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28 votes

Why is it believed that a single-layer perceptron can't solve XOR? Doesn't this example disprove that?

The perceptron has a step activation. This does not. But at a deeper level, what you are showing is that, if we define the neuron's activation function to be XOR (essentially what the mod 2 addition ...
chessprogrammer's user avatar
3 votes

Why this single layer perceptron for the add operation not learning the correct weights?

The activation function you are using is not differentiable, because it has a step at every half-integer value of $x$. This could be a problem for training. I would expect a better result using the ...
Jaume Oliver Lafont's user avatar
3 votes
Accepted

Direct formula for calculating the optimum matrix which minimizes the perceptron error

The idea is correct, the last formula is wrong. In general $X$ will not be square, usually one has much more data than parameters. The data points will also be in general position, so that $X$ has ...
Lutz Lehmann's user avatar
2 votes

Direct formula for calculating the optimum matrix which minimizes the perceptron error

As you understand, $E$ is the definition of loss function. This function defines square of the difference between weights applied to $X_i$, namely output of the perception, and $Y_i$ the desired ...
OmG's user avatar
  • 1,826
1 vote

Why this single layer perceptron for the add operation not learning the correct weights?

I advise to change the cost function to a mean squared error (as commonly done in regression problems): $\mathcal L(y,\hat{y}) = \frac{1}{2B}\sum_{i=0}^{B-1} (y^{(i)}-\hat{y}^{(i)})^2$; where you ...
Luca Anzalone's user avatar
1 vote
Accepted

Is my single layer perceptron getting biased input some way or the other?

The direct reason that your AI always moves the top-left piece first (assuming the computer pieces take up the bottom 2 rows) is the way your model interacts with the environment. Because you score ...
Quitting Due To Antisemitism's user avatar

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