Unraveling the geometry of visual relational reasoning

Abstract: Humans and other animals readily generalize abstract relations, such as recognizing constant in shape or color, whereas neural networks struggle. To investigate how neural networks generalize abstract relations, we introduce SimplifiedRPM, a novel benchmark for systematic evaluation. In parallel, we conduct human experiments to benchmark relational difficulty, enabling direct model-human comparisons. Testing four architectures--ResNet-50, Vision Transformer, Wild Relation Network, and Scattering Compositional Learner (SCL)--we find that SCL best aligns with human behavior and generalizes best. Building on a geometric theory of neural representations, we show representational geometries that predict generalization. Layer-wise analysis reveals distinct relational reasoning strategies across models and suggests a trade-off where unseen rule representations compress into training-shaped subspaces. Guided by our geometric perspective, we propose and evaluate SNRloss, a novel objective balancing representation geometry. Our findings offer geometric insights into how neural networks generalize abstract relations, paving the way for more human-like visual reasoning in AI.