Deep Learning PyTorch Course, Deep Belief Neural Networks

Deep learning is a field of artificial intelligence that uses deep neural networks to learn patterns from data and make predictions. Today, we will introduce Deep Belief Networks (DBN) and explore how to implement them using PyTorch.

1. What is a Deep Belief Network?

A Deep Belief Network is an artificial neural network with multiple layers, characterized particularly by the following features:

• It primarily learns the latent structure of data through unsupervised learning.
• It is composed of several stacked Restricted Boltzmann Machines (RBM).
• Each RBM learns the probability distribution of the data and passes information to the upper layer.

DBN plays an important role in deep learning models. This model allows input data to be represented as probability distributions across multiple layers, enabling it to learn complex features.

1.1 Restricted Boltzmann Machine

A Restricted Boltzmann Machine (RBM) is a probabilistic model used in unsupervised learning, consisting of two layers:

• Visible Layer: The layer that receives input data.
• Hidden Layer: The layer that extracts features from the data.

An RBM has connections between the neurons in each layer, and these connections learn a probability distribution based on survival probability.

2. Implementing DBN with PyTorch

Now, let’s look at how to implement a Deep Belief Network using PyTorch. Here, we will construct a DBN using a simple MNIST digit recognition dataset.

2.1 Loading the Dataset

First, we load and preprocess the MNIST dataset.

import torch
from torchvision import datasets, transforms

# Define data transformations
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

# Download MNIST dataset
train_dataset = datasets.MNIST(root='./data', train=True, transform=transform, download=True)
test_dataset = datasets.MNIST(root='./data', train=False, transform=transform, download=True)

# Define data loaders
train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=64, shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=64, shuffle=False)

2.2 Implementing DBN

DBN can be built by stacking multiple RBMs. Below is an example of how to implement DBN using PyTorch.

class RBM:
    def __init__(self, n_visible, n_hidden):
        self.W = torch.randn(n_hidden, n_visible) * 0.1
        self.h_bias = torch.zeros(n_hidden)
        self.v_bias = torch.zeros(n_visible)

    def sample_h(self, v):
        h_prob = torch.sigmoid(torch.matmul(self.W, v.t()) + self.h_bias.unsqueeze(1))
        return h_prob, torch.bernoulli(h_prob)

    def sample_v(self, h):
        v_prob = torch.sigmoid(torch.matmