In one project, we reported results that shed light on input-output transformations in cortical networks. We recorded spiking responses from visual cortex (V1) of awake mice of either sex while pairing sensory stimuli with optogenetic perturbation of excitatory and parvalbumin-positive inhibitory neurons. We found V1 neurons average responses were primarily additive (linear). We used a recurrent cortical network model to determine if these data, as well as past observations of nonlinearity, could be described by a common circuit architecture. Simulations showed cortical input-output transformations can be changed from linear to sublinear with moderate (20%) strengthening of connections between inhibitory neurons, but this change away from linear scaling depends on the presence of feedforward inhibition. Simulating a variety of recurrent connection strengths showed that, compared to when input arrives only to excitatory neurons, networks produce a wider range of output spiking responses in the presence of feedforward inhibition. In a second project, we are examining how the cortex controls the gain of responses by using a learning paradigm. Animals and humans improve their performance in sensory tasks with practice. But it is not known in general whether cortical representations become stronger (response gain increases) with practice, or whether downstream decoding becomes more effective. To examine the neural basis of learning, we are training animals to perform controlled learning tasks and examining how neural responses change with learning. We will adapt the models from project 1 to predict what circuit changes might lead to any response changes, and follow up that work with experimental tests of the predictions. This work will explain how the brain, particularly the cerebral cortex, changes during learning to support improved behavior. Understanding the circuit elements that change with learning is made possible by insights from theoretical work on networks that relates neural activity to circuit and anatomical features.