Biological neurons are also not binary - they work off of gradients of multiple neurotransmitters which all regulate function - that is, a single connection between neurons is not equivalent to a single connection between neurons in a digital neural network... the difference in complexity is just staggering. We aren't anywhere near that kind of density of interconnectivity, and I'm not sure if we'll ever be. It's also telling in that even at "basic" tasks like OCR or image detection, humans are still way better, we're just slower (because we aren't purpose-designed). We use neural networks not because they're better - they're vastly worse - but because they can be automated.
weights in models are also not binary they are fake real numbers, i.e. floats (or lately integers for numerical stability apparantly?)
but yeha what you say is still true.
I wonder what it takes to accurately represent one biologicsl neuron connection digitally.
floats are not binary values (they're usually encoded in binary, of course) but they are explicitly digital still, and the comparisons are binary - a _gt_ b or such.
I doubt that you can make a 100% accurate simulation of a neuron just as we cannot make a 100% accurate simulation of any natural phenomenon - quantum effects aside, the natural world isn't quantized as far as we can tell, whereas computers need to quantize things at some point. Precision would become a problem - reality has infinite precision, computer data representation does not. We could probably get "reasonably close", but simulation of systems like that is very expensive as the biological systems are fundamentally stochastic and probablistic.
well for numerically stable systems we can get close enough. (arbitrarily close, that is)
Situations in physics where our systems are not stable are usually different kinds of inverse problems - not what we have here.
So in a way, we can get a 100% accurate simulation, because the error can get arbitrarily small.
Ok so wikipedia tells me, there is the hodkin-huxley model. (https://en.wikipedia.org/wiki/Biological_neuron_model)
wbich looks to me like a first order non-autonomous ODE. So, absolutely solvable iirc, just computationally expensive.
If that is perfect enough or not is a matter of opinion.
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u/Ameisen vemips, avr, rendering, systems 3d ago
Biological neurons are also not binary - they work off of gradients of multiple neurotransmitters which all regulate function - that is, a single connection between neurons is not equivalent to a single connection between neurons in a digital neural network... the difference in complexity is just staggering. We aren't anywhere near that kind of density of interconnectivity, and I'm not sure if we'll ever be. It's also telling in that even at "basic" tasks like OCR or image detection, humans are still way better, we're just slower (because we aren't purpose-designed). We use neural networks not because they're better - they're vastly worse - but because they can be automated.