Answers.Body: <p>The section of the book <a href="https://russell-davidson.arts.mcgill.ca/e706/Perceptrons.pdf" rel="nofollow noreferrer">Perceptrons: An Introduction to Computational Geometry</a> (expanded edition, third printing, 1988) that shows the limitations of the perceptron should be <strong>11.8 The Nonseparable Case</strong> (p. 181), where the authors write</p>
  
  <blockquote>
    <p>There are many reasons for studying the operation of the perceptron learning program when there is no <span class="math-container">$\mathbf{A}^*$</span> with the property <span class="math-container">$\mathbf{A}^* \cdot \mathbf{\Phi} &gt; 0$</span> for all <span class="math-container">$\mathbf{\Phi} \in \mathbf{F}$</span>. Some of these are practical reasons. For example, one might want to use the program to <em>test</em> whether such an <span class="math-container">$\mathbf{A}^*$</span> 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.</p>
  </blockquote>
  
  <p>In section 12.1.1 (p. 189), the authors further write</p>
  
  <blockquote>
    <p>The PERCEPTRON scheme works perfectly only under the restriction that the data is linearly separable.</p>
  </blockquote>
  
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Body: <p>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?</p>
  
  <p>I have been already scanned it, but I did not find the part. Or am I missing something?</p>
  
Tags: <machine-learning><perceptron><books><xor-problem>
Title: Which part of "Perceptrons: An Introduction to Computational Geometry" tells that a perceptron cannot solve the XOR problem?
UserDisplayName: rimbaerl
ThreadText: # Which part of "Perceptrons: An Introduction to Computational Geometry" tells that a perceptron cannot solve the XOR problem?
  
  (Asked by: username_0 on 2019-11-05)
  
  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?
  
  **Tags:** machine-learning, perceptron, books, xor-problem
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-03-10. Score: 2
  
  The section of the book [Perceptrons: An Introduction to Computational Geometry](https://russell-davidson.arts.mcgill.ca/e706/Perceptrons.pdf) (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.
  
  
  ---
  
  