xor is a non-linear dataset. It cannot be solved with any number of perceptron based neural network but when the perceptions are applied the sigmoid activation function, we can solve the xor dataset.
But I came across a source where the following statement is stated as
A two layer (one input layer; one output layer; no hidden layer) neural network can represent the XOR function.
However, I have trained a model with no hidden layers, gives the following result:
[INFO] data=[0 0],ground-truth=0, pred=0.5161, step=1 [INFO] data=[0 1],ground-truth=1, pred=0.5000, step=1 [INFO] data=[1 0],ground-truth=1, pred=0.4839, step=0 [INFO] data=[1 1],ground-truth=0, pred=0.4678, step=0
So, in if I apply a softmax classifier, I can separate the xor dataset with a nn without any hidden layer. This makes the statement incorrect.
Is it true that we cannot separate a non linear dataset without any hidden layers in a neural network? If yes, where am I wrong in my reasoning from the training of the nn I have done above