code: ## TODO: define the convolutional neural network architecture
  
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  # can use the below import should you choose to initialize the weights of your Net
  import torch.nn.init as I
  
  
  class Net(nn.Module):
  
      def __init__(self):
          super(Net, self).__init__()
          
          ## TODO: Define all the layers of this CNN, the only requirements are:
          ## 1. This network takes in a square (same width and height), grayscale image as input
          ## 2. It ends with a linear layer that represents the keypoints
          ## it's suggested that you make this last layer output 136 values, 2 for each of the 68 keypoint (x, y) pairs
          
          # As an example, you've been given a convolutional layer, which you may (but don't have to) change:
          # 1 input image channel (grayscale), 32 output channels/feature maps, 5x5 square convolution kernel
          self.conv1 = nn.Conv2d(1, 32, 5, padding=2)
          self.pool1 = nn.MaxPool2d(4, 4)
          
          self.conv2 = nn.Conv2d(32, 64, 3, padding=1)
          self.pool2 = nn.MaxPool2d(2, 2)
          
          self.conv3 = nn.Conv2d(64, 128, 1)
          self.pool3 = nn.MaxPool2d(2, 2)
          
  #         self.conv4 = nn.Conv2d(128, 256, 1)
  #         self.pool4 = nn.MaxPool2d(2, 2)
          
          #calculate input size 32 * 52 * 52
          fc1_input_size = 128 * 14 * 14
          self.lin1 = nn.Linear(fc1_input_size, 1000)
          self.lin2 = nn.Linear(1000, (68 * 2))
  
          
          ## Note that among the layers to add, consider including:
          # maxpooling layers, multiple conv layers, fully-connected layers, and other layers (such as dropout or batch normalization) to avoid overfitting
          
  
          
      def forward(self, x):
          ## TODO: Define the feedforward behavior of this model
          ## x is the input image and, as an example, here you may choose to include a pool/conv step:
  #         x = self.pool1(F.relu(self.conv1(x)))
  
          drop1 = nn.Dropout(0.1)
          drop2 = nn.Dropout(0.2)
          drop3 = nn.Dropout(0.3)
          drop4 = nn.Dropout(0.4)
          
          x = drop1(self.pool1(F.relu(self.conv1(x))))
          x = drop2(self.pool2(F.relu(self.conv2(x))))
          x = drop3(self.pool3(F.relu(self.conv3(x))))
          
          x = x.view(x.size(0), -1)
          x = drop4(F.relu(self.lin1(x)))
          x = self.lin2(x)
               
          # a modified x, having gone through all the layers of your model, should be returned
          return x
  
apis: torch.nn.Linear torch.nn.MaxPool2d torch.nn.Conv2d torch.nn.Dropout