A canonically agglutinative language or morphological pattern is traditionally analyzed as building words out of independent morphemes. Using data from Choguita Rarámuri (Uto-Aztecan), we attempt to quantify this notion by examining the extent to which meanings are predictable from their exponents without reference to context. We show that two-layer connectionist networks, computational models that map form onto meaning directly, can be used for this purpose. We also show that learning the meanings of morphemes can pose significant challenges to such models and constrains the design of the learning algorithm. In particular, models trained to equilibrium tend to focus on unreliable cues to the meanings they try to predict, especially when trained on a small corpus typical of underresourced languages. Some of these issues can be alleviated by a slow learning rate. However, one issue — which we call the problem of spurious excitement — is shown to be inherent to the learning algorithm, and always arises by the time the model achieves equilibrium. Spurious excitement means that a cue becomes associated with a meaning that it does not co-occur with, simply because of co-occurring with cues that disfavor the meaning. This case raises larger implications with respect to the type of learning mechanism involved in the acquisition of natural languages. Solutions to spurious excitement are discussed. The logistic activation function is shown to improve the performance of the model in detecting reliable cues to meanings that recur across many word types (i.e., cues of high type frequency), as well as eliminating spurious excitement.