Generative networks as inverse problems with Scattering transforms

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.Comment: International Conference on Learning Representations, 201

Kymatio: Scattering Transforms in Python

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

Understanding Deep Convolutional Networks

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.Comment: 17 pages, 4 Figure

On Lipschitz Bounds of General Convolutional Neural Networks

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically and compared to the theoretical bounds. Next, concentration inequalities of the output distribution to a stationary random input signal expressed in terms of the Lipschitz bound are established. The Lipschitz bound is further used to establish a nonlinear discriminant analysis designed to measure the separation between features of different classes.Comment: 26 pages, 20 figure

Intelligent Nanophotonics: Merging Photonics and Artificial Intelligence at the Nanoscale

Nanophotonics has been an active research field over the past two decades, triggered by the rising interests in exploring new physics and technologies with light at the nanoscale. As the demands of performance and integration level keep increasing, the design and optimization of nanophotonic devices become computationally expensive and time-inefficient. Advanced computational methods and artificial intelligence, especially its subfield of machine learning, have led to revolutionary development in many applications, such as web searches, computer vision, and speech/image recognition. The complex models and algorithms help to exploit the enormous parameter space in a highly efficient way. In this review, we summarize the recent advances on the emerging field where nanophotonics and machine learning blend. We provide an overview of different computational methods, with the focus on deep learning, for the nanophotonic inverse design. The implementation of deep neural networks with photonic platforms is also discussed. This review aims at sketching an illustration of the nanophotonic design with machine learning and giving a perspective on the future tasks.Comment: 46 pages, 14 figures. To appear in Nanophotonic

Rigid-Motion Scattering for Texture Classification

A rigid-motion scattering computes adaptive invariants along translations and rotations, with a deep convolutional network. Convolutions are calculated on the rigid-motion group, with wavelets defined on the translation and rotation variables. It preserves joint rotation and translation information, while providing global invariants at any desired scale. Texture classification is studied, through the characterization of stationary processes from a single realization. State-of-the-art results are obtained on multiple texture data bases, with important rotation and scaling variabilities.Comment: 19 pages, submitted to International Journal of Computer Visio

Deep Injective Prior for Inverse Scattering

In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.Comment: 13 pages, 11 figure

Interpretable Transformations with Encoder-Decoder Networks

Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the relative feature space relationship between two rotated images? What is decoded when we interpolate in feature space? Ideally, we want to disentangle confounding factors, such as pose, appearance, and illumination, from object identity. Disentangling these is difficult because they interact in very nonlinear ways. We propose a simple method to construct a deep feature space, with explicitly disentangled representations of several known transformations. A person or algorithm can then manipulate the disentangled representation, for example, to re-render an image with explicit control over parameterized degrees of freedom. The feature space is constructed using a transforming encoder-decoder network with a custom feature transform layer, acting on the hidden representations. We demonstrate the advantages of explicit disentangling on a variety of datasets and transformations, and as an aid for traditional tasks, such as classification.Comment: Accepted at ICCV 201

Physics-Constrained Predictive Molecular Latent Space Discovery with Graph Scattering Variational Autoencoder

Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and design. In this work, we assess the predictive capabilities of a molecular generative model developed based on variational inference and graph theory in the small data regime. Physical constraints that encourage energetically stable molecules are proposed. The encoding network is based on the scattering transform with adaptive spectral filters to allow for better generalization of the model. The decoding network is a one-shot graph generative model that conditions atom types on molecular topology. A Bayesian formalism is considered to capture uncertainties in the predictive estimates of molecular properties. The model's performance is evaluated by generating molecules with desired target properties