In a traditional neural node, all inputs are multiplied against their respective weights, then the node's output is the sum of all those values plus a bias offset:
y = X1*W1 + X2*W2 + ... Xn*Wn + B
I'm playing around with the inverted idea: all inputs have an associated bias, then those values are multiplied together along with a single local weight:
y = (X1+W1) * (X2+W2) * ... (Xn+Wn) * B
The specific applications where I would like to use this begin with trivial situations, i.e. where some answer y is the product of two inputs X1 * X2, which is not easily solve-able by a traditional (small) neural network.
Instead of re-inventing the wheel, I'd like to read any whitepapers and/or shortcomings of using a node like this. Is there a name for this proposed type of node?