Feature Resemblance: Towards a Theoretical Understanding of Analogical Reasoning in Transformers

Understanding reasoning in large language models is complicated by evaluations that conflate multiple reasoning types. We isolate analogical reasoning, where a model transfers an attribute between entities that share known properties, and study when such transfer can emerge from training. To make the problem analytically tractable, we study a minimal transformer-style abstraction that isolates how learned representations support analogical reasoning. Within this setting, we prove three key results. First, joint training on similarity and attribution premises enables analogical reasoning through aligned representations. Second, sequential training succeeds only when similarity structure is learned before specific attributes, revealing a curriculum asymmetry. Third, in our stylized setting, two-hop reasoning $(a \to b, b \to c \Rightarrow a \to c)$ can be viewed as analogical reasoning with identity bridges $(b=b)$, which appear explicitly in training data. Together, these results reveal a unified mechanism: entities with shared properties become aligned in representation space, enabling property transfer through feature resemblance. Experiments with architectures up to 8B parameters show qualitative agreement with the theory and suggest that representational geometry plays an important role in analogical reasoning beyond the stylized model.

AI models sometimes seem able to make a useful guess by comparing two similar things. For example, if a model knows that two objects share some features, and it knows another fact about one of them, it may guess that the same fact also applies to the other. This paper studies how this kind of “learning by comparison” can appear during training. The main idea is that training can make the model represent similar things in similar ways. When this happens, a fact learned about one thing can more easily carry over to another related thing. This gives a simple explanation for how a model may make analogies. We find that the order of training matters. A model is more likely to make good analogies if it first learns which things are similar and then learns facts about them. If it learns separate facts first, it may memorize the examples without learning how to connect them. We also show that some multi-step reasoning needs explicit examples that teach the model how to connect the middle step. Experiments with both simple models and larger language models show similar patterns. Overall, the paper helps explain how AI models may learn to transfer knowledge from one thing to another.