backward propagation of errors | artificial neural networks | deep neural networks

Backpropagation, short for backward propagation of errors, is an algorithm commonly used to train artificial neural networks, particularly those with multiple layers, known as deep neural networks.
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It is a key component of gradient based optimization methods such as stochastic gradient descent, which are used to update the weights of a neural network during the learning process.
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The basic idea behind back propagation is to compute the gradient of the loss function with respect to the weights of the network, which indicates how the loss changes as the weights are adjusted.
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This gradient is then used to update the weights in a way that minimizes the loss.
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The backpropagation algorithm consists of two main phases, the forward pass and the backward pass.
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Forward pass.
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During the forward pass, the input data is fed into the neural network, and the activations of each neuron in each layer are computed successively from the input layer to the output layer.
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This process is often referred to as the forward propagation of the input through the network.
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The activations are computed using the current weights and biases of the network.
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Backward pass.
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In the backward pass the error between the networks predicted output and the desired output target is calculated.
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This error is then propagated backward through the network layer by layer, by computing the gradients of the error with respect to the weights and biases of each layer.
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The chain rule of calculus is used to calculate these gradients by multiplying the gradients of subsequent layers.
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The gradients indicate how the error would change with respect to small changes in the weights and biases.
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Once the gradients are computed, an optimization algorithm such as stochastic gradient descent is typically used to update the weights and biases of the network.
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The weights are adjusted in the opposite direction of the gradients, scaled by a learning rate to gradually minimize the loss function.
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The back propagation algorithm enables neural networks to learn from labeled training data by iteratively adjusting the weights based on the computed gradients.
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By repeating the forward and backward passes on batches of training data, the network can gradually improve its performance and make better predictions on unseen data.
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It's important to note that backpropagation assumes differentiable activation functions and requires A sufficient amount of training data to generalize well.
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Additionally, techniques like regularization, dropout and batch normalization are often employed to enhance the training process and prevent overfitting.

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