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Have you ever wondered how neural networks learn? Do you know how they adapt their weights and biases to generate accurate predictions from complex data? The answer to this lies in an algorithm known as backpropagation. In simple terms, backpropagation is the workhorse behind training neural networks. It is an algorithm that helps the network to learn by adjusting its internal parameters (weights and biases) based on the errors made during prediction. You can think of it as a teacher who gently guides the network towards the correct answers. The Process: Forward, Backward, and Descent |
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Backpropagation consists of three main phases: Forward Pass: The network takes the input data and makes a prediction by propagating the information forward through its layers. This prediction is then compared to the expected output, and an error is calculated. Backward Pass: The algorithm then works backwards, starting from the output layer and propagating the error gradients through the network's layers. This process determines how much each weight and bias contributed to the overall error. Gradient Descent: Armed with the error gradients, the network adjusts its weights and biases in the opposite direction of the gradients, effectively minimizing the error. |
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Forward Pass In the forward pass, we propagate the inputs in a forward direction, layer-by-layer, until the output is generated. To simplify the derivation of the learning algorithm, we will treat the bias as if it were the weight w of an input neuron x that has a constant value of 1. |
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Backward Pass In the backward pass we propagate the gradients of the error from the output layer back to the input layer. Definition of the Error and Loss Functions We first define the error of the network on the training set with respect to its weights. Let's denote by w the vector that contains all the weights of the network. ... The specific loss function that we use depends on the task the network is trying to accomplish: 1. For regression problems, we use the squared loss function. 2. For binary classification problems, we use log loss (also known as the binary cross-entropy loss). 3. For multi-class classification problems, we use the cross-entropy loss function. |
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Our goal is to find the weights w that minimize E(w). Unfortunately, this function is non-convex because of the non-linear activations of the hidden neurons. |
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There are various techniques that can be used to prevent gradient descent from getting stuck in a local minimum, such as momentum. These techniques will be covered in future articles. |
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