```python
from torch.autograd import Variable 

N_PARAMS = {'affine': 6, 
            'translation':2, 
            'rotation':1, 
            'scale':2, 
            'shear':2, 
            'rotation_scale':3,
            'translation_scale':4,
            'rotation_translation':3,
            'rotation_translation_scale':5}

# Spatial transformer network forward function
def stn(x, theta, mode='affine'):
        if mode == 'affine':
            theta1 = theta.view(-1, 2, 3)
        else: 
            theta1 = Variable( torch.zeros([x.size(0), 2, 3], dtype=torch.float32, device=x.get_device()), requires_grad=True)
            theta1 = theta1 + 0
            theta1[:,0,0] = 1.0
            theta1[:,1,1] = 1.0
            if mode == 'translation':
                theta1[:,0,2] = theta[:,0]
                theta1[:,1,2] = theta[:,1]
            elif mode == 'rotation':
                angle = theta[:,0]
                theta1[:,0,0] = torch.cos(angle)
                theta1[:,0,1] = -torch.sin(angle)
                theta1[:,1,0] = torch.sin(angle)
                theta1[:,1,1] = torch.cos(angle)
            elif mode == 'scale':
                theta1[:,0,0] = theta[:,0]
                theta1[:,1,1] = theta[:,1]
            elif mode == 'shear':
                theta1[:,0,1] = theta[:,0]
                theta1[:,1,0] = theta[:,1]
            elif mode == 'rotation_scale':
                angle = theta[:,0]
                theta1[:,0,0] = torch.cos(angle) * theta[:,1]
                theta1[:,0,1] = -torch.sin(angle)
                theta1[:,1,0] = torch.sin(angle)
                theta1[:,1,1] = torch.cos(angle) * theta[:,2]
            elif mode == 'translation_scale':
                theta1[:,0,2] = theta[:,0]
                theta1[:,1,2] = theta[:,1]
                theta1[:,0,0] = theta[:,2]
                theta1[:,1,1] = theta[:,3]
            elif mode == 'rotation_translation':
                angle = theta[:,0]
                theta1[:,0,0] = torch.cos(angle)
                theta1[:,0,1] = -torch.sin(angle)
                theta1[:,1,0] = torch.sin(angle)
                theta1[:,1,1] = torch.cos(angle)
                theta1[:,0,2] = theta[:,1]
                theta1[:,1,2] = theta[:,2]
            elif mode == 'rotation_translation_scale':
                angle = theta[:,0]
                theta1[:,0,0] = torch.cos(angle) * theta[:,3]
                theta1[:,0,1] = -torch.sin(angle)
                theta1[:,1,0] = torch.sin(angle)
                theta1[:,1,1] = torch.cos(angle) * theta[:,4]
                theta1[:,0,2] = theta[:,1]
                theta1[:,1,2] = theta[:,2]
        grid = F.affine_grid(theta1, x.size())
        x = F.grid_sample(x, grid)
        return x
    
class Net(nn.Module):
    def __init__(self, stn_mode='affine'):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)
        self.stn_mode = stn_mode
        self.stn_n_params = N_PARAMS[stn_mode]

        # Spatial transformer localization-network
        self.localization = nn.Sequential(
            nn.Conv2d(1, 8, kernel_size=7),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True),
            nn.Conv2d(8, 10, kernel_size=5),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True)
        )

        # Regressor for the 3 * 2 affine matrix
        self.fc_loc = nn.Sequential(
            nn.Linear(10 * 3 * 3, 32),
            nn.ReLU(True),
            nn.Linear(32, self.stn_n_params)
        )

        # Initialize the weights/bias with identity transformation
        self.fc_loc[2].weight.data.fill_(0)
        self.fc_loc[2].weight.data.zero_()
        if self.stn_mode == 'affine': 
            self.fc_loc[2].bias.data.copy_(torch.tensor([1, 0, 0, 0, 1, 0], dtype=torch.float))
        elif self.stn_mode in ['translation','shear']: 
            self.fc_loc[2].bias.data.copy_(torch.tensor([0,0], dtype=torch.float))
        elif self.stn_mode == 'scale':
            self.fc_loc[2].bias.data.copy_(torch.tensor([1,1], dtype=torch.float))
        elif self.stn_mode == 'rotation': 
            self.fc_loc[2].bias.data.copy_(torch.tensor([0], dtype=torch.float))
        elif self.stn_mode == 'rotation_scale':
            self.fc_loc[2].bias.data.copy_(torch.tensor([0,1,1], dtype=torch.float))
        elif self.stn_mode == 'translation_scale':
            self.fc_loc[2].bias.data.copy_(torch.tensor([0,0,1,1], dtype=torch.float))
        elif self.stn_mode == 'rotation_translation':
            self.fc_loc[2].bias.data.copy_(torch.tensor([0,0,0], dtype=torch.float))
        elif self.stn_mode == 'rotation_translation_scale':
            self.fc_loc[2].bias.data.copy_(torch.tensor([0,0,0,1,1], dtype=torch.float))

    def stn(self, x):
        x = stn( x, self.theta(x), mode=self.stn_mode)
        return x 
    
    def theta(self, x):
        xs = self.localization(x) 
        xs = xs.view(-1, 10 * 3 * 3)
        theta = self.fc_loc(xs)
        return theta 

    def forward(self, x):
        # transform the input
        x = self.stn(x)
        # Perform the usual forward pass
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x)