full_rank_test.py

import torch
import torch.nn as nn
import torchvision
import torchvision.transforms as transforms

# Check Device configuration
device = torch.device('cuda:1' if torch.cuda.is_available() else 'cpu')

# Define Hyper-parameters 
input_size = 784
hidden_size = 2000
num_classes = 10
num_epochs = 5
batch_size = 100
learning_rate = 0.001

# MNIST dataset 
train_dataset = torchvision.datasets.MNIST(root='./data', 
                                           train=True, 
                                           transform=transforms.ToTensor(),  
                                           download=True)

test_dataset = torchvision.datasets.MNIST(root='./data', 
                                          train=False, 
                                          transform=transforms.ToTensor())

# Data loader
train_loader = torch.utils.data.DataLoader(dataset=train_dataset, 
                                           batch_size=batch_size, 
                                           shuffle=True)

test_loader = torch.utils.data.DataLoader(dataset=test_dataset, 
                                          batch_size=batch_size, 
                                          shuffle=False)

# Fully connected neural network
class NeuralNet(nn.Module):
    def __init__(self, input_size, hidden_size, num_classes):
        super(NeuralNet, self).__init__()
        self.fc1 = nn.Linear(input_size, hidden_size) 
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(hidden_size, num_classes)  
    
    def forward(self, x):
        out = self.fc1(x)
        out = self.relu(out)
        out = self.fc2(out)
        return out

model = NeuralNet(input_size, hidden_size, num_classes).to(device)

# Loss and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)  

# Train the model
total_step = len(train_loader)
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):  
        # Move tensors to the configured device
        images = images.reshape(-1, 28*28).to(device)
        labels = labels.to(device)
        
        # Forward pass
        outputs = model(images)
        loss = criterion(outputs, labels)
        
        # Backprpagation and optimization
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        
        if (i+1) % 100 == 0:
            print ('Epoch [{}/{}], Step [{}/{}], Loss: {:.4f}' 
                   .format(epoch+1, num_epochs, i+1, total_step, loss.item()))

# Test the model
# In the test phase, don't need to compute gradients (for memory efficiency)
with torch.no_grad():
    correct = 0
    total = 0
    for images, labels in test_loader:
        images = images.reshape(-1, 28*28).to(device)
        labels = labels.to(device)
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()

    print('Accuracy of the network on the 10000 test images: {} %'.format(100 * correct / total))

# Save the model checkpoint
torch.save(model.state_dict(), 'fcn_mnist_model.ckpt')

# re-run some code to test the hypothesis that activations are full rank even if the original matrix
# is not!

# Define Hyper-parameters 
input_size = 784
hidden_size = 2000
num_classes = 10
num_epochs = 5
batch_size = 1
learning_rate = 0.001


train_dataset = torchvision.datasets.MNIST(root='./data', 
                                           train=True, 
                                           transform=transforms.ToTensor(),  
                                           download=True)

# Data loader
train_loader = torch.utils.data.DataLoader(dataset=train_dataset, 
                                           batch_size=batch_size, 
                                           shuffle=True)


class NeuralNet(nn.Module):
    def __init__(self, input_size, hidden_size, num_classes):
        super(NeuralNet, self).__init__()
        self.fc1 = nn.Linear(input_size, hidden_size) 
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(hidden_size, num_classes)  
    
    def forward(self, x):
        out = self.fc1(x)
        out = self.relu(out)
        out = self.fc2(out)
        return out

model = NeuralNet(input_size, hidden_size, num_classes).to(device)

ckpt = torch.load("fcn_mnist_model.ckpt", map_location=device)
model.load_state_dict(ckpt)


X = []
for i, (images, labels) in enumerate(train_loader):
	images = images.reshape(-1, 28*28).to(device)
	X.append(images)
	if i == 999:
		break
X = torch.cat(X)

x_mat = copy.deepcopy(X)

print("Rank of X: {}".format(torch.matrix_rank(x_mat)))

weights = list(model.parameters())
w1 = weights[0]

x1 = model.relu(model.fc1(x_mat))

print("Rank of X1: {}".format(torch.matrix_rank(x1)))