  Efficient coding theory posits that sensory circuits transform natural
signals into neural representations that maximize information transmission
subject to resource constraints. Local interneurons are thought to play an
important role in these transformations, shaping patterns of circuit activity
to facilitate and direct information flow. However, the relationship between
these coordinated, nonlinear, circuit-level transformations and the properties
of interneurons (e.g., connectivity, activation functions, response dynamics)
remains unknown. Here, we propose a normative computational model that
establishes such a relationship. Our model is derived from an optimal transport
objective that conceptualizes the circuit's input-response function as
transforming the inputs to achieve a target response distribution. The circuit,
which is comprised of primary neurons that are recurrently connected to a set
of local interneurons, continuously optimizes this objective by dynamically
adjusting both the synaptic connections between neurons as well as the
interneuron activation functions. In an application motivated by redundancy
reduction theory, we demonstrate that when the inputs are natural image
statistics and the target distribution is a spherical Gaussian, the circuit
learns a nonlinear transformation that significantly reduces statistical
dependencies in neural responses. Overall, our results provide a framework in
which the distribution of circuit responses is systematically and nonlinearly
controlled by adjustment of interneuron connectivity and activation functions.
