A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes a perceptron’s capacity for linearly classifying object categories based on the underlying neural manifolds’ structural properties. Next, we will describe how such methods can, in fact, open the ‘black box’ of distributed neuronal circuits in a range of experimental neural datasets. In particular, our method overcomes the limitations of traditional dimensionality reduction techniques, as it operates directly on the high-dimensional representations, rather than relying on low-dimensionality assumptions for visualization. Furthermore, this method allows for simultaneous multi-level analysis, by measuring geometric properties in neural population data, and estimating the amount of task information embedded in the same population. These geometric frameworks are general and can be used across different brain areas and task modalities, as demonstrated in the work of ours and others, ranging from the visual cortex to parietal cortex to hippocampus, and from calcium imaging to electrophysiology to fMRI datasets. Finally, we will discuss our recent efforts to fully extend this multi-level description of neural populations, by (1) investigating how single neuron properties shape the representation geometry in early sensory areas, and by (2) understanding how task-efficient neural manifolds emerge in biologically-constrained neural networks. By extending our mathematical toolkit for analyzing representations underlying complex neuronal networks, we hope to contribute to the long-term challenge of understanding the neuronal basis of tasks and behaviors.

To generate brain circuits that are both flexible and stable requires the coordination of powerful developmental mechanisms acting at different scales, including activity-dependent synaptic plasticity and changes in single neuron properties. The brain prepares to efficiently compute information and reliably generate behavior during early development without any prior sensory experience but through patterned spontaneous activity. After the onset of sensory experience, ongoing activity continues to modify sensory circuits, and plays an important functional role in the mature brain. Using quantitative data analysis, experiment-driven theory and computational modeling, I will present a framework for how neural circuits are built and organized during early postnatal development into functional units, and how they are modified by intact and perturbed sensory-evoked activity. Inspired by experimental data from sensory cortex, I will then show how neural circuits use the resulting non-random connectivity to flexibly gate a network’s response, providing a mechanism for routing information.