从头开始测试神经网络构建 (XOR)

Question

So, I have recently implemented a neural network from scratch in python by following 3Blue1Brown's videos and I am currently doing the testing part of my implementation. This is done by doing the AND, OR, and XOR problems. It seems like the network works in the AND and OR problems, however, not in the XOR problem. I Get the following predictions:

AND

Input:     Output:
0, 0       0.048
1, 0       0.018
0, 1       0.020
1, 1       0.974

OR

Input:     Output:
0, 0       0.026
1, 0       0.984
0, 1       0.988
1, 1       0.997

XOR

Input:     Output:
0, 0       0.049
1, 0       0.842
0, 1       0.842
1, 1       0.844 <- WRONG!

These results have been predicted with a model of 1 hidden layer with 2 neurons, and the sigmoid function in both the hidden layer and in the output layer.

I have tried different amounts of testing data, epochs, dimensions in the hidden layers, and hidden layers, and nothing seems to work.

So, my question is if anyone has any idea why i get the wrong result in the XOR problem but not in the AND and the OR problems? And if so, how to fix it?

Answer 1

typically the XOR function requires a more complex model. Add another hidden layer of two neurons and that should be sufficient.