Interview about the Institute of Cognitive Science

1 minute read


I had a lot of fun working with the marketing team for the institute to explain the master’s program from the view of an international student. It is not apparent from a short clip, but there were many hours of raw footage required to produce each minute of video. I happened to be experimenting that day with mapping images to a Hilbert curve space to see if it improved classification of digits using a neural network.


The familiar Jupyter notebook

The motivation for using a Hilbert curve is that when images are flattened into a one-dimensional vector, a technique used in training convolutional neural networks, some of the spatial relations between pixels are lost. Hilbert curves preserve the spatial relations by mapping each pixel onto a 1-dimensional curve:

In the end, mapping the image space onto a Hilbert curve didn’t improve image classification, but I enjoyed learning about the algorithm for mapping to Hilbert spaces.


I contribute to development of the linear algebra library Normaliz developed by the Institute of Mathematics at the University of Osnabrueck, where I made a visualization of Hilbert bases using D3JS and Python for the wikipedia article.

Play with me

What is the Hilbert basis?

Starting with the lattice (all the black dots in this 2-dimensional example) and a convex (bounded) polyhedral (many-sided) cone (imagine the gray shaded part extended infinitely) with generators (the yellow circles) and


there is a finite set of generating integral vectors that can produce all the lattice points in the cone.

Simply put, the Hilbert basis of a convex cone is the unique minimal generating set (the small red circles) which can be extended or combined to produce the entire monoid (all the lattice points in the cone).

Leave a Comment