Gradient Descent and Neural Networks Quiz
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Questions and Answers

What is the purpose of computing the gradient in the Gradient Descent Algorithm?

  • To classify the input data
  • To find the maximum of the function
  • To perform data normalization
  • To adjust weights towards a minimum (correct)
  • In Gradient Descent, increasing the learning rate will always lead to faster convergence.

    False

    What does the symbol $ heta$ represent in the context of Gradient Descent?

    The parameters or weights being optimized

    The update rule for the weights in Gradient Descent can be expressed as $ heta_{new} = heta_{old} - ext{} abla ext{L}( heta{old})$, where $ ext{_}$ represents the learning rate.

    <p>α</p> Signup and view all the answers

    Match the components of the Gradient Descent algorithm with their correct descriptions:

    <p>$ heta_{old}$ = The previous values of parameters $ abla ext{L}( heta_{old})$ = The gradient of the loss function with respect to $ heta$ $ heta_{new}$ = The updated values of parameters α = The learning rate used for updates</p> Signup and view all the answers

    What is the primary characteristic of neural networks (NNs) with at least one hidden layer?

    <p>They are universal approximators.</p> Signup and view all the answers

    Deep neural networks have the same representational power as a single-layer neural network.

    <p>True</p> Signup and view all the answers

    What type of learning can neural networks perform?

    <p>Both unsupervised and supervised learning.</p> Signup and view all the answers

    The basic processing element in a neural network is called a __________.

    <p>perceptron</p> Signup and view all the answers

    Match the following terms with their descriptions:

    <p>W = Weights assigned to input x = Input vector y = Output of the perceptron error = Difference between target output and actual output</p> Signup and view all the answers

    Why did deep learning start outperforming other machine learning techniques around 2010?

    <p>Improved hardware capabilities and larger datasets.</p> Signup and view all the answers

    What is a characteristic of gradient descent algorithm in neural networks?

    <p>It may reach different local minima on different runs.</p> Signup and view all the answers

    The forward propagation process refers to passing the outputs backward toward the inputs.

    <p>False</p> Signup and view all the answers

    Neural networks only require small datasets to perform effectively.

    <p>False</p> Signup and view all the answers

    What method is employed in modern neural networks for calculating gradients of the loss function?

    <p>Backpropagation</p> Signup and view all the answers

    What is one key reason deep neural networks function better than simpler models?

    <p>Empirical observation.</p> Signup and view all the answers

    In the formula for a perceptron, the output is calculated as y = Σ wj xj + w0, where w is the __________.

    <p>weights vector</p> Signup and view all the answers

    Gradient descent may not reach a ______ minimum for the loss surface.

    <p>global</p> Signup and view all the answers

    Match the following neural network components with their functions:

    <p>Input Layer = Receives raw data Hidden Layer = Processes inputs through weights Output Layer = Produces the final output Activation Function = Applies non-linearity</p> Signup and view all the answers

    What is a common goal of weight adjustment during training in a neural network?

    <p>Minimize the error.</p> Signup and view all the answers

    What does automatic differentiation in deep learning libraries do?

    <p>Simplifies implementation by automating gradient calculation.</p> Signup and view all the answers

    The loss function is calculated after performing backward propagation.

    <p>False</p> Signup and view all the answers

    Neural networks are effective in both speech recognition and natural language processing tasks.

    <p>True</p> Signup and view all the answers

    Why is it considered wasteful to compute loss over the entire training dataset for a single update?

    <p>Because it is inefficient for large datasets.</p> Signup and view all the answers

    What is one adjustment made during the training of a neural network?

    <p>Adjusting weights based on error.</p> Signup and view all the answers

    ____ is the method used to generate predictions through the layers before calculating loss.

    <p>Forward propagation</p> Signup and view all the answers

    Neural networks compute complex decision boundaries through __________ mapping of inputs to outputs.

    <p>nonlinear</p> Signup and view all the answers

    What is the primary purpose of performing a backward pass during training?

    <p>To calculate the gradients of the loss function.</p> Signup and view all the answers

    What does the output of a max pooling layer report?

    <p>The maximum value within a neighborhood</p> Signup and view all the answers

    Convolutional Neural Networks primarily use larger filters and shallower architectures.

    <p>False</p> Signup and view all the answers

    What is the shape of the activation map generated by a CONV layer for a 5 filter setup based on the provided size (28x28) ?

    <p>28x28x5</p> Signup and view all the answers

    The convolutional layer typically involves __________ filters.

