Chaos in the brain's networks
Eric Shea-Brown (University of Washington)
At first thought, it doesn't seem like a good thing that we may have ended up with chaotic brains -- that is, neural networks which produce highly sensitive dependence on their initial states. Indeed, chaotic dynamics produce variability that threatens to interfere with the signals that neural networks encode and process.
At the first MBI Workshop of the Theme Year on Mathematical Neuroscience held in October 2012, a new view on chaotic dynamics in neural networks seemed to taking shape. Classical work in theoretical neuroscience established that networks operating with a "balance" of positive (excitatory) and negative (inhibitory) connections produce chaotic dynamics. This is important, as such balanced networks may be present and even typical in the cortex. Results from Guillaume Lajoie, Kevin Lin, and Eric Shea-Brown -- which built on joint work with Lai-Sang Young -- took a closer look at the structure of this chaos. They found that, while the chaos is very strong by some measures, it is also very restricted: of the hundreds of ways that chaos could in principle scramble neural trajectories, only tens actually occurred. Thus, chaotic though they may be overall, from many angles (literally) neural networks produce outputs that, in fact, highly repeatable. An example of a of highly-structured chaos in a model neural network is presented in figure below which illustrates a snapshot of neuronal on-off activity.
But why this chaos in the first place? Results from Hansel and van Vreeswijk showed that balanced neural networks can produce neurons with strong signal preferences even when connectivity seems disordered -- giving a new explanation for puzzling properties of sensory cortex known as "salt and pepper." Boerlin and Deneve took a novel approach to network dynamics, by asking what network configurations could optimally perform "predictive" computations on inputs. Once again, balanced (and chaotic) networks were the answer. This completed a hat-trick for chaotic networks at the workshop -- and left participants wondering what new feats these fascinating systems might have in store.