Biology has an incredible set of priors for this, given that actual neurons have been experimenting with topologies for millions of years. The neuron itself can be thought of as a meta-topology in that it constructs potentially arbitrary hypergraphs with the basic building block of axon/dendrites, albeit with a locality bias.
Neurons actually have different topologies across different brain regions, such as the more striated hippocampus versus the stratified cerebral lobes. These have been hypothesized to function as different forms of gradient descent, as pure back propagation style bidirectional communication is perhaps only present in a few specific brain regions or body extremities. But I think a more popular interpretation is that these are neighborhoods of co-activation that emphasize different kinds of distributed learning.
Y_Y 8 days ago [-]
The discrete topology[∅].
Not only is it mathematically perfect that every set is clopen, as a network topology it is perfect because connecting computers to one another has made many people very angry and has widely been regarded as a bad move.
Neurons actually have different topologies across different brain regions, such as the more striated hippocampus versus the stratified cerebral lobes. These have been hypothesized to function as different forms of gradient descent, as pure back propagation style bidirectional communication is perhaps only present in a few specific brain regions or body extremities. But I think a more popular interpretation is that these are neighborhoods of co-activation that emphasize different kinds of distributed learning.
Not only is it mathematically perfect that every set is clopen, as a network topology it is perfect because connecting computers to one another has made many people very angry and has widely been regarded as a bad move.
[∅] https://en.wikipedia.org/wiki/Discrete_space
(Anyway doesn't the Evil Queen say "Magic mirror on the wall"?)