White paper for the "Physical and Mathematical Principles of Brain Structure and Function" workshop.
One of the major obstacles for understanding how the brain works is the paucity of theoretical ideas to guide and provoke neuroscience research; good theory does not naturally emerge from large piles of data, but is essential for knowing "what to look for" in any big data effort.
One of the ultimate goals of neuroscience is to understand precisely how neural circuits process, store and generate information. While much progress has been made towards understanding the responses of individual neurons to various stimuli, the question of how observed neural activity is generated by the underlying neural networks is still largely unanswered. We can, and should, collect ever-more detailed data about network connectivity and neural activity. However, what are we to do with this data? High-quality data is, of course, essential to testing our understanding of how exactly the brain works; so is building candidate theories that capture "our understanding" in the first place.
As an example, consider the possibility that one is handed a detailed connectome for a given (large) network of neurons, including data about the synaptic strengths. What can we say about this network? What kinds of structures should we be looking for (and developing statistical tests for)? Without a menu of concrete theoretical alternatives, it's difficult to imagine what exactly one should be fishing.
It is also important to go beyond a superficial interplay between theory and experiment. A typical "good" paper in neuroscience goes along these lines: There is a high quality data set that exhibits an interesting phenomenon. A single viable theoretical explanation is proposed. A series of analyses are performed on the data to validate the theory, which is contrasted with a simpler "straw man" hypothesis that nobody believes to be true. A vague scientific lesson is learned, and few people ever revisit or build upon the particular model again.
It would be nice if the neuroscience community could agree (or, more likely, disagree) on a concrete list of theoretical ideas and principles that are considered important enough for further theoretical development and experimental testing. This could focus efforts more efficiently, and inspire scientists working at different levels to address big questions that go beyond the fine details of a particular neural system or model. It would also lead to a richer interaction between theory and experiment at all levels.