Stephen Downes

Knowledge, Learning, Community

My Pocket recommender served up Robert Epstein's The Empty Brain today, a paper I first documented here in 2016. If you haven't read it you absolutely should, because it's the most thorough refutation of the idea of 'the brain as a computer' that I've read. As I reread this paper, along with the Arthur Schopenhauer paper (see below), I started thinking about the major objection to neural network theory, namely, that neural networks are not able to perform logical tasks on their own, such as mathematical reasoning, grammatical construction, inference - you know, what Chomsky called Plato's problem. We can represent that challenge by asking whether neural networks are 'Turing complete", in other words, computationally universal. In the past, the answer to that question has been "no" - as Schopenhauer might say, you need a will as well as a representation. But when I searched through Google today I found this paper (36 page PDF), which shows two popular neural network architectures "to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data," and even more importantly, "neither ... requires access to an external memory to become Turing complete."

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Stephen Downes Stephen Downes, Casselman, Canada

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Last Updated: Mar 31, 2021 6:51 p.m.