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Description: Learning invariances allows us to generalise. In the visual modality, invariant representations allow us to recognise objects despite translations or rotations in physical space. However, how we learn the invariances that allow us to generalise abstract patterns of sensory data (“concepts”) is a longstanding puzzle. Here, we study how humans generalise relational patterns in stimulation sequences that are defined by either transitions on a nonspatial two-dimensional feature manifold, or by transitions in physical space. We measure rotational generalisation, that is the ability to recognise concepts even when their corresponding transition vectors are rotated. We find that humans naturally generalise to rotated exemplars when stimuli are defined in physical space, but not when they are defined as positions on a nonspatial feature manifold. However, if participants are first pre-trained to map auditory or visual features to spatial locations, then rotational generalisation becomes possible even in nonspatial domains. These results imply that space acts as a scaffold for learning more abstract conceptual invariances.