I have a prepreprint on relationship between deep neural networks and cortical pathways. Will link you when done!
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The relationship is not anywhere near as simple as not similar at all. Taking into account Matt's levels we 1/2
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can tell apart what is and is not brain-/mind-like without becoming reductionists/HPB-level bad. 2/2
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This all being said though the concept of what is and not "natural" or "biological" or even dirtier words like 1/2
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"neuroplausible" is not simple to pin down because they're often incoherent. Altho see: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.155.793&rep=rep1&type=pdf …
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At the end of the day if you are on the e.g., computational level and you perform an appropriate computation 1/2
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with your model then your model is indeed *insert one of those weasel words*. 2/2 https://en.wikipedia.org/wiki/David_Marr_(neuroscientist)#Levels_of_analysis …
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Final thought: I teach ANNs and I plan to do some outreach stuff for lay ppl so I might ask you for feedback. 
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