An important question in neuroscience is understanding the relationship between high-dimensional electrophysiological data and complex, dynamic behavioral data. One general strategy to address this problem is to define a low-dimensional representation of essential cognitive features describing this relationship. Here we describe a general state-space method to model and fit a low-dimensional cognitive state process that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas. In particular, we apply this model to data recorded in the lateral prefrontal cortex (PFC) and caudate nucleus of non-human primates as they perform learning and adaptation in a rule-switching task. First, we define a model for a cognitive state process related to learning, and estimate the progression of this learning state through the experiments. Next, we formulate a point process generalized linear model to relate the spiking activity of each PFC and caudate neuron to the stimated learning state. Then, we compute the posterior densities of the cognitive state using a recursive Bayesian decoding algorithm. We demonstrate that accurate decoding of a learning state is possible with a simple point process model of population spiking. Our analyses also allow us to compare decoding accuracy across neural populations in the PFC and caudate nucleus.