Train an MLP Using Your Brain Rather Than a GPU to Address the XOR Classification Challenge

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2024-10-11 12:00:06

A classic example is the XOR challenge. Surprisingly, when searching for solutions online, several sources 1 2 3 claim that the backpropagation algorithm can estimate the parameters of an MLP that solves the challenge but fail to provide the estimated parameters. Others 4 suggest that an MLP should mimic the logical equation x1 XOR x2 == NOT (x1 AND x2) AND (x1 OR x2), but they do not explain how. A few even present incorrect parameters. This inspired me to attempt solving the XOR challenge manually.

Consider some points on a 2D plane, each colored either blue or red. The points are linearly classifiable if you can draw a straight line such that all red points lie on one side and all blue points on the other.

For programmers, this definition makes sense because it’s computable. Given the coordinates and colors of points, a linear regression model estimated using error backpropagation can determine where this line should be.

For example, if all red points have a y-coordinate greater than 10, and all blue points have y-values less than 10, the line \(y = 10\) perfectly separates them by color.