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The human brain as studied by neuroscientists, or neurobiologists, generally focus on what I would call

  • implementation details (how specifically does information transport between synaptic channels, i.e. what are the chemical processes)

  • vague generalities (e.g. about "memory" as a psychological concept and in very vague terms what types of memory there are without studying them mathematically)

There is nothing intrinsically wrong with this.

But I am interested in the brain as a computational system. Of course we don't yet understand the brain very well, but is there a book on the brain that a computer scientist or machine learning professional could read to get a computational/systematic understanding of what we know about the brain? e.g. what is the computational role of various neurotransmitters (without going into chemistry), etc.

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There is no "textbook" on this. However, there is a book! It is How to Create a Mind by Raymond Kurzweil, the director of engineering at Google. Excellent book that explains the brain from a computer-science perspective. It goes into a lot of detail.

Check out the intro sound bytes on Audible.

For a closer to the metal (i.e. actual implementations of models of the brain), check out Cognitive Architectures, such as ACT-R, Soar, CLARION, ICARUS, EPIC, LIDA, etc. Here is a survey.

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