Current neural networks require n squared numerical operations for a network
layer of width of n.
You can reduce that to nlog(n):
https://discourse.processing.org/t/fixed-filter-bank-neural-networks/13424
That is the same efficiency difference between bubble sort and quick sort.
There is also the fact that current lack memory except for a limited amount of
internal state.
There have been some attempts to link neural networks to external memory. Eg.
Neural Turing Machines. They have used very crude attempts at creating soft
memory. However there are very effective associative memory algorithms
available:
http://gamespace.eu5.org/associativememory/index.html
Improvements in algorithms are possible and can lead to sudden massive
improvements of capability.
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Artificial General Intelligence List: AGI
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