    <p>multiple</p> Signup and view all the answers

    Match each type of pooling with its definition:

    <p>Average pooling = Reports the average output within a neighborhood Max pooling = Reports the maximum output within a neighborhood</p> Signup and view all the answers

    How many dimensions does the dot product between the filter and an image part result in if the filter has a size of 5x5 and depth of 3?

    <p>75</p> Signup and view all the answers

    Pooling layers only operate over the entire input at once.

    <p>False</p> Signup and view all the answers

    What is the role of fully connected layers in a Convolutional Neural Network?

    <p>To connect neurons to the entire input volume.</p> Signup and view all the answers

    Pooling layers reduce the __________ size of the feature maps.

    <p>spatial</p> Signup and view all the answers

    What happens when a pooling layer with a 2x2 filter and a stride of 2 is applied?

    <p>It reduces the spatial dimensions.</p> Signup and view all the answers

    Which of the following correctly describes a loss function?

    <p>A metric that measures the difference between predicted and true labels</p> Signup and view all the answers

    The mean squared error loss function is used solely for classification tasks.

    <p>False</p> Signup and view all the answers

    What does SGD stand for in the context of optimizing neural networks?

    <p>Stochastic Gradient Descent</p> Signup and view all the answers

    The formula for cross-entropy loss function is given by ___ (fill in with the appropriate notation).

    <p>ℒ 𝜃 = − ∑ ∑ 𝑦𝑘 log 𝑦̂𝑘 + (1 − 𝑦𝑘) log(1 − 𝑦̂𝑘𝑖)</p> Signup and view all the answers

    Match the following loss functions with their primary use:

    <p>Cross-entropy = Classification tasks Mean Squared Error = Regression tasks Mean Absolute Error = Regression tasks Hinge Loss = Support Vector Machines</p> Signup and view all the answers

    What does the gradient of a loss function indicate?

    <p>The direction of fastest increase of the loss function</p> Signup and view all the answers

    Gradient descent is only applicable to linear models.

    <p>False</p> Signup and view all the answers

    What is the purpose of finding optimal parameters 𝜃 * in neural networks?

    <p>To minimize the total loss ℒ 𝜃.</p> Signup and view all the answers

    The loss function for regression tasks can be calculated using ___ and ___.

    <p>Mean Squared Error, Mean Absolute Error</p> Signup and view all the answers

    Which loss function is best suited for multi-class classification problems?

    <p>Cross-entropy</p> Signup and view all the answers

    The total loss is calculated by averaging individual losses over all images in the training set.

    <p>True</p> Signup and view all the answers

    Which approach reduces the learning rate by a constant whenever validation loss stops improving?

    <p>ReduceLROnPlateau</p> Signup and view all the answers

    Weight decay applies a penalty for small weights during the parameter update process.

    <p>False</p> Signup and view all the answers

    What mathematical operation is applied to the inputs to calculate the total loss in neural networks?

    <p>Summation</p> Signup and view all the answers

    The gradient descent algorithm uses the ___ direction of the gradient to update model parameters.

    <p>opposite</p> Signup and view all the answers

    What is the primary purpose of dropout in neural networks?

    <p>To prevent overfitting by randomly dropping units during training.</p> Signup and view all the answers

    In gradient descent, which of the following best describes the role of the learning rate?

    <p>It specifies how quickly to adjust weights during training.</p> Signup and view all the answers

    The learning rate decay technique of reducing the learning rate by a factor every few epochs is referred to as ______.

    <p>step decay</p> Signup and view all the answers

    What is one effect of using batch normalization?

    <p>Reduces internal covariate shift</p> Signup and view all the answers

    Exponential decay gradually increases the learning rate over time.

    <p>False</p> Signup and view all the answers

    What does the patience parameter represent in early stopping?

    <p>The number of epochs to wait before stopping training if no improvement is observed.</p> Signup and view all the answers

    A large weight decay coefficient induces a stronger ______ for weights with large values.

    <p>penalty</p> Signup and view all the answers

    Which method is often preferred over grid search for hyper-parameter tuning?

    <p>Random search</p> Signup and view all the answers

    K-Fold cross-validation can help improve the reliability of model performance estimates.

    <p>True</p> Signup and view all the answers

    Name one common hyper-parameter in neural network training.

    <p>Initial learning rate</p> Signup and view all the answers

    Using _____ act similarly to data preprocessing, normalizing data to zero mean and unit variance.

