On simplicity and complexity in the brave new world of large-scale neuroscience

•High dimensional statistics and neural circuit theory must guide modern neuroscience.•Recording more neurons while repeating simple behaviors may not yield richer datasets.•Phase transitions in high dimensional statistics can guide experimental design.•Confronting artificial neural networks can help us design neuroscience experiments.•Our goal should be to understand the space of all models consistent with data.

Technological advances have dramatically expanded our ability to probe multi-neuronal dynamics and connectivity in the brain. However, our ability to extract a simple conceptual understanding from complex data is increasingly hampered by the lack of theoretically principled data analytic procedures, as well as theoretical frameworks for how circuit connectivity and dynamics can conspire to generate emergent behavioral and cognitive functions. We review and outline potential avenues for progress, including new theories of high dimensional data analysis, the need to analyze complex artificial networks, and methods for analyzing entire spaces of circuit models, rather than one model at a time. Such interplay between experiments, data analysis and theory will be indispensable in catalyzing conceptual advances in the age of large-scale neuroscience.