Backpropagation: Difference between revisions

Latest revision as of 07:30, 19 May 2023

Case study notes^[1]

Backpropagation, or "backward propagation of errors," is a method used in artificial neural networks to calculate the gradient that is needed in the optimization process. It is used for training the network and is a key part of many machine learning algorithms. Here's a step-by-step description:

Forward Pass: During this step, the network makes a prediction based on the input data. This prediction will initially be fairly inaccurate, as the network's weights are initialized randomly.
Calculate Loss: The prediction is compared to the actual output, and the difference between the two is calculated. This difference is called the "loss" or "error." There are various methods to calculate this loss, but all aim to represent how far off the network's prediction was from the actual output.
Backward Pass (Backpropagation): This is where backpropagation really comes into play. The network propagates the error backwards, starting from the output layer and moving through each hidden layer until it reaches the input layer. The goal is to calculate the gradient, or the rate of change of the error with respect to the weights and biases in the network. To do this, it uses the chain rule from calculus to iteratively compute these gradients for each layer.
Update Weights: The final step is to use these gradients to adjust the weights and biases in the network. This is typically done using an optimization algorithm, such as stochastic gradient descent (SGD), which adjusts the weights in the opposite direction of the gradient to minimize the loss. The size of the adjustments is governed by a parameter called the "learning rate."

The above steps are repeated for a number of iterations (or "epochs") until the network is adequately trained. The end goal is to adjust the weights and biases of the network so as to minimize the error on the output, and in doing so, the network "learns" the relationship between the input data and the output data.

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-== Introduction ==
+Backpropagation, or "backward propagation of errors," is a method used in artificial neural networks to calculate the gradient that is needed in the optimization process. It is used for training the network and is a key part of many machine learning algorithms. Here's a step-by-step description:
-Backpropagation is a method to calculate the gradient of the loss function with respect to the weights in an artificial neural network. It is commonly used as a part of algorithms that optimize the performance of the network by adjusting the weights, for example in the gradient descent algorithm. It is also called backward propagation of errors.<ref>https://en.wikipedia.org/wiki/Backpropagation</ref>
-Backpropagation, short for "backward propagation of errors," is an algorithm for supervised learning of artificial neural networks using gradient descent. Given an artificial neural network and an error function, the method calculates the gradient of the error function with respect to the neural network's weights. It is a generalization of the delta rule for perceptrons to multilayer feedforward neural networks.<ref>https://brilliant.org/wiki/backpropagation/</ref>
+# Forward Pass: During this step, the network makes a prediction based on the input data. This prediction will initially be fairly inaccurate, as the network's weights are initialized randomly.
+# Calculate Loss: The prediction is compared to the actual output, and the difference between the two is calculated. This difference is called the "loss" or "error." There are various methods to calculate this loss, but all aim to represent how far off the network's prediction was from the actual output.
+# Backward Pass (Backpropagation): This is where backpropagation really comes into play. The network propagates the error backwards, starting from the output layer and moving through each hidden layer until it reaches the input layer. The goal is to calculate the gradient, or the rate of change of the error with respect to the weights and biases in the network. To do this, it uses the chain rule from calculus to iteratively compute these gradients for each layer.
+# Update Weights: The final step is to use these gradients to adjust the weights and biases in the network. This is typically done using an optimization algorithm, such as stochastic gradient descent (SGD), which adjusts the weights in the opposite direction of the gradient to minimize the loss. The size of the adjustments is governed by a parameter called the "learning rate."
+The above steps are repeated for a number of iterations (or "epochs") until the network is adequately trained. The end goal is to adjust the weights and biases of the network so as to minimize the error on the output, and in doing so, the network "learns" the relationship between the input data and the output data.