Compression as a path to simpler models of collective neural activity

Experiments now make it possible to observe, simultaneously, the electrical activity of hundreds or even thousands of neurons in a small region of the brain. But making models that capture the behavior of these real neural networks easily leads to a combinatorial explosion of complexity and we need explicit strategies for simplification. In many condensed matter systems, interactions are local, but this is not an effective guide for neurons. More abstractly, interactions may be compressible, so that the influence of the whole system on each degree of freedom can be represented by just a few bits of information. We test this idea, analyzing experiments from the vertebrate retina and the mouse hippocampus. Data sets are large enough to provide reliable sampling of activity patterns in subgroups of neurons, and within these groups we find, for example, that the influence of eight neurons on one neuron can be captured almost completely with just ten states, much less than the 256 possible states. This compression can be iterated, providing a path to describing the influence of the whole network on each neuron with a much reduced number of parameters.