Error back-propagation learning using polynomial energy function

The authors derived a gradient descent weight update law using a polynomial energy function for supervised error backpropagation learning for feedforward artificial neural networks (FFANNs). The polynomial energy function used in this study is a combination of the L ₁ and the L₂ norms of the errors in the output of the network. It is shown analytically that the learning performance may improve if the polynomial energy function is used instead of the sum-of-the-squared energy function. The XOR problem was used for the simulation evidence to support the above analysis. The analysis indicates that the polynomial learning dynamics is faster at each point in the weight space. On the other hand, the simulations on the XOR problem seem to support a much stronger and desirable viewpoint; the polynomial learning dynamics is faster along each trajectory in weight space as compared to the sum-of-the-squared learning dynamics