For rapid non-linear information processing in the brain, small synaptic impulses are key: "At issue was the conventional theory of spiking neuronal networks, which approximates impulses in the limit where they become vanishingly tiny and infinitely numerous, limiting the capabilities of individual neurons to simple addition of inputs.
Using a newly-developed high-precision method for simulating nonlinear neuron models (see references), the team had previously uncovered contradictions in this theory. To unravel this mystery, the researchers developed a new analytic framework which explicitly incorporates the finite effect of each input at the critical boundary near the firing threshold. With this change, they show that not only can neurons process information far faster than previously believed, they can also perform nonlinear operations such as multiplication that are key to complex information processing.
While more accurately capturing the network aspect of neural dynamics, the new framework also reveals how cooperation between seemingly uncoordinated input signals enables neurons to perform many non-linear operations at the same time."