Based at AMLab (University of Amsterdam)
We advance the foundations of Ideal Machine Intelligence. We view AI not as an artificial mind, but as a representational instrument — an interface between the abstract and the concrete. Our research focuses on building systems grounded in the fundamental laws of nature and geometry, enabling AI to better comprehend the world while helping us make sense of it.
Reliable AI for science, medicine, and robotics has to respect the structure of the world it models, and that structure is geometric. This is what we mean by ideal: the most structure-respecting form a simulated intelligence can take. It is also ideal in a second, older sense, that of idealism, where mind and matter are aspects of one structured reality, and observers (scientists, engineers, users) are inseparable from it, knowing it only through representation.
Our premise is the same whether you come at it from metaphysics or from practice:
AI has to reason about data that is grounded in a shared reality.
All data we work with, physical (images, scientific measurements) or mental (mathematics,
language), derives from that reality, and its organization is geometric. Even language does not
escape this. It is a symbolic projection of the same structured world, compressed by the minds
that use it. The structure left in data is the trace of symmetry and physical law, so an
architecture that ignores it discards what is most principled about its data. Geometry is more
than a convenient inductive bias: data is geometry, because the world that cast it is.
The representations AI builds must respect that geometry.
Equivariance, for example, is not optional.
The Philosophical Stance. Mind and matter are aspects of one reality, governed by the same geometric structure. AI, on this view, is not a mind but a representational instrument — and like any instrument, it must be structurally compatible with the reality it represents and the minds that use it.
The Computational Paradigm. We embed the symmetries of physics (equivariance) and manifold structures into our architectures, ensuring that learned representations remain mathematically consistent with the physical world.
Scientific & Practical Impact. Our research is driven by critical use-cases where grounding is essential: distinguishing signal from noise in scientific discovery (e.g., computational chemistry) and ensuring reliability in medical imaging and robotics.
Building symmetry into networks, at no cost to efficiency.
Data as continuous fields, with geometry in the latents.
Flow matching on manifolds, for molecules and materials.
Message passing beyond pairwise connections.
Molecules, proteins, PDEs, and wave propagation.
Cardiac MRI, ECG, histopathology, and retinal OCT as windows on one state.