Familiarity, or memory strength, is a central construct in models of cognition. In previous categorization and long-term memory research, correlations have been found between psychological measures of memory strength and activation in the medial temporal lobes (MTLs), which suggests a common neural locus for memory strength. However, activation alone is insufficient for determining whether the same mechanisms underlie neural function across domains. Guided by mathematical models of categorization and long-term memory, we develop a theory and a method to test whether memory strength arises from the global similarity among neural representations. In human subjects, we find significant correlations between global similarity among activation patterns in the MTLs and both subsequent memory confidence in a recognition memory task and model-based measures of memory strength in a category learning task. Our work bridges formal cognitive theories and neuroscientific models by illustrating that the same global similarity computations underlie processing in multiple cognitive domains. Moreover, by establishing a link between neural similarity and psychological memory strength, our findings suggest that there may be an isomorphism between psychological and neural representational spaces that can be exploited to test cognitive theories at both the neural and behavioral levels.