Experimenting with momentum

In this exercise, your goal is to find the optimal momentum such that the optimizer can find the minimum of the following non-convex function \(x^{4} + x^{3} - 5x^{2}\) in 20 steps. You will experiment with two different momentum values. For this problem, the learning rate is fixed at 0.01.

You are provided with the optimize_and_plot() function that accepts as input the momentum parameter. This function will run 20 steps of the SGD optimizer and display the results.

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Introduction to Deep Learning with PyTorch

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# Try a first value for momentum
mom0 = ____
optimize_and_plot(momentum=mom0)

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Introduction to Deep Learning with PyTorch

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Self-driving cars, smartphones, search engines... Deep learning is now everywhere. Before you begin building complex models, you will become familiar with PyTorch, a deep learning framework. You will learn how to manipulate tensors, create PyTorch data structures, and build your first neural network in PyTorch with linear layers.

Exercise 1: Introduction to deep learning with PyTorch Exercise 2: Getting started with PyTorch tensors Exercise 3: Checking and adding tensors Exercise 4: Neural networks and layers Exercise 5: Linear layer network Exercise 6: Understanding weights Exercise 7: Hidden layers and parameters Exercise 8: Your first neural network Exercise 9: Stacking linear layers Exercise 10: Counting the number of parameters

To train a neural network in PyTorch, you will first need to understand additional components, such as activation and loss functions. You will then realize that training a network requires minimizing that loss function, which is done by calculating gradients. You will learn how to use these gradients to update your model's parameters.

Exercise 1: Discovering activation functions Exercise 2: Activate your understanding!Exercise 3: The sigmoid and softmax functions Exercise 4: Running a forward pass Exercise 5: Building a binary classifier in PyTorch Exercise 6: From regression to multi-class classification Exercise 7: Using loss functions to assess model predictions Exercise 8: Creating one-hot encoded labels Exercise 9: Calculating cross entropy loss Exercise 10: Using derivatives to update model parameters Exercise 11: Accessing the model parameters Exercise 12: Updating the weights manually Exercise 13: Using the PyTorch optimizer

Now that you've learned the key components of a neural network, you'll train one using a training loop. You'll explore potential issues like vanishing gradients and learn strategies to address them, such as alternative activation functions and tuning learning rate and momentum.

Exercise 1: A deeper dive into loading data Exercise 2: Using TensorDataset Exercise 3: Using DataLoader Exercise 4: Writing our first training loop Exercise 5: Using the MSELoss Exercise 6: Writing a training loop Exercise 7: ReLU activation functions Exercise 8: Implementing ReLU Exercise 9: Implementing leaky ReLU Exercise 10: Understanding activation functions Exercise 11: Learning rate and momentum Exercise 12: Experimenting with learning rate Exercise 13: Experimenting with momentum

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Training a deep learning model is an art, and to make sure our model is trained correctly, we need to keep track of certain metrics during training, such as the loss or the accuracy. We will learn how to calculate such metrics and how to reduce overfitting.

Exercise 1: Layer initialization and transfer learning Exercise 2: Fine-tuning process Exercise 3: Freeze layers of a model Exercise 4: Layer initialization Exercise 5: Evaluating model performance Exercise 6: Writing the evaluation loop Exercise 7: Calculating accuracy using torchmetrics Exercise 8: Fighting overfitting Exercise 9: Experimenting with dropout Exercise 10: Understanding overfitting Exercise 11: Improving model performance Exercise 12: Implementing random search Exercise 13: Wrap-up video