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I've been trying to learn how back-propagation works with neural networks, but yet to find a good explanation from a less technical aspect.

How does back-propagation work? How does it learn from a training dataset provided? I will have to code this, but until then I need to gain a stronger understanding of it.

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The backpropagation follows a decent gradient approach to train the Artificial Neural Network. It uses supervised learning for training the multi-layer perceptron in ANN. The Backpropagation algorithm takes the minimum value of the error function in weight space using a gradient descent technique. The weights that minimize the error function is then considered to be a solution to the learning problem of the model. 

Here is a step by step implementation of how the backpropagation algorithm works:

http://neuralnetworksanddeeplearning.com/chap2.html

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