In the book "Perceptrons: An Introduction to Computational Geometry" by Minsky and Papert (1969), which part of this book tells that a single-layer perceptron could not solve the XOR problem?

I have been already scanned it, but I did not find the part. Or am I missing something?


1 Answer 1


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 Case (p. 181), where the authors write

There are many reasons for studying the operation of the perceptron learning program when there is no $\mathbf{A}^*$ with the property $\mathbf{A}^* \cdot \mathbf{\Phi} > 0$ for all $\mathbf{\Phi} \in \mathbf{F}$. Some of these are practical reasons. For example, one might want to use the program to test whether such an $\mathbf{A}^*$ exists, or one might wish to make a learning machine of this sort and be worried about the possible effects of feedback errors and other "noise". Other motives are theoretical. One cannot claim to have completely understood the "separable case" without at least some broader knowledge of other cases.

In section 12.1.1 (p. 189), the authors further write

The PERCEPTRON scheme works perfectly only under the restriction that the data is linearly separable.


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