On the Ambiguity in Classification

We develop a theoretical framework for geometric deep learning that incorporates ambiguous data in learning tasks. This framework uncovers deep connections between noncommutative geometry and learning tasks. Namely, it turns out that learning tasks naturally arise from groupoids, and vice versa. We also find that learning tasks are closely linked to the geometry of its groupoid -algebras. This point of view allows us to answer the question of what actually constitutes a classification problem and link unsupervised learning tasks to random walks on the second groupoid cohomology of its groupoid.