提出新基准与几何方法，揭示视觉关系推理的通用机制。

Humans readily generalize abstract relations, such as recognizing "constant" in shape or color, whereas neural networks struggle, limiting their flexible reasoning. To investigate mechanisms underlying such generalization, we introduce SimplifiedRPM, a novel benchmark for systematically evaluating abstract relational reasoning, addressing limitations in prior datasets. In parallel, we conduct human experiments to quantify relational difficulty, enabling direct model-human comparisons. Testing four models, ResNet-50, Vision Transformer, Wild Relation Network, and Scattering Compositional Learner (SCL), we find that SCL generalizes best and most closely aligns with human behavior. Using a geometric approach, we identify key representation properties that accurately predict generalization and uncover a fundamental trade-off between signal and dimensionality: novel relations compress into training-induced subspaces. Layer-wise analysis reveals where relational structure emerges, highlights bottlenecks, and generates concrete hypotheses about abstract reasoning in the brain. Motivated by these insights, we propose SNRloss, a novel objective explicitly balancing representation geometry. Our results establish a geometric foundation for relational reasoning, paving the way for more human-like visual reasoning in AI and opening promising avenues for extending geometric analysis to broader cognitive tasks.