時間：2024-09-03 來源：合肥網hfw.cc 作者：hfw.cc 我要糾錯
FIT3181: Deep Learning (2024)
Deep Neural Networks
Due: 11:55pm Sunday, 8 September 2024 (Sunday)
Important note: This is an individual assignment. It contributes 25% to your final mark. Read the assignment instructions carefully.
What to submit
This assignment is to be completed individually and submitted to Moodle unit site. By the due date, you are required to submit one single zip file, named xxx_assignment01_solution.zip where xxx is your student ID, to the corresponding Assignment (Dropbox) in Moodle. You can use Google Colab to do Assigmnent 1 but you need to save it to an *.ipynb file to submit to the unit Moodle.
More importantly, if you use Google Colab to do this assignment, you need to first make a copy of this notebook on your Google drive .
For example, if your student ID is 12356, then gather all of your assignment solution to folder, create a zip file named 123456_assignment01_solution.zip and submit this file.
Within this zipfolder, you must submit the following files:
1. Assignment01_solution.ipynb: this is your Python notebook solution source file.
2. Assignment01_output.html: this is the output of your Python notebook solution exported in html format.
3. Any extra files or folder needed to complete your assignment (e.g., images used in your answers).
Since the notebook is quite big to load and work together, one recommended option is to split solution into three parts and work on them seperately. In that case, replace Assignment01_solution.ipynb by three notebooks: Assignment01_Part1_solution.ipynb, Assignment01_Part2_solution.ipynb and Assignment01_Part3_solution.ipynb
You can run your codes on Google Colab. In this case, you have to make a copy of your Google colab notebook including the traces and progresses of model training before submitting.
Part 1: Theory and Knowledge Questions [Total marks for this part: 30 points]
The first part of this assignment is to demonstrate your knowledge in deep learning that you have acquired from the lectures and tutorials materials. Most of the contents in this assignment are drawn from the lectures and tutorials from weeks 1 to 4. Going through these materials before attempting this part is highly recommended.
Question 1.1 Activation function plays an important role in modern Deep NNs. For each of the activation functions below, state its output range, find its derivative (show your steps), and plot the activation fuction and its derivative
(b) Gaussian Error Linear Unit (GELU): GELU(x) = xΦ(x) where Φ(x) is the probability cummulative function of the standard Gaussian distribution or Φ(x) = P (X ≤ x) where X ~ N (0, 1) . In addition, the GELU activation fuction (the link for the main paper (https://arxiv.org/pdf/1606.08415v5.pdf)) has
been widely used in the state-of-the-art Vision for Transformers (e.g., here is the link for the main ViT paper (https://arxiv.org/pdf/2010.11929v2.pdf)). [1.5 points]
Write your answer here. You can add more cells if needed.
Question 1.2: Assume that we feed a data point x with a ground-truth label y = 2 to the feed-forward neural network with the ReLU activation function as shown in the following figure
(a) What is the numerical value of the latent presentation h1 (x)? [1 point]
(b) What is the numerical value of the latent presentation h2 (x)? [1 point]
(c) What is the numerical value of the logith3 (x)? [1 point]
(d) What is the corresonding prediction probabilities p(x)? [1 point]
(e) What is the predicted label y(^)? Is it a correct and an incorect prediction? Remind that y = 2. [1 point]
(f) What is the cross-entropy loss caused by the feed-forward neural network at (x, y)? Remind that y = 2. [1 point]
(g) Why is the cross-entropy loss caused by the feed-forward neural network at (x, y) (i.e., CE(1y, p(x))) always non-negative? When does this CE(1y, p(x)) loss get the value 0? Note that you need to answer this question for a general pair (x, y) and a general feed-forward neural network with, for example M = 4 classes? [1 point]
You must show both formulas and numerical results for earning full mark. Although it is optional, it is great if you show your PyTorch code for your computation.
Question 1.3:
For Question 1.3, you have two options:
· (1) perform the forward, backward propagation, and SGD update for one mini-batch (10 points), or
· (2) manually implement a feed-forward neural network that can work on real tabular datasets (20 points).
You can choose either (1) or (2) to proceed.
Option 1 [Total marks for this option: 10 points]
Assume that we are constructing a multilayered feed-forward neural network for a classification problem with three classes where the model parameters will be generated randomly using your student ID. The architecture of this network is 3(Input) → 5(ELU) → 3(output) as shown in the following figure. Note that the ELU has the same formula as the one in Q1.1.
We feed a batch X with the labels Y as shown in the figure. Answer the following questions.
You need to show both formulas, numerical results, and your PyTorch code for your computation for earning full marks.
