[heavenlyhash]

Computationally? Think something like "NP hard", except the "verifier" function isn't even plausibly cheap either.

Experimentally from the real thing? I'm not even sure we know how many new pieces of technology we'd need.

It's not even clear that "the weights" are the only variable we're still needing. Even in the pure-computer-science conceptualization of neural networks, things like the activation functions matter; so, it's not unreasonable to suppose there are similar important features to track in biological systems... and whatever those are, we probably aren't getting them captured in a purely geographic connectivity scan.

[aperrien]

Doesn't it really depend on how you define the weights? If you can't answer that question, you'll have no idea what to look for. For example, I understand that FIB-SEM microscopy can currently sample the chemical makeup of the voxels where the synapses lie. Those should be the answer to this question, if we agree that the neurotransmitter type and density are the weights. However, if you define the weights as the type and quality of dendrites that lead up to the synapse, you'll get a different answer. Perhaps a better answer to the question is that we are still studying what the weights should be, and having a complete connectome will make it much easier to test the different theories.

[perl4ever]

Not an original comment, but people occasionally point out that neurons like other cells are descended from self-sufficient life-forms that do all tasks all by themselves, so it would be weird if they were as simple as the mathematical concept we want to assign to them. If a neuron is not itself intelligent in some sense, how does a single cell "decide" what to do?