    <p>batch normalization layers</p> Signup and view all the answers

    Match the following regularization techniques with their descriptions:

    <p>L2 regularization = Penalizes large weights in the loss function L1 regularization = Penalizes the sum of absolute weights Dropout = Randomly removes units during training Elastic net = Combines L1 and L2 regularization techniques</p> Signup and view all the answers

    Study Notes

    Introduction to Machine Learning AI 305 - Deep Learning

    • Neural networks gained popularity in the 1980s, with successes and notable conferences like NeurIPS and Snowbird
    • Support Vector Machines (SVMs), Random Forests, and Boosting became prominent in the 1990s, prompting a "backseat" position for neural networks
    • Deep Learning re-emerged around 2010, fueled by improvements in computing power, larger datasets, and software tools like TensorFlow and PyTorch.
    • Pioneers like Yann LeCun, Geoffrey Hinton, and Yoshua Bengio were awarded the 2019 ACM Turing Award for their work in neural networks.

    Machine Learning Basics

    • Machine learning empowers computers to learn without explicit programming.
    • Labeled training data is used to build a learned model, which is then used to make predictions on new data.

    ML vs. Deep Learning

    • Most machine learning methods rely on human-designed representations and input features that best allow the computer to understand the issue.
    • Machine learning methods simply optimize the weights assigned to these features to make predictions.

    What is Deep Learning (DL)?

    • Deep learning is a machine learning subfield focused on learning representations of data.
    • DL excels at learning patterns and uses a hierarchy of multiple layers to better understand input data. If large amounts of information are provided, the system can use this to better learn and respond in useful ways.

    Why is DL Useful?

    • Manually designed features can be overly-specific, incomplete, and time-consuming to develop.
    • Learned features in deep learning are adaptable and fast to learn.
    • Deep learning offers a flexible and almost universal framework for representing various types of information (visual, linguistic).
    • DL enables effective end-to-end learning of complex systems.
    • Deep learning can utilize large amounts of training data.
    • DL outperformed other methods in speech, vision, and natural language processing beginning around 2010.

    Representational Power

    • Neural networks with at least one hidden layer can approximate any complex continuous function.
    • Deep neural networks often perform better empirically than shallow networks in complex tasks, although they have the same theoretical representational power as a single-layer network

    Perceptron

    • A perceptron is a basic processing element in a neural network.
    • Perceptrons can receive input from the environment or from other perceptrons.

    Single Layer Neural Network

    • A single-layer neural network consists of an input layer, a hidden layer, and an output layer.
    • The output (Y) of the network is a function of the input (X), calculated using predetermined weights (w) and biases (b)

    Example of Neural Network

    • A neural network functions by passing inputs through multiple layers (hidden layers), with each layer containing neurons designed to use the prior layers' outputs for the next level of computations.
    • Calculations at each layer rely on a specific function (activation functions), which converts the sum of each neuron's weighted input signals to its output.

    Matrix Operation

    • In neural networks, matrix operations are used to calculate the output at each layer efficiently.

    Neural Network

    • Neural networks are comprised of multiple interconnected layers, with each layer consisting of simple computational units called neurons. The different neurons are connected to other neurons in the adjacent layers by weights, which determine how much influence one neuron has on other nearby neurons.

    Softmax Layer

    • In multi-class classification tasks, the output layer typically uses a softmax function, producing probability values in the range of 0 to 1 for each output category.
    • These outputs, when properly normalized, add up to 1.0.

    Activation: Sigmoid

    • A sigmoid function converts a real-valued input into a value between 0 and 1.
    • It's a widely used activation function but less frequent in modern deep networks because the gradients can vanish when a very large or small input is passed to the function.

    Activation: Tanh

    • A tanh function transforms a real-valued input to a value between -1 and 1.
    • It is similar to the sigmoid function but zero-centered.

    Activation: ReLU

    •  A rectified linear unit (ReLU) function outputs the same value as the input if the input is positive, and outputs 0 otherwise.
    • ReLU acts as an activation function for most modern deep neural networks (DNNs).
    • The ReLU function is easy to compute compared to sigmoids and tanh. ReLU accelerates gradient descent.  

    Activation: Leaky ReLU

    • The leaky ReLU function is a variation of ReLU and helps prevent neurons from "dying."
    • It outputs ax when x < 0, and x otherwise for a small value of a (e.g., 0.01), keeping a small gradient on activation below zero, stopping neurons from not having sufficient gradient for weights to update.

    Activation: Linear Function

    • The linear activation function outputs an output that's linearly proportional to the input.
    • In many regression tasks, the last layer uses a linear activation function to generate numbers rather than class membership.

    Training NNs

    • Network parameters (weights and biases) are learned through optimization

    Data Preprocessing

    • Data preprocessing improves model convergence.
    • Techniques include: mean subtraction, normalization to obtain zero-mean and unit variance.

    Training NNs: loss functions

    • A loss function calculates the difference between the model's prediction and the true label.
    • Examples include mean-squared error, cross-entropy, etc.

    Training NNs: optimizing loss function

    • Optimal parameters are sought that minimize the calculated loss for the given dataset. Often done through iterative steps of applying gradient descent.

    Gradient Descent Algorithm

    • Gradient descent is used to optimize the loss function.
    • It involves iteratively adjusting parameters based on the calculated loss function, following negative gradients.

    Gradient Descent with Momentum

    Gradient descent with momentum adds a momentum (accumulation of previous gradients) factor for parameter update. This improves optimization when dealing with oscillations or plateaus.

    Adam

    • Adam is an adaptive optimization algorithm that combines momentum and adaptive learning rates based on past gradients.
    • It's a popular optimizer for many deep learning tasks.

    Learning Rate

    • Learning rate (step size) is the magnitude by which gradients are used for parameter update.
    • It's a key hyperparameter that affects model training.
    • Small learning rates lead to slow convergence, while large learning rates result in overshooting or non-convergent behavior.

    Learning Rate Scheduling

    • Learning rate scheduling dynamically changes the learning rate during training to achieve optimal convergence.
    • Common strategies include exponential decay, cosine decay, and warmup.

    Vanishing Gradient Problem

    • Gradients can become vanishingly small during training, slowing down or preventing parameter update. The problem is especially common in deep networks.

    Generalization

    • Deep learning models can struggle to generalize, showing high performance on training data but poor performance on novel test data. This phenomenon is known as overfitting. Insufficient training can also negatively impact generalization (underfitting).

    Regularization: Weight Decay

    • Weight decay adds a penalty to the loss function for large weights (or absolute values of weights).
    • It aims to keep the weights small, reducing overfitting.

    Regularization: Dropout

    • Dropout randomly removes (sets to zero) neurons during training.
    • This technique can help the network avoid overfitting to the training data, increasing its ability to generalize.

    Regularization: Early Stopping

    • Early stopping monitors the validation error during training and terminates the process when the validation error starts to increase again after having decreased. This is an optimization to prevent the model from overfitting the training set.

    Batch Normalization

    • Batch normalization normalizes the input data to each layer by subtracting the mean and dividing by the variance of the input batch.
    • This can improve the stability and convergence of the training process.

    Hyperparameter Tuning

    • Hyperparameters are settings of parameters that are not determined through training, like the learning rate.
    • Techniques used in tuning include grid search, random search, and Bayesian optimization to find optimal parameters.

    k-Fold Cross-Validation

    • A technique to improve the reliability of hyperparameter tuning processes.
    • It involves splitting the available data into multiple folds (e.g., 5), and repeatedly training and evaluating a model on different combinations of training and validation segments of the data.

    Ensemble Learning

    • Ensemble learning combines the predictions of multiple models, typically producing better performance than a single model on various tasks.
    •  Common approaches include bagging and boosting.

    Deep vs. Shallow Networks

    • Deeper networks (with more layers) have the potential to learn more complex patterns than shallow networks (with fewer layers), as they enable a nonlinear transformation of the data.
    • Still, deeper networks may face performance diminishing returns after a certain depth.

    Convolutional Neural Networks (CNNs)

    • CNNs are specifically designed for data with grid-based structure.
    • CNNs exploit spatial relationships and use convolution and pooling layers to create feature maps.
    • Filters slide over image areas determining important features.

    How CNNs Work

    • CNNs use hierarchical feature extraction to learn increasingly complex image features, from edges and shapes to complete objects
    • They use convolution and pooling layers

    Other CNNs components

    •  A convolutional layer in a CNN performs calculations to discover various features from the input data.
    •  A fully connected layer converts the learned features into a predicted output. -Pooling layers condense the spatial image by taking the maximum or average of values within a local region (spatial resolution reduction).

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    This quiz covers fundamental concepts of the Gradient Descent algorithm and the characteristics of neural networks. Test your understanding of gradient computation, learning rates, and neural network architecture. Ideal for students delving into machine learning and deep learning topics.

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