Pascal Mettes

Research

My name is Pascal Mettes and I am a tenured Assistant Professor at the University of Amsterdam. The mission of me and my team is to advance the field of hyperbolic deep learning. Currently, deep learning is centred around Euclidean geometry. Euclidean geometry however has critical blindspots, ones which cannot be undone by adding more data and making bigger networks. Among the most important issues with modern deep learning is dealing with hierarchies and this has a fundamental reason: hierarchies are hyperbolic in nature due to their exponential growth. We develop the theory and algorithms to perform deep learning in hyperbolic geometry, the natural geometry of hierarchies. Below, I highlight our key research domains.

Vision-language models should be hyperbolic

Vision-language models play a central role in computer vision. The optimization of current vision-language models however contain two crucial mistakes. These mistakes can only be solved through hyperbolic embeddings. Today's vision-language models assume that vision and language are symmetrical and that vision-language alignment is flat. Language is more general than vision however (a picture is worth a thousand words) and vision-language alignment is deeply hierarchical. Hyperbolic vision-language models are the future, see our latest research on this below:

Hierarchical deep learning with hyperbolic embeddings

Hierarchies exhibit an exponential growth in nodes as a function of depth. Since Euclidean space only grows polynomially with its radius, there is an inherent mismatch between both. Luckily, hyperbolic space also exhibits exponential growth. If you want to do deep learning with hierarchical knowledge, or embed hierarchies in a continuous space, hyperbolic geometry is the way to go. Hierarchical learning is key towards avoiding large errors and generalizing to new classes, as shown in our research highlighted below:

Robust deep learning in hyperbolic space

Current deep networks are not robust. They have trouble dealing with out-of-distribution data, are sensitive to adversarial attacks, are difficult for planning, and can make arbitrarily bad mistakes. In our research, we have found that hyperbolic geometry has the potential to make deep learning far more robust, with out-of-distribution detection as highlight. See below papers on this topic:

Resources and reading materials

In our journey towards hyperbolic deep learning, we have compiled a survey, a software library, and hours of video material with context, background, and deeper information on this exciting new research field. Below are recommended materials if you want to get started in the field: