Welcome to deel-lip documentation!¶

Controlling the Lipschitz constant of a layer or a whole neural network has many applications ranging from adversarial robustness to Wasserstein distance estimation.

This library provides an efficient implementation of k-Lispchitz layers for keras.

The library contains:¶

k-Lipschitz variant of keras layers such as Dense, Conv2D and Pooling,
activation functions compatible with keras,
kernel initializers and kernel constraints for keras,
loss functions that make use of Lipschitz constrained networks (see our paper for more information),
tools to monitor the singular values of kernels during training,
tools to convert k-Lipschitz network to regular network for faster inference.

Example and usage¶

In order to make things simple the following rules have been followed during development: - deel-lip follows the keras package structure. - All elements (layers, activations, initializers, …) are compatible with standard the keras elements. - When a k-Lipschitz layer overrides a standard keras layer, it uses the same interface and the same parameters. The only difference is a new parameter to control the Lipschitz constant of a layer.

Here is an example showing how to build and train a 1-Lipschitz network:

from deel.lip.layers import SpectralDense, SpectralConv2D, ScaledL2NormPooling2D
from deel.lip.model import Sequential
from deel.lip.activations import GroupSort
from deel.lip.losses import HKR_multiclass_loss
from tensorflow.keras.layers import Input, Flatten
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.datasets import mnist
from tensorflow.keras.utils import to_categorical
import numpy as np

# Sequential (resp Model) from deel.model has the same properties as any lipschitz model.
# It act only as a container, with features specific to lipschitz
# functions (condensation, vanilla_exportation...)
model = Sequential(
    [
        Input(shape=(28, 28, 1)),
        # Lipschitz layers preserve the API of their superclass ( here Conv2D )
        # an optional param is available: k_coef_lip which control the lipschitz
        # constant of the layer
        SpectralConv2D(
            filters=16,
            kernel_size=(3, 3),
            activation=GroupSort(2),
            use_bias=False,
            kernel_initializer="orthogonal",
        ),
        # usual pooling layer are implemented (avg, max...), but new layers are also available
        ScaledL2NormPooling2D(pool_size=(2, 2), data_format="channels_last"),
        SpectralConv2D(
            filters=32,
            kernel_size=(3, 3),
            activation=GroupSort(2),
            use_bias=False,
            kernel_initializer="orthogonal",
        ),
        ScaledL2NormPooling2D(pool_size=(2, 2), data_format="channels_last"),
        # our layers are fully interoperable with existing keras layers
        Flatten(),
        SpectralDense(
            100,
            activation=GroupSort(2),
            use_bias=False,
            kernel_initializer="orthogonal",
        ),
        SpectralDense(
            10, activation=None, use_bias=False, kernel_initializer="orthogonal"
        ),
    ],
    # similary model has a parameter to set the lipschitz constant
    # to set automatically the constant of each layer
    k_coef_lip=1.0,
    name="hkr_model",
)

# HKR (Hinge-Krantorovich-Rubinstein) optimize robustness along with accuracy
model.compile(
    loss=HKR_multiclass_loss(alpha=5.0, min_margin=0.5),
    optimizer=Adam(lr=0.01),
    metrics=["accuracy"],
)

model.summary()

# load data
(x_train, y_train), (x_test, y_test) = mnist.load_data()
# standardize and reshape the data
x_train = np.expand_dims(x_train, -1)
mean = x_train.mean()
std = x_train.std()
x_train = (x_train - mean) / std
x_test = np.expand_dims(x_test, -1)
x_test = (x_test - mean) / std
# one hot encode the labels
y_train = to_categorical(y_train)
y_test = to_categorical(y_test)

# fit the model
model.fit(
    x_train,
    y_train,
    batch_size=256,
    epochs=15,
    validation_data=(x_test, y_test),
    shuffle=True,
)

# once training is finished you can convert
# SpectralDense layers into Dense layers and SpectralConv2D into Conv2D
# which optimize performance for inference
vanilla_model = model.vanilla_export()

See the full documentation for a complete API description.

Installation¶

You can install deel-lip directly from pypi:

pip install deel-lip

In order to use deel-lip, you also need a valid tensorflow installation. deel-lip supports tensorflow versions 2.x

Cite this work¶

This library has been built to support the work presented in the paper Achieving robustness in classification using optimaltransport with Hinge regularization which aim provable and efficient robustness by design.

This work can be cited as:

@misc{2006.06520,
Author = {Mathieu Serrurier and Franck Mamalet and Alberto González-Sanz and Thibaut Boissin and Jean-Michel Loubes and Eustasio del Barrio},
Title = {Achieving robustness in classification using optimal transport with hinge regularization},
Year = {2020},
Eprint = {arXiv:2006.06520},
}

Contributing¶

To contribute, you can open an issue, or fork this repository and then submit changes through a pull-request. We use black to format the code and follow PEP-8 convention. To check that your code will pass the lint-checks, you can run:

tox -e py36-lint

You need tox in order to run this. You can install it via pip:

pip install tox

Indices and tables¶

Contents: