We describe a connectionist network that performs a com- plex, cognitive task. In contrast, the majority of neural net- work research has been devoted to connectionist networks that perform low-level tasks, such as vision. Higher cogni- tive tasks, like categorization, analogy, imd similarity may ultimately rest on alignment of the structured representa- tions of two domains. W e model human judgments of simi- larity, as predicted by Structure-Mapping Theory, in the one-shot mapping task. W e use a localist connectionist representation in a Maricov Random Field formalism to perform cross-product matching on graph representations of propositions. The network performs structured analo- gies in its domain flexibly and robustly, resolving local and non-local constraints at multiple levels of abstraction.