If hierarchies are so important, why are they not central in neural networks already? The reason is geometry. The main advances in neural networks are built on the same geometric foundation, namely Euclidean geometry. This choice however leads to fundamental limitations that cannot be overcome with bigger models and larger datasets. A critical issue is the embedding of hierarchies, for which a different geometry is better suited, namely hyperbolic geometry. Seminal works have shown that for embedding hierarchies, we should abandon Euclidean geometry altogether and operate in hyperbolic space [1]. Our lab has published multiple papers showing that hyperbolic deep learning has strong potential for computer vision, from hyperbolic image segmentation [2] to hyperbolic tree embeddings [3] and hyperbolic vision-language models [4,5].

[1] Nickel, Maximillian, and Douwe Kiela. "Poincaré embeddings for learning hierarchical representations." NeurIPS. 2017.
[2] Atigh, Mina Ghadimi, Julian Schoep, Erman Acar, Nanne Van Noord, and Pascal Mettes. "Hyperbolic image segmentation." CVPR. 2022.
[3] van Spengler, Max, and Pascal Mettes. "Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space." ICML. 2025.
[4] Pal, Avik, Max van Spengler, Guido Maria D'Amely di Melendugno, Alessandro Flaborea, Fabio Galasso, and Pascal Mettes. "Compositional entailment learning for hyperbolic vision-language models." ICLR. 2025.
[5] Poppi, Tobia, Tejaswi Kasarla, Pascal Mettes, Lorenzo Baraldi, and Rita Cucchiara. "Hyperbolic Safety-Aware Vision-Language Models." CVPR. 2025.

Your goal will be to bring hyperbolic deep learning for computer vision to the next level. This goal includes directions such as building hyperbolic vision transformers, making it possible to learn from multiple hierarchies, developing theory and implementations to make hyperbolic learning stable and scalable, and creating the next generation of vision-language models in hyperbolic space.

Specifically, we are looking for one PhD student with a keen interest in the theoretical side of hyperbolic deep learning and one PhD student with a keen interest in the algorithmic side of hyperbolic deep learning.

Tasks and responsibilities:

• Conduct high-impact research on hyperbolic deep learning for computer vision, resulting in publications at top-tier international conferences and journals;
• Develop theory, implementations, and open-source software for hyperbolic deep learning;
• Collaborate with other PhD students and researchers on hyperbolic deep learning;
• Assist with teaching by being Teaching Assistantand supervising BSc or MSc students;
• Present your work at local and international conferences.

• A MSc degree in Artificial Intelligence, Computer Science, Mathematics, or related discipline;
• A strong interest in developing creative solutions to advance hyperbolic deep learning;
• A background in machine learning, deep learning, and/or computer vision;
• Experience in programming. Python is a must, lower-level GPU programming experience is a bonus;
• Strong grasp on the English language;
• Eager to collaborate and to publish high-impact papers.

A temporary contract for 38 hours per week for the duration of 4 years (the initial contract will be for a period of 18 months and after satisfactory evaluation it will be extended for a total duration of 4 years). The preferred starting date is March 1st 2026. This should lead to a dissertation (PhD thesis). We will draft an educational plan that includes attendance of courses and (international) meetings. We also expect you to assist in teaching undergraduates and master students.

The gross monthly salary, based on 38 hours per week and dependent on relevant experience, ranges between € 3,059 to € 3,881 (scale P). This does not include 8% holiday allowance and 8,3% year-end allowance. The UFO profile PhD candidate is applicable. A favourable tax agreement, the ‘30% ruling’, may apply to non-Dutch applicants. The Collective Labour Agreement of Universities of the Netherlands is applicable.

Curious about our extensive secondary benefits package? You can read more about it here.