Deep Network Classification by Scattering and Homotopy Dictionary LearningJohn Zarka, Louis Thiry, Tomás Angles et al.
We introduce a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a higher classification accuracy than AlexNet over the ImageNet 2012 dataset. The network first applies a scattering transform that linearizes variabilities due to geometric transformations such as translations and small deformations. A sparse $\ell^1$ dictionary coding reduces intra-class variability while preserving class separation through projections over unions of linear spaces. It is implemented in a deep convolutional network with a homotopy algorithm having an exponential convergence. A convergence proof is given in a general framework that includes ALISTA. Classification results are analyzed on ImageNet.
Kymatio: Scattering Transforms in PythonMathieu Andreux, Tomás Angles, Georgios Exarchakis et al.
The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks. All transforms may be executed on a GPU (in addition to CPU), offering a considerable speed up over CPU implementations. The package also has a small memory footprint, resulting inefficient memory usage. The source code, documentation, and examples are available undera BSD license at https://www.kymat.io/
Generative networks as inverse problems with Scattering transformsTomás Angles, Stéphane Mallat
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz continuous to deformations so that generators transform linear interpolations between input white noise vectors into deformations between output images. This embedding is computed with a wavelet Scattering transform. Numerical experiments demonstrate that the resulting Scattering generators have similar properties as GANs or VAEs, without learning a discriminative network or an encoder.
NYTRO: When Subsampling Meets Early StoppingTomas Angles, Raffaello Camoriano, Alessandro Rudi et al.
Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackle this issue. In this paper we ask whether early stopping and subsampling ideas can be combined in a fruitful way. We consider the question in a least squares regression setting and propose a form of randomized iterative regularization based on early stopping and subsampling. In this context, we analyze the statistical and computational properties of the proposed method. Theoretical results are complemented and validated by a thorough experimental analysis.