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<torch._C.Generator at 0x7dc439f98810>
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#Code to generate random matrices and biases for W1, b1, W2, b2 |
Forward propagation
(a) What is the value of h(¯)1 (x) (the pre-activation values of h1 )? [0.5 point]
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(b) What is the value of h1 (x)? [0.5 point]
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(c) What is the predicted value y(^)? [0.5 point]
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(d) Suppose that we use the cross-entropy (CE) loss. What is the value of the CE loss l incurred by the mini-batch? [0.5 point]
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Backward propagation
(e) What are the derivatives , , and ? [3 points]
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(f) What are the derivatives , , , and ? [3 points]
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SGD update
(g) Assume that we use SGD with learning rate η = 0.01 to update the model parameters. What are the values of W 2 , b2 and W 1 , b1 after updating? [2 points]
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Option 2 [Total marks for this option: 20 points]
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import torch from torch.utils.data import DataLoader from torchvision import datasets, transforms |
In Option 2, you need to implement a feed-forward NN manually using PyTorch and auto-differentiation of PyTorch. We then manually train the model on the MNIST dataset.
We first download the MNIST dataset and preprocess it.
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Each data point has dimension [28,28] . We need to flatten it to a vector to input to our FFN.
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train_dataset.data = train_data.data.view(-1, 28*28) test_dataset.data = test_data.data.view(-1, 28*28) train_data, train_labels = train_dataset.data, train_dataset.targets test_data, test_labels = test_dataset.data, test_dataset.targets print(train_data.shape, train_labels.shape) print(test_data.shape, test_labels.shape) |
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train_loader = DataLoader(dataset=train_dataset, batch_size=64, shuffle=True) test_loader = DataLoader(dataset=test_dataset, batch_size=64, shuffle=False) |
Develop the feed-forward neural networks
(a) You need to develop the class MyLinear with the following skeleton. You need to declare the weight matrix and bias of this linear layer. [3 points]
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(b) You need to develop the class MyFFN with the following skeleton [7 points]
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myFFN = MyFFN(input_size = 28*28, num_classes = 10, hidden_sizes = [100, 100], act = torch.nn.ReLU) myFFN.create_FFN() print(myFFN) |
(c) Write the code to evaluate the accuracy of the current myFFN model on a data loader (e.g., train_loader or test_loader). [2.5 points]
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(c) Write the code to evaluate the loss of the current myFFN model on a data loader (e.g., train_loader or test_loader). [2.5 points]
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def compute_loss(model, data_loader): """ This function computes the loss of the model on a data loader """ #Your code here |
Train on the MNIST data with 50 epochs using updateSGD .
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(d) Implement the function updateSGDMomentum in the class and train the model with this optimizer in 50 epochs. You can update the corresponding function in the MyFNN class. [2.5 points]
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(e) Implement the function updateAdagrad in the class and train the model with this optimizer in 50 epochs. You can update the corresponding function in the MyFNN class. [2.5 points]
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Part 2: Deep Neural Networks (DNN) [Total marks for this part: 25 points]
The second part of this assignment is to demonstrate your basis knowledge in deep learning that you have acquired from the lectures and tutorials materials. Most of the contents in this assignment are drawn from the tutorials covered from weeks 1 to 2. Going through these materials before attempting this assignment is highly recommended.
In the second part of this assignment, you are going to work with the FashionMNIST dataset for image recognition task. It has the exact same format as MNIST (70,000 grayscale images of 28 × 28 pixels each with 10 classes), but the images represent fashion items rather than handwritten digits, so each class is more diverse, and the problem is significantly more challenging than MNIST.
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import torch from torch.utils.data import DataLoader from torchvision import datasets, transforms torch.manual_seed(1234) |
Load the Fashion MNIST using torchvision
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torch.Size([60000, 28, 28]) torch.Size([60000]) torch.Size([10000, 28, 28]) torch.Size([10000]) torch.Size([60000, 784]) torch.Size([60000])
torch.Size([10000, 784]) torch.Size([10000])
Number of training samples: 18827 Number of training samples: 16944 Number of validation samples: 1883
Question 2.1: Write the code to visualize a mini-batch in train_loader including its images and labels. [5 points]
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####Question 2.2: Write the code for the feed-forward neural net using PyTorch [5 points]
We now develop a feed-forward neural network with the architecture 784 → 40(ReLU) → 30(ReLU) → 10(softmax) . You can choose your own way to implement your network and an optimizer of interest. You should train model in 50 epochs and evaluate the trained model on the test set.
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Question 2.3: Tuning hyper-parameters with grid search [5 points]
Assume that you need to tune the number of neurons on the first and second hidden layers n1 ∈ {20, 40} , n2 ∈ {20, 40} and the used activation function act ∈ {sigmoid, tanh, relu} . The network has the architecture pattern 784 → n1 (act) → n2 (act) → 10(softmax) where n1 , n2 , and act are in their
grides. Write the code to tune the hyper-parameters n1 , n2 , and act. Note that you can freely choose the optimizer and learning rate of interest for this task.
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