Recent progress in the statistical physics of real neural networks

Single neurons have fascinating properties, and make measurable contributions to perception and action. Nonetheless many of the most interesting phenomena in the brain seem to be collective or emergent. There is a long history of trying to use ideas from statistical physics to describe these phenomena, with many beautiful and influential results. Nonetheless it remained difficult to see how theory and experiment could be connected, quantitatively. This became more urgent as the 21st century brought new experimental tools for recording the electrical activity of more and more neurons simultaneously. Maximum entropy methods emerged as a strategy for building models that are grounded in statistical physics but connected directly to these data, so that we end up with (for example) a spin-glass like model for a particular population of neurons rather than some guess at the family from which this model might be drawn. After some initial uncertainties, it now is clear that these models can provide extraordinarily precise descriptions of ~100 cells, for example correctly predicting the ~100,000 triplet correlations in such networks within experimental errors. When models work this well it makes to take them seriously as statistical mechanics problems and ask, for example, where real networks are in phase diagram of possible networks. In cases where the simplest maximum entropy models fail, several alternatives have been suggested, and I will review some of these. We also need methods that have even better scaling with network size. In a different direction, recordings from 1000+ (or even 100,000+) neurons offer opportunities to explore coarse-graining, or more generally to ask if we can use the renormalization group to inspire new methods of data analysis. This has led to the observation of very precise and reproducible scaling behaviors, holding out that these networks might be described by theories that live at an RG fixed point.