DAVIDSTUTZ

Check out our latest research on adversarial robustness and generalization of deep networks.

TAG»MATHEMATICS«

Denoising Variational Auto-Encoders

A variational auto-encoder trained on corrupted (that is, noisy) examples is called denoising variational auto-encoder. While easily implemented, the underlying mathematical framework changes significantly. As the second article in my series on variational auto-encoders, this article discusses the mathematical background of denoising variational auto-encoders.

Categorical Variational Auto-Encoders and the Gumbel Trick

In the third article of my series on variational auto-encoders, I want to discuss categorical variational auto-encoders. This variant allows to learn a latent space of discrete (e.g. categorical or Bernoulli) latent variables. Compared to regular variational auto-encoders, the main challenge lies in deriving a working reparameterization trick for discrete latent variables — the so-called Gumbel trick.

The Mathematics of Variational Auto-Encoders

As part of my master thesis, I made heavy use of variational auto-encoders in order to learn latent spaces of shapes — to later perform shape completion. Overall, I invested a big portion of my time in understanding and implementing different variants of variational auto-encoders. This article, a first in a small series, will deal with the mathematics behind variational auto-encoders. The article covers variational inference in general, the concrete case of variational auto-encoder as well as practical considerations.

11thJANUARY2018

12thDECEMBER2017

PROJECT

The Simplex algorithm for solving linear programs implemented in PHP.

12thDECEMBER2017

PROJECT

Common matrix decompositions, including LU, Cholesky and QR decompositions, implemented in PHP; also includes an interactive application to demonstrate and explain the material.

27thSEPTEMBER2017

Seminar Paper “iPiano: Inertial Proximal Algorithms for Non-Convex Optimization”

In the course of a seminar on “Selected Topics in Image Processing”, I worked on iPiano, an algorithm for non-convex and non-smooth optimization proposed by Ochs et al. [1]. iPiano combines forward-backward splitting with an inertial force. This article presents the corresponding seminar paper including an implementation in C++ with applications to image denoising, image segmentation and compressed sensing.

09thMAY2016

PROJECT

Efficient C++ implementation of iPiano, a proximal algorithm with inertial force for non-convex and non-smooth optimization; including applications to image segmentation.

06thMAY2016