The paper Complex gated recurrent neural networks explores machine learning in the complex domain. For gradient descent to work the functions involved must be differentiable. In the complex domain holomorphic functions, which satisfy the Cauchy-Riemann partial differential equations are differentiable. Finding functions which fulfill this requirement and are useful for machine learning tasks is very …

# Author Archives: moritz

## Spectral-RNN

Fourier methods have a long and proven track record as an excellent tool in data processing. Integrating Fourier methods into complex recurrent neural network architectures is therefore an important goal. I integrated the short-time Fourier transform into a recurrent (complex-valued) network structure. This helps when dealing with hard prediction tasks such as human motion prediction, …

## Control Engineering

My favorite control project thus far as been a quad-copter control project. The project consisted of three steps. In a first step a state space model for a quad-copter had to be found. After testing the model with some simple simulations, an LQR controller based in this model was designed. Secondly a small weight disturbance …

## Listen, Attend and Spell

During my Master Thesis project I re-implemented Listen, attend and Spell, an attention based speech recognition system. A key problem in speech recognition is that often it is unknown what is said when. In other words the speech signal and its transcription is unaligned. Attention based system such as the one I wrote solve this …

## Medical Image Analysis

As coursework for my computer vision class in Leuven I looked into support vector machines on medical data. The task was to locate incisor teeth. For every window the svm generates the probabilities for a miss and hit. In this example the frame with the largest hit probability was chosen, as all images where known …

## Linear Algebra

One of the most interesting things I have encountered in linear algebra are pseudospectra and their relation to toeplitz symbol functions, as well as their associated circulant matrix eigenvalues. Below I have included plots which illustrate this beautiful relation (click to enlarge in new tab): Shown on the left are the Symbol functions (yellow), Toeplitz …

## PDEs and iGem

One of the first equations I discretized and simulated was the wave equation using a finite difference scheme. I ended up with a simulation, which is quite pretty: The biggest PDE project I have done so far was with the Leuven iGem-Team. We simulated the behavior of pattern forming bacteria using pure PDE and a …

## Ray Tracing

Ray tracing is a fascinating algorithm used for image synthesis. I have written a rudimentary ray tracer consisting of more then 5000 lines of code. The video below shows it render a high resolution triangle mesh representation of the Stanford dragon: Fast implementations depend on binary trees to reduce the number …