One of the most interesting, and mysterious, aspects of biological brains is that they form representations of environments that are richer than an interlinked series of associations, and more ‘conceptual’ than partitions in a multidimensional representation of the sensory input. Our best intuition about how this happens is that brains have evolved to pick up on, and exploit, the ubiquity of structure in the natural world and in the types of tasks that animals might have to solve over their life span, efficiently forming structured relational models of the animal’s world that can be used for planning and action. But even with that intuition, we know little about how structured knowledge is acquired or updated, especially when the extraction of the relevant structure must happen incidentally, without explicit instruction or feedback. We describe an experimental framework using rat as a model system, where the relationship between the incidentally acquired structured knowledge and the neural activity is strong enough that we can begin to decode it with confidence on single trials. Going forward, this puts us in a position to probe how structured knowledge about the world is acquired by the brain, and how it is updated with experience.