<p>The study of animal cognition has hosted a long debate about the nature of mental representation. Specifically, whether spatial (map-like) or associative (node-like) models better explain learning and behavior. To explore this, the present experiments tested three pigeons using a novel spatial discrimination task to assess how they learn to discriminate different multidimensional geometric structures. Each trial involved a go/no-go procedure in which a 1.5 cm green target appeared at a random location in an unmarked 15 × 15 cm touchscreen display area. Food reinforcement depended on the target’s location. Across experiments, pigeons were tested on discriminations defined by three invisible spatial structures of varying complexity. In the first two experiments, they successfully learned discriminations based on well-formed geometric divisions involving either a vertical or a diagonal discriminative boundary, respectively. In contrast, they failed to learn a mosaic discrimination involving complex, irregular, non-linear divisions of the space. These findings indicate pigeons can learn invisible multidimensional visuospatial discriminations and do so better when the underlying structure is geometrically coherent. Further, this learning appears independent of the discriminative boundary’s orientation. The latter matches previous findings testing analogous rule-based (vertical) and information-integration (diagonal) organizations using visual dimensions. It is consistent with the hypothesis that a single non-analytic associative mechanism mediates learning in both cases. Implications for understanding the discriminative representations used by pigeons in solving problems involving fundamental dimensions, like space, are considered.</p>