Kymatio is an implementation of the wavelet scattering transform in the Python programming language, suitable for large-scale numerical experiments in signal processing and machine learning. Scattering transforms are translation-invariant signal representations implemented as convolutional networks whose filters are not learned, but fixed (as wavelet filters).

Use Kymatio if you need a library that:

- supports 1-D, 2-D, and 3-D wavelets,
- integrates wavelet scattering in a deep learning architecture, and
- runs seamlessly on CPU and GPU hardware, with major deep learning APIs, such as PyTorch and TensorFlow.

The Kymatio organization associates the developers of several pre-existing packages for wavelet scattering, including `ScatNet`

, `scattering.m`

, `PyScatWave`

, `WaveletScattering.jl`

, and `PyScatHarm`

.

The resort to PyTorch tensors as inputs to Kymatio allows the programmer to backpropagate the gradient of wavelet scattering coefficients, thus integrating them within an end-to-end trainable pipeline, such as a deep neural network.

Each of these algorithms is written in a high-level imperative paradigm, making it portable to any Python library for array operations as long as it enables complex-valued linear algebra and a fast Fourier transform (FFT).

Each algorithm comes packaged with a frontend and backend. The frontend takes care of interfacing with the user. The backend defines functions necessary for computation of the scattering transform.

Currently, there are eight available frontend–backend pairs, NumPy (CPU), scikit-learn (CPU), pure PyTorch (CPU and GPU), PyTorch<=1.7 (CPU and GPU), PyTorch+scikit-cuda (GPU), PyTorch<=1.7+scikit-cuda (GPU), TensorFlow (CPU and GPU), and Keras (CPU and GPU).

Kymatio integrates the construction of wavelet filter banks in 1D, 2D, and 3D, as well as memory-efficient algorithms for extracting wavelet scattering coefficients, under a common application programming interface.

Running Kymatio on a graphics processing unit (GPU) rather than a multi-core conventional central processing unit (CPU) allows for significant speedups in computing the scattering transform. The current speedup with respect to CPU-based MATLAB code is of the order of 10 in 1D and 3D and of the order of 100 in 2D.

We refer to our official benchmarks for further details.

If you use this package, please cite the following paper:

Andreux M., Angles T., Exarchakis G., Leonarduzzi R., Rochette G., Thiry L., Zarka J., Mallat S., Andén J., Belilovsky E., Bruna J., Lostanlen V., Hirn M. J., Oyallon E., Zhang S., Cella C., Eickenberg M. (2019). Kymatio: Scattering Transforms in Python. arXiv preprint arXiv:1812.11214. (paper)

Kymatio requires:

- Python (>= 3.5)
- SciPy (>= 0.13)

We strongly recommend running Kymatio in an Anaconda environment, because this simplifies the installation of other
dependencies. You may install the latest version of Kymatio using the package manager `pip`

, which will automatically download
Kymatio from the Python Package Index (PyPI):

```
pip install kymatio
```

Linux and macOS are the two officially supported operating systems.

To explicitly call the `numpy`

frontend, run:

```
from kymatio.numpy import Scattering2D
scattering = Scattering2D(J=2, shape=(32, 32))
```

After installing the latest version of scikit-learn, you can call `Scattering2D`

as a `Transformer`

using:

```
from kymatio.sklearn import Scattering2D
scattering_transformer = Scattering2D(2, (32, 32))
```

After installing the latest version of PyTorch, you can call `Scattering2D`

as a `torch.nn.Module`

using:

```
from kymatio.torch import Scattering2D
scattering = Scattering2D(J=2, shape=(32, 32))
```

After installing the latest version of TensorFlow, you can call `Scattering2D`

as a `tf.Module`

using:

```
from kymatio.tensorflow import Scattering2D
scattering = Scattering2D(J=2, shape=(32, 32))
```

Alternatively, with TensorFlow installed, you can call `Scattering2D`

as a Keras `Layer`

using:

```
from tensorflow.keras.layers import Input
from kymatio.keras import Scattering2D
inputs = Input(shape=(32, 32))
scattering = Scattering2D(J=2)(inputs)
```

Assuming the Kymatio source has been downloaded, you may install it by running

```
pip install -r requirements.txt
python setup.py install
```

Developers can also install Kymatio via:

```
pip install -r requirements.txt
python setup.py develop
```

Certain frontends, `numpy`

and `sklearn`

, only allow processing on the CPU and are therefore slower. The `torch`

, `tensorflow`

, and `keras`

frontends, however, also support GPU processing, which can significantly accelerate computations. Additionally, the `torch`

backend supports an optimized `skcuda`

backend which currently provides the fastest performance in computing scattering transforms. In 2D, it may be instantiated using:

```
from kymatio.torch import Scattering2D
scattering = Scattering2D(J=2, shape=(32, 32), backend='torch_skcuda')
```

This is particularly useful when working with large images, such as those in ImageNet, which are of size 224×224.

To run Kymatio on a graphics processing unit (GPU), you can either use the PyTorch-style `cuda()`

method to move your
object to GPU. Kymatio is designed to operate on a variety of backends for tensor operations. For extra speed, install
the CUDA library and the `skcuda`

dependency by running the following pip command:

```
pip install scikit-cuda cupy
```

The user may control the choice of backend at runtime via for instance:

```
from kymatio.torch import Scattering2D
scattering = Scattering2D(J=2, shape=(32, 32)), backend='torch_skcuda')
```

The documentation of Kymatio is officially hosted on the kymat.io website.

The documentation can also be found in the `doc/`

subfolder of the GitHub repository.
To build the documentation locally, please clone this repository and run

```
pip install -r requirements_optional.txt
cd doc; make clean; make html
```

We wish to thank the Scientific Computing Core at the Flatiron Institute for the use of their computing resources for testing.

We would also like to thank École Normale Supérieure for their support.

Kyma (*κύμα*) means *wave* in Greek. By the same token, Kymatio (*κυμάτιο*) means *wavelet*.

Note that the organization and the library are capitalized (*Kymatio*) whereas the corresponding Python module is written in lowercase (`import kymatio`

).

The recommended pronunciation for Kymatio is *kim-ah-tio*. In other words, it rhymes with patio, not with ratio.

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