I learned in class that perceptrons cannot simulate the XOR operation. My professor told me that one fix was to left the points onto a higher dimensional space. That is pretty obvious, you just use the feature $x_1x_2$. He also said that you can use multiple weighted hyperplanes and nonlinear functions to do so. I'm not sure how to do that. Here is all the formal definitions and whatnot:Suppose you have the following four points (with labels) $(1,1): +1; (-1, -1): +1; (-1, 1): -1;$ and $(1, -1): -1$ (i.e. the XOR function).Find a weighted combination of hyperplanes $\mathrm{Sign}(w_1h_1(x) +    + w_kh_k(x))$ that classifies all 4 points correctly. A hyperplane is a function of the form $h_i(x) = \mathrm{Sign}(v_i  x + b_i)$. In other words, $h_i(x) = 1$ when $x$ is on one side, and $h_i(x) = 1$ when $x$ is on the other side.Now, lets generalize to $d$ dimensions. There are $2^d$ input points of the form $(1, 1, . . . , 1)$. The label of a point is $+1$ if an even number of coordinates were $1$, and the label is 1 if an odd number of coordinates were 1. Find a weighted combination of hyperplanes that correctly classifies theseinputs. 
Multiple Weighted Hyerplanes to Classify XOR
machine learning;artificial intelligence;perceptron