Thomas Wiatowski

• M.Sc. in Mathematics
• PhD Student at ETH Zurich

Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the energy contained in the propagated signals (a.k.a. feature maps) decays across layers. In addition, it is desirab...

Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and 10,000s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to be carried out; in addition, a large number of parameters needs to be learned and stored. Very deep and wide CNNs m...

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of such networks was initiated by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on semi-discrete shift-invariant wavelet frames and modulus non-linearities in each network la...

First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathematical framework for their anal...

We propose a highly structured neural network architecture for semantic segmentation of images that combines i) a Haar wavelet-based tree-like convolutional neural network (CNN), ii) a random layer realizing a radial basis function kernel approximation, and iii) a linear classifier. While stages i) and ii) are completely pre-specified, only the lin...

Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and $10$,$000$s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to be carried out; in addition, a large number of parameters needs to be learned and stored. Very deep and wide CN...

Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how many layers are actually needed to have most of the input signal's features be contained in the feature vector generated b...

Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the energy contained in the propagated signals (a.k.a. feature maps) decays across layers. In addition, it is desirab...

We present a novel machine learning-based method for heart sound classification which we submitted to the Phy-sioNet/CinC Challenge 2016. Our method relies on a robust feature representation—generated by a wavelet-based deep convolutional neural network (CNN)—of each cardiac cycle in the test recording, and support vector machine classification. In...

Wiatowski and B\"olcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result applies to square-integrable func...

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction and then feed the results ther...

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer, and proved translation-invar...

The reconstruction of images from data modeled by the spherical Radon transform plays an important role in photoacoustic tomography-a rapidly developing modality for in vivo imaging. We provide two novel kernel based reconstruction algorithms adapted to this type of data: Optimal recovery and algebraic reconstruction technique. The thesis details t...