Description
You are trying to minimize the L2 divergence (as defined in the class) of the RELU function 𝑦 = max (0, 0.5𝑤) with respect to parameter 𝑤, when the target output is 1.0. Note that this corresponds to optimizing the RELU function 𝑦 = max (0, 𝑤𝑥) given only the training input (𝑥, 𝑑(𝑥)) = (0.5, 1). You are using momentum updates. Your current estimate (in the k-th step) is 𝑤(1) = 1. The last step you took was Δ𝑤(1) = 0.5. Using the notation from class, you use 𝛽 = 0.9 and 𝜂 = 0.1. What is the value of 𝑤(167) when using momentum update? Truncate the answer to three decimals (do not round up).
Question 2
You are trying to minimize the cross-entropy loss of the logistic function 𝑦 = 1/ (1 + exp (0.5𝑤)) with respect to parameter 𝑤, when the target output is 1.0. Note that this corresponds to optimizing the logistic function 𝑦 = 1/ (1 + exp (−𝑤𝑥)), given only the training input (𝑥, 𝑑(𝑥)) = (−0.5, 1). You are using momentum updates. Your current estimate (in the k-th step) is 𝑤(1) = 0. The last step you took was Δ𝑤(1) = 0.5. Using the notation from class, you use 𝛽 = 0.9 and 𝜂 = 0.1. What is the value of 𝑤(167) when using momentum update? Truncate the answer to three decimals (do not round up).
Question 3 – Implement 1D convolutional layer
In this section, you need to implement convolutional neural networks using the NumPy library only
Implement the Conv1D class in layers.py. The class Conv1D has four arguments: in channel, out channel, kernel size and stride. We do not consider other arguments such as padding.
The detail meaning of the arguments has been discussed in class and you can also find them in PyTorch document: https://pytorch.org/docs/stable/ nn.html#torch.nn.Conv1d.
Implement the Conv1D class so that it has similar usage and functionality to torch.nn.Conv1d. There are three parts to be implemented.
Forward
Finish the returned value for the forward part.
The input x is the input of the convolutional layer and the shape of x is (batch size, in channel, in width). The return value is the output of the convolutional layer and the shape is (batch size, out channel, out width). Note that in width is an arbitrary possitive integer and out width is determined by in width, kernel size and stride.
Backward
You will write the code of the backward method. Its argument is the backpropagated delta, i.e. the derivative of the loss w.r.t the output of the current layer (dW and db)
The input delta is the derivative of the loss with respect to the convolutional layer output. It has the same shape as the convolutional layer output. self.dW and self.db represent the unaveraged gradients of the loss w.r.t self.W and self.b. Their shapes are the same as the weight self.W and the bias self.b. We have already initialized them for you.
dx: Finish the returned value for the backward part. It is the derivative of the loss with respect to the input of the convolutional layer and has the same shape as the input.
Test: To test your implementation, we will compare the results of the three parts with Pytorch function torch.nn.Conv1d. Details can be found in function test cnn correctness once in the local grader.py file. Here are some brief codes to show the testing.
| import torch import torch.nn as nn import numpy as np
from torch.autograd import Variable from layers import Conv1D ## initialize your layer and PyTorch layer net1 = Conv1D(8, 12, 3, 2) ## Your own convolution net2 = torch.nn.Conv1d(8, 12, 3, 2) ## generated by torch ## initialize the inputs x1 = np.random.rand(3, 8, 20) x2 = Variable(torch.tensor(x1),requires_grad=True) ## Copy the parameters from the Conv1D class to PyTorch layer net2.weight = nn.Parameter(torch.tensor(net1.W)) net2.bias = nn.Parameter(torch.tensor(net1.b)) ## Your forward and backward y1 = net1(x1) b, c, w = y1.shape delta = np.random.randn(b,c,w) dx = net1.backward(delta) ## PyTorch forward and backward y2 = net2(x2) delta = torch.tensor(delta) y2.backward(delta) ## Compare def compare(x,y): y = y.detach().numpy() print(abs(x).max()) return |
| compare(y1, y2) compare(dx, x2.grad)
compare(net1.dW, net2.weight.grad) compare(net1.db, net2.bias.grad) |
Question 4 Image Classification (60 points) – Competition
In this exercise, your task is to create a Convolutional Neural Network (CNN) based image classifier for the CIFAR-10 dataset of images.
Feel free to experiment with different architectures, hyper-parameters, and training procedures to make yourself familiar with training and tuning CNN models. Once you have the model implemented and working, start playing around with the number of layers, their sizes, the activation function, using dropout, stride, etc… whatever you would like!
The dataset you will be using is the CIFAR-10 Dataset which consists of a collection of 60,000 images of 32×32 pixels with three 8-bit RGB channels. 50,000 images for training nd 10,000 images for testing. The training data is devided into 5 batchs. Here is an example to read feature and label from each batch:
| def load_cfar10_batch(cifar10_dataset_folder_path, batch_id):
with open(cifar10_dataset_folder_path + ‘/data_batch_’ + str(batch_id), mode=’rb’) as file: # note the encoding type is ‘latin1’ batch = pickle.load(file, encoding=’latin1′)
features = batch[‘data’].reshape((len(batch[‘data’]), 3, 32, 32)).transpose(0, 2, 3, 1) labels = batch[‘labels’] return features, labels |
The label data is just a list of 10,000 numbers ranging from 0 to 9, which corresponds to each of the 10 classes in CIFAR-10. The classes are: [‘airplane’, ‘automobile’, ‘bird’, ‘cat’,
‘deer’, ‘dog’, ‘frog’, ‘horse’, ‘ship’, ‘truck’]
Before process, you may need to convert the label into one-hot-vector
Detail about CIFAR 10: https://www.cs.toronto.edu/~kriz/cifar.html
An input to your system is an image and you have to predict the ID of the image. The true image ID will be present in the training data and so the network will be doing 10-way classification to get the prediction. You are provided with the train set and have the option to split it into a training and validation set. With the validation set, you can fine-tune the model based on the accuracy you get. Loading Dataset
import torch import torchvision
from torchvision.datasets import CIFAR10
TRAIN_TRANSFORMS = torchvision.transforms.ToTensor()
TEST_TRANSFORMS = TRAIN_TRANSFORMS
BATCH_SIZE = 16
### DO NOT MODIFY ANY CODE STARTING HERE ###
cifar_train = CIFAR10(‘./data’, download=True, train=True, transform=TRAIN_TRANSFORMS) cifar_test = CIFAR10(‘./data’, download=True, train=False,
transform=TEST_TRANSFORMS) train_dataloader = torch.utils.data.DataLoader(cifar_train, batch_size=BATCH_SIZE, shuffle=True) test_dataloader = torch.utils.data.DataLoader(cifar_test, del cifar_train, cifar_test
It’s very important to note that, for classification, the train, validation, and test contain the same set of images. That means your network cannot classify images unless it has seen it before, and the dataset is set up that way. In other words, the exact images are not the same between the train, validation, and test set but rather they are all sampled from the same distribution.
You will have one folder that will download after you run the provided script. Further, two data loaders will be generated:
Repository: https://github.com/pytorch/tutorials
Documentation: https://pytorch.org/docs/stable/index.html
Write up for your own reference describing what model architecture, loss function, hyperparameters, any other interesting detail led to your best result for the above. Such a writeup should limit the content to one page.
Output from your network is a text file (.txt) which the following format:
Image ID (name) Predicted Label
