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> when in 1969 Marvin Minsky and Seymour Papert published the book “Perceptrons” with a mathematical proof about the limitations of two-layer feed-forward perce
by _a_a_a_ 4y ago
> when in 1969 Marvin Minsky and Seymour Papert published the book “Perceptrons” with a mathematical proof about the limitations of two-layer feed-forward perceptrons ... The book's only proven result — that linear functions cannot model non-linear ones — was trivial
A question: IIRC Minsky & Papert proved XOR couldn't be done in that limited perceptron, but that implies (given "that linear functions cannot model non-linear ones") that XOR is non-linear. Is this right, if so how is it not? What does non-linear mean here, actually?
- AndrewOMartin 4y agoDraw a 2d graph, on the vertical axis put A-is-false at the bottom and A-is-true at the top. On the horizontal axis put B-is-false on the left and B-is-true on the right. Now 'fill in' this graph with an X if the combination of A and B is True according to the XOR function, and a O otherwise. You'll find you get similar symbols in opposite corners and can't separate the two groups of symbols by drawing a single straight line. Now try the same for OR, NOT, AND, NOR and NAND.
- AndrewOMartin 4y agoI think it's worth pointing out that "Perceptions" also says it's trivially obvious that any network with a hidden layer could be used to approximate any curve because then you're basically manually tweaking an arbitrarily complex function. This was significant at the time because no one had published a training algorithm for networks with hidden layers (e.g. backpropogation)