## 🧪 Experiments

You can find the main experiment in this Colab notebook.

You can run the four-digit MNIST experiment as

python experiments/main.py -n 5 -m odd_even -s 10 -d mnist

or for the bitonic network

python experiments/main.py -n 16 -m bitonic -s 20 -d mnist

or for SVHN

python experiments/main.py -n 5 -m odd_even -s 10 -d svhn

## 📖 Citing

@inproceedings{petersen2022monotonic,
title={Monotonic Differentiable Sorting Networks},
author={Petersen, Felix and Borgelt, Christian and Kuehne, Hilde and Deussen, Oliver},
booktitle={International Conference on Learning Representations (ICLR)},
year={2022}
}

@inproceedings{petersen2021diffsort,
title={Differentiable Sorting Networks for Scalable Sorting and Ranking Supervision},
author={Petersen, Felix and Borgelt, Christian and Kuehne, Hilde and Deussen, Oliver},
booktitle={International Conference on Machine Learning (ICML)},
year={2021}
}

diffsort is released under the MIT license. See LICENSE for additional details about it.

Differentiable Sorting Networks

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