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Original post by ROBERTREAD1
Thanks, but can I get away with JUST biasing the input pattern? (to simplify implementation).
Posted 12 November 2005 - 12:09 AM
Original post by kirkd
I don't have any mathematical proof, but intuitively, I would suspect that with any bias on the hidden layers, you will be limiting the ability of your net. The bias allows your fit curve to shift and have an arbitrary intercept. If you think about it in one dimension, consider an X-axis with a sigmoidal curve going through the origin. Without the bias, you're stuck with the curve going through the origin. If you add in a bias term, you can now move that interception point on the X-axis around. This would translate to the hidden layers as well. Without a bias, they can only have one possible point of intercept without shifting, which may limit the ability to model a given curve.
I should point out that an earlier post said that the bias was necessary to address linearly inseperable problems, but that is not correct. Linear inseperability is addressed by having hidden layers. Without hidden layers, you essentially have a linear function approximator - the perceptron. When you add in a hidden layer, you start allowing for nonlinear transformations of the input variables.
I hope that helps.
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