Back Error Propagation
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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 https://www.willamette.edu/~gorr/classes/cs449/backprop.html popularity in the 1950s. It took 30 years before the error backpropagation (or in short: backprop) algorithm popularized a way to train hidden units, leading to a new wave of neural network research and applications. (Fig. 1) https://www.quora.com/What-is-back-propagation-in-neural-networks In principle, 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 error propagation 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 (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; back error propagation 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: 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 extern
Udacity.comMaster Machine Learning with a course created by Google.Become a Machine Learning Engineer in this self-paced course. Job offer guaranteed, or your money back.Learn More at Udacity.comAnswer Wiki3 Answers Stephen WelchWritten 91w agoBackpropagation is just a special name given to finding the gradient of the cost function in a neural network. There's really no magic going on, just some reasonably straight forward calculus. Backpropagation really threw me off when I first learned NNs, because I thought it was some highly specialized technique - It's not. This is not to say it's not a difficult, but under the hood it's straight forward calculus. 2.5k Views · View UpvotesRelated QuestionsMore Answers BelowWhat is the sequence to build back propagation for neural network?How do you explain back propagation algorithm to a beginner in neural network?In neural networks, how important is back-propagation? What is its significance?How does back propagation work?What would you add to current Artificial Neural Network to resemble more of Biological Neural Network? Hasan PoonawalaWritten 174w agoWhen you use a neural network, the inputs are processed by the (ahem) neurons using certain weights to yield the output. This is like a signal propagating through the network. When training the network, you generate an error signal when the inputs are `propagated' through to the outputs (usually the difference between outputs and the expected known values). Now the errors are used to change the weights, that is, the errors are processed to generate a change in the weights, also called an update. It's like the errors are propagating backwards through the network to yield a better set of weights that would match the inputs to the outputs, at least on the training data. That's a crude way to understand `back propagation'. The back propagation step yields new weights for the neurons, through a process of optimization via gradient descent (this is the most basic method). You could also call the step a feedback step.2.4k Views · View Upvotes Ankur Nayak, computer science EngineerUpdated 159w agoLets say your Neural network NN has random wieghts( or all 1),Now u want to update your weights to get the required output. You are getting (EXpected - actual) output difference. Now this differennce in output called ERROR will act as a feedback to update the weights,This ERROR is function of input(s), output and all weightsOne can calculate the (partial differenciation or GRADIENT or variation ) of Error with respect to a particalar weight on a