9 votes

Did Minsky and Papert know that multi-layer perceptrons could solve XOR?

There does not appear to be a historical consensus on this. The Wikipedia page on the Perceptrons book (which does not come down on either side) gives an argument that the ability of MLPs to compute ...
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4 votes

Did Minsky and Papert know that multi-layer perceptrons could solve XOR?

Whether Minsky knew or not, it was definitely known to Rosenblatt, as he published those results in his really pioneering report - Principles of Neurodynamics: Perceptrons and the Theory of Brain ...
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  • 41
4 votes
Accepted

Why can't the XOR linear inseparability problem be solved with one perceptron like this?

It can be done. The activation function of a neuron does not have to be monotonic. The activation that Rahul suggested can be implemented via a continuously differentiable function, for example $ f(s)...
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3 votes
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Is there a proof to explain why XOR cannot be linearly separable?

Before proving that XOR cannot be linearly separable, we first need to prove a lemma: Lemma 1 Lemma: If 3 points are collinear and the middle point has a different label than the other two, then ...
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  • 1,210
3 votes

Why can't the XOR linear inseparability problem be solved with one perceptron like this?

The main problems are that your activation function is not monotonic (as pointed out by csrev), and that it is not continuously differentiable. These make it very difficult / impossible to use ...
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  • 9,316
2 votes

Did Minsky and Papert know that multi-layer perceptrons could solve XOR?

In section 13.2 Other Multilayer Machines (pp. 231-232) of the book Perceptrons: An Introduction to Computational Geometry (expanded edition, third printing, 1988) Minsky and Papert actually talk ...
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  • 33k
2 votes
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What is the best XOR neural network configuration out there in terms of low error?

The initialization of the weights has a big impact on the results. I'm not sure specifically for the XOR gate, but the error can have a local minimum that the network can get "stuck" in ...
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  • 181
2 votes

Why can't the XOR linear inseparability problem be solved with one perceptron like this?

Indeed I think the problem is with the way you've defined the activation function. By selecting it arbitrarily, you could solve many specific problems. In practice, activation functions used are ...
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  • 31
2 votes

Is there a proof to explain why XOR cannot be linearly separable?

Here is a similar contradiction based answer using basic coordinate geometry. Is there a proof to explain why $XOR$ cannot be linearly separable? Let us suppose, if possible, that the $XOR$ function,...
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2 votes

Which part of "Perceptrons: An Introduction to Computational Geometry" tells that a perceptron cannot solve the XOR problem?

The section of the book Perceptrons: An Introduction to Computational Geometry (expanded edition, third printing, 1988) that shows the limitations of the perceptron should be 11.8 The Nonseparable ...
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  • 33k
1 vote

What is the simplest classification problem which cannot be solved by a perceptron?

Anything that is not linearly separable cant be solved perceptrons, unless you use feature maps on data to map them to a higher dimension in which it is linearly separable. As a simple, concrete ...
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1 vote

What is the best XOR neural network configuration out there in terms of low error?

I'd bet, you're doing something wrong, though I can't tell what it is. Try to change the learning rate dynamically, try to train in varying order, .... On the seconds thought, it looks like you're ...
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1 vote

What is the best XOR neural network configuration out there in terms of low error?

2 perceptrons without bias (+1 in the output layer, to get the result as 1 number).
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