Back Propagation Error
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a playout is propagated up the search tree in Monte Carlo tree search This article has multiple issues. Please help improve back propagation error calculation it or discuss these issues on the talk page. (Learn
Backpropagation
how and when to remove these template messages) This article may be expanded with text translated from back propagation algorithm in neural network the corresponding article in German. (March 2009) Click [show] for important translation instructions. View a machine-translated version of the German article. Google's machine translation is a back propagation algo useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Do not translate text that appears unreliable or low-quality. If possible, verify the text with references provided in the foreign-language article. After translating, {{Translated|de|Backpropagation}} must
Understanding Backpropagation
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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 out of favor after an initial period of high popularity in back propagation algorithm in ann the 1950s. It took 30 years before the error backpropagation (or in short: backprop) algorithm why use back propagation popularized a way to train hidden units, leading to a new wave of neural network research and applications. (Fig. 1) In principle,
Bp Algorithm Neural Network
backprop provides a way to train networks with any number of hidden units arranged in any number of layers. (There are clear practical limits, which we will discuss later.) In fact, the network does not have to be organized https://en.wikipedia.org/wiki/Backpropagation 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 (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 https://www.willamette.edu/~gorr/classes/cs449/backprop.html 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: The first factor is the error of unit i. The second is Putting the two together, we get . To compute this gradient, we thus need to know the activity and the error for all relevant nodes in the network. Forward activaction. The activity of the input units is determined by the network's external input x. For all other units, the a
define the cost function with respect to that single example to be: This is a (one-half) squared-error cost function. Given a training set of m examples, we then define the overall cost function to be: The first term in the definition of J(W,b) is an average sum-of-squares error term. The second term is a regularization term (also called a weight decay term) that tends to decrease the magnitude of the weights, and helps prevent overfitting. [Note: Usually weight decay is not applied to the bias terms , as reflected in our definition for J(W,b). Applying weight decay to the bias units usually makes only a small difference to the final network, however. If you've taken CS229 (Machine Learning) at Stanford or watched the course's videos on YouTube, you may also recognize this weight decay as essentially a variant of the Bayesian regularization method you saw there, where we placed a Gaussian prior on the parameters and did MAP (instead of maximum likelihood) estimation.] The weight decay parameter λ controls the relative importance of the two terms. Note also the slightly overloaded notation: J(W,b;x,y) is the squared error cost with respect to a single example; J(W,b) is the overall cost function, which includes the weight decay term. This cost function above is often used both for classification and for regression problems. For classification, we let y = 0 or 1 represent the two class labels (recall that the sigmoid activation function outputs values in [0,1]; if we were using a tanh activation function, we would instead use -1 and +1 to denote the labels). For regression problems, we first scale our outputs to ensure that they lie in the [0,1] range (or if we were using a tanh activation function, then the [ − 1,1] range). Our goal is to minimize J(W,b) as a function of W and b. To train our neural network, we will initialize each parameter and each to a small random value near zero (say according to a Normal(0,ε2) distribution for some small ε, say 0.01), and then apply an optimization algorithm such as batch gradient descent. Since J(W,b) is a non-convex function, gradient descent is susceptible to local optima; however, in practice gradient descent usually works fairly well. Finally, note that it is important to initialize the parameters randomly, rather than to all 0's.