Neural correlates of sparse coding and dimensionality reduction

Supported by recent computational studies, there is increasing evidence that a wide range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC), an efficient population coding scheme based on dimensionality reduction and sparsity constraints. We review evidence that NSC might be employed by sensory areas to efficiently encode external stimulus spaces, by some associative areas to conjunctively represent multiple behaviorally relevant variables, and possibly by the basal ganglia to coordinate movement. In addition, NSC might provide a useful theoretical framework under which to understand the often complex and nonintuitive response properties of neurons in other brain areas. Although NSC might not apply to all brain areas (for example, motor or executive function areas) the success of NSC-based models, especially in sensory areas, warrants further investigation for neural correlates in other regions. Author summary Brains face the fundamental challenge of extracting relevant information from high-dimensional external stimuli in order to form the neural basis that can guide an organism's behavior and its interaction with the world. One potential approach to addressing this challenge is to reduce the number of variables required to represent a particular input space (i.e., dimensionality reduction). We review compelling evidence that a range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC)-a form of efficient population coding due to dimensionality reduction and sparsity constraints.