The combinations of concepts in the world are practically infinite. An AI learns only a fraction. Yet it still recognises combinations it has never seen. A new study proves, and confirms in modern vision models, that the secret lies in the geometry of a model's internal representations.

A cat curled on a person's lap is a common sight online (figure, left). A person sitting on top of a giant cat is almost never seen (right). An AI is unlikely to have met such a flipped scene in training. Even so, a modern AI still picks out both the person and the cat in this unfamiliar photo. How does it recognise a scene it has never seen?

The world is built from objects, colours, shapes, and positions in endless combination, and the number of those combinations is astronomical. However vast its training data, an AI sees only a handful. The ability to read an unfamiliar scene cannot come from memory.

The clue sits inside the AI. When it receives an image, the model turns it into hundreds of numbers, and that bundle marks a single point in a vast internal space. Similar scenes settle on nearby points, unrelated ones far apart. Recognition, then, comes down to geometry - to where in this space a picture lands.

The study worked out, mathematically, what shape this space must take to recognise unseen combinations. Colour, shape, and position must each occupy their own direction, and those directions must meet at right angles. Held apart this way, the pieces can be freely mixed and matched - a colour can join any shape in any position, including pairings never shown during training. The freedom carries a cost: the more concepts a model must handle, the more directions it needs, and the wider its space must grow.

This is not just a theory. The same structure was identified inside today's leading image-recognition systems, even though no one had designed it in - it had emerged on its own as the models learned from data. And the more cleanly a model kept its concepts at right angles, the better it handled combinations it had never seen.

This opens a path towards the next generation of AI. A model's internal representation must be steered to hold its concepts along right-angled directions. When this structure is followed, the AI no longer stumbles on combinations it never met in training.

This research was led by Arnas Uselis, a Ph.D. candidate at the Tübingen AI Center, University of Tübingen, together with Andrea Dittadi (Helmholtz Munich and the Technical University of Munich) and Professor Seong Joon Oh of the KAIST Kim Jaechul Graduate School of AI. It was presented as an oral at the International Conference on Machine Learning (ICML) in July 2026. The paper, code and experimental results are available at https://arxiv.org/abs/2602.24264 and https://github.com/oshapio/necessary-compositionality