Back-propagation in Neural Networks

The loss function indicates how far the predictions are from the true labels.

Backpropagation calculates each weight's contribution to the error, enabling the network to adjust its parameters accordingly.

The gradient represents how sensitive the loss function (£) is to changes in the weight matrix (W(l)). It tells us how much the loss will change if the weights in layer l are adjusted slightly.

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<p>The chain rule breaks down the gradient into smaller, manageable parts, allowing us to compute the contribution of each weight to the overall loss.</p> Signup and view all the answers

<p>Backpropagation relies on the chain rule of calculus to compute gradients of the loss function with respect to the weights.</p> Signup and view all the answers

<p>∂L/∂a(l) is the derivative of the loss function with respect to the activation a(l) at layer l.</p> Signup and view all the answers

<p>z(l) = W(l)a(l-1) + b(l)</p> Signup and view all the answers

<p>The two most commonly used optimization algorithms are Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam).</p> Signup and view all the answers

<p>SGD updates the weights by computing the gradient based on small batches of data.</p> Signup and view all the answers

<p>W = W - η ∂L/∂W</p> Signup and view all the answers

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<p>Random batches of data help the model avoid getting stuck in bad solutions by introducing noise.</p> Signup and view all the answers

<p>The learning rate controls the step size of weight updates.</p> Signup and view all the answers

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<p>Learning rate schedules adjust the learning rate during training to ensure optimal performance.</p> Signup and view all the answers

<p>A common technique is to start with a high learning rate and gradually decrease it as training progresses.</p> Signup and view all the answers

<p>The Adam optimizer aims to improve upon SGD by using adaptive learning rates for each parameter.</p> Signup and view all the answers

<p>Adam combines Momentum and RMSProp techniques to accelerate convergence.</p> Signup and view all the answers

<p>The Momentum optimizer helps speed up learning and smooth out the gradient updates.</p> Signup and view all the answers

<p>mt = β1mt-1 + (1 - β1)gt</p> Signup and view all the answers

<p>The Momentum optimizer smooths updates and speeds up movement in the right direction.</p> Signup and view all the answers

<p>The RMSprop optimizer adapts the learning rate for each parameter to handle cases where gradients vary widely.</p> Signup and view all the answers

<p>RMSprop keeps track of the squared gradients and adjusts the learning rate for each parameter by dividing the gradient by the square root of its recent squared gradients.</p> Signup and view all the answers

<p>vt = β2vt-1 + (1 - β2)gt^2</p> Signup and view all the answers

<p>RMSprop adapts the learning rate for each parameter based on how volatile its gradient is, making training more stable.</p> Signup and view all the answers

<p>RMSprop adjusts the learning rate by considering the history of squared gradients but not the gradient itself like momentum.</p> Signup and view all the answers

<p>Momentum focuses on smoothing the direction of updates by considering past gradients.</p> Signup and view all the answers

<p>Momentum &quot;remembers&quot; past gradients themselves, while RMSprop &quot;remembers&quot; the squared gradients.</p> Signup and view all the answers

<p>Wt = Wt - η * mt / √(vt + ε)</p> Signup and view all the answers

<p>mt / √(vt + ε) scales the learning rate by both the momentum and the magnitude of recent gradients.</p> Signup and view all the answers

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<p>Backpropagation calculates the gradient at the output layer and propagates this information backward through the network.</p> Signup and view all the answers

<p>The gradient flows backward through the network, from the output layer to the input layer.</p> Signup and view all the answers

<p>Backpropagation allows the model to 'assign blame' for the error to individual weights by identifying which ones contributed most and by how much.</p> Signup and view all the answers

<p>Regularization is a technique used to prevent a model from overfitting (performing well on training data but poorly on new data).</p> Signup and view all the answers

<p>Regularization adds a penalty to the model's complexity during training, encouraging it to be simpler and more generalizable.</p> Signup and view all the answers

<p>Dropout is a technique used to prevent overfitting in neural networks.</p> Signup and view all the answers

<p>Dropout randomly 'drops out' (turns off) a percentage of neurons in a layer during training, forcing the model to not rely too much on specific neurons and encouraging it to learn more robust patterns.</p> Signup and view all the answers

<p>p = 1 - dropout-rate</p> Signup and view all the answers

<p>Neurons that are not dropped out during training continue to participate in the forward and backward passes of the network, while those dropped out are temporarily ignored.</p> Signup and view all the answers

<p>Standard dropout scales activations during testing, while inverted dropout scales them during training.</p> Signup and view all the answers

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<p>The chapter introduces the fundamentals of deep learning, focusing on multilayer perceptrons.</p> Signup and view all the answers

<p>The chapter covered feedforward and backpropagation algorithms, optimization techniques like SGD and Adam, and the regularization method Dropout.</p> Signup and view all the answers

A process that calculates the gradient of the loss function with respect to each weight in the network, allowing the model to adjust its parameters to minimize the error.

A function that measures how far away model predictions are from actual target values.

How sensitive the loss function is to changes in a particular weight.

An algorithm that updates weights by using gradient descent on small batches of data.

A mathematical rule that allows us to decompose complex gradients into smaller, manageable parts.

A parameter that controls the step size of weight updates during training.

A process of adjusting the learning rate during training. It typically starts with a high rate and gradually decreases it.

An optimization algorithm that combines Momentum and RMSprop to adjust learning rates for each parameter.

A technique that helps speed up learning by incorporating past gradients into weight updates.

A technique that adjusts the learning rate for each parameter based on the volatility (variability) of its gradient.

A technique that randomly 'drops out' neurons during training to prevent overfitting.

The probability that a neuron is kept during training.

The probability that a neuron is dropped out during training.

A technique used to prevent overfitting by adding a penalty to the model's complexity.

A type of neuron that takes a weighted sum of its inputs, adds a bias, and applies an activation function.

The process of calculating the output of a neural network by passing input signals through its layers.

The act of updating weights in a neural network to reduce the difference between predicted and actual values.

A process of propagating the gradient of the loss function backward through the network, allowing the model to allocate blame for errors to individual weights.

A technique that scales activations during training to account for dropout during testing.

A collection of neurons organized in layers, with connections between them that allow information to flow.

The ability of a model to perform well on new data that it has not been trained on.

The process of making predictions with a neural network based on input signals.

The act of training a neural network using a large dataset to learn patterns and improve its performance.

A set of data used to evaluate the performance of a trained neural network.

The measure of how well a model performs on a specific task.

A representation of data used by a neural network to make predictions.

The act of using a trained neural network to make predictions on new data.

A mathematical function that maps input values to output values within a neuron.

A number that represents the strength of the connection between two neurons.

A value that is added to the weighted sum of inputs before applying an activation function.

The act of selecting a subset of data for training or testing.

The process of evaluating the performance of a model on a separate dataset to ensure it generalizes well.

A technique that combines multiple models together to improve overall performance.