dendrocentric compartmentalization, spike timing, bandpass in the dendrites, spike retiming etc... aren't covered in the above.
But it is probably important to define 'computable'
Typically that means being able that can take a number position as input and output the digit in that location.
So if f(x) = pi, f(3) would return 4
Even the real numbers are uncomputable 'almost everywhere', meaning choose almost any real number, and no algorithm exists to produce it as f(x)
Add in ion channels and neurotransmitters and continuous input and you run into indeterminate features like riddled basins, where even with perfect information and precision and you can't predict what exit basin it is in.
Basically look at the counterexamples to Laplace's demon.
MLPs with at least one hidden layer can approximate within an error bounds with potentially infinite neurons, but it can only produce a countable infinity of outputs, while biological neurons, being continuous input will potentially have an uncountable infinity.
Riddled basins, being sets with no open subsets is another way to think about it.
But it is probably important to define 'computable'
Typically that means being able that can take a number position as input and output the digit in that location.
So if f(x) = pi, f(3) would return 4
Even the real numbers are uncomputable 'almost everywhere', meaning choose almost any real number, and no algorithm exists to produce it as f(x)
Add in ion channels and neurotransmitters and continuous input and you run into indeterminate features like riddled basins, where even with perfect information and precision and you can't predict what exit basin it is in.
Basically look at the counterexamples to Laplace's demon.
MLPs with at least one hidden layer can approximate within an error bounds with potentially infinite neurons, but it can only produce a countable infinity of outputs, while biological neurons, being continuous input will potentially have an uncountable infinity.
Riddled basins, being sets with no open subsets is another way to think about it.
Here is a paper for that.
https://arxiv.org/abs/1711.02160