The fact that you can selectively turn off parts of cortex (e.g. via cooling) and the brain keeps working fine with only very specific deficits probably tells us all we need to know about the importance of backprop in biological learning.
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Neither of these is a perfect example of what David is asking for. But as Konrad and Greg and I wrote in 2016, the use of backprop like credit assignment signals internally does not imply a monolithic end to end training from a single objective...pic.twitter.com/BUSoQKazlp
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