Error Backpropagation Training
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be an insurmountable problem - how could we tell the hidden units just what to do? This unsolved question was in fact the reason why neural networks fell back propagation training algorithm out of favor after an initial period of high popularity in the 1950s. It error back propagation algorithm ppt took 30 years before the error backpropagation (or in short: backprop) algorithm popularized a way to train hidden units, leading
Back Propagation Error Calculation
to a new wave of neural network research and applications. (Fig. 1) In principle, backprop provides a way to train networks with any number of hidden units arranged in any number of layers.
Error Back Propagation Algorithm Derivation
(There are clear practical limits, which we will discuss later.) In fact, the network does not have to be organized in layers - any pattern of connectivity that permits a partial ordering of the nodes from input to output is allowed. In other words, there must be a way to order the units such that all connections go from "earlier" (closer to the input) to "later" ones back propagation learning (closer to the output). This is equivalent to stating that their connection pattern must not contain any cycles. Networks that respect this constraint are called feedforward networks; their connection pattern forms a directed acyclic graph or dag. The Algorithm We want to train a multi-layer feedforward network by gradient descent to approximate an unknown function, based on some training data consisting of pairs (x,t). The vector x represents a pattern of input to the network, and the vector t the corresponding target (desired output). As we have seen before, the overall gradient with respect to the entire training set is just the sum of the gradients for each pattern; in what follows we will therefore describe how to compute the gradient for just a single training pattern. As before, we will number the units, and denote the weight from unit j to unit i by wij. Definitions: the error signal for unit j: the (negative) gradient for weight wij: the set of nodes anterior to unit i: the set of nodes posterior to unit j: The gradient. As we did for linear networks before, we expand the gradient into two factors by use of the chain rule: T
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