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Is a Neural network with 2 input nodes, 2 hidden nodes and an output supposed to be able to solve the XOR problem provided there is no bias? Or can it get stuck?
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The XOR problem with neural networks can be solved by using Multi-Layer Perceptrons or a neural network architecture with an input layer, hidden layer, and output layer. So during the forward propagation through the neural networks, the weights get updated to the corresponding layers and the XOR logic gets executed.
MLP solves the XOR problem efficiently by visualizing the data points in multi-dimensions and thus constructing an n-variable equation to fit in the output values.
Linearly separable data basically means that you can separate data with a point in 1D, a line in 2D, a plane in 3D and so on. A perceptron can only converge on linearly separable data. Therefore, it isn't capable of imitating the XOR function.
A two layer (one input layer; one output layer; no hidden layer) neural network can represent the XOR function . So, in if I apply a softmax classifier, I can separate the xor dataset with a nn without any hidden layer.
Leave the bias in. It doesn't see the values of your inputs.
In terms of a one-to-one analogy, I like to think of the bias as the offsetting c-value in the straight line equation: y = mx + c; it adds an independent degree of freedom to your system that is not influenced by the inputs to your network.
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If I remember correctly it's not possible to have XOR without a bias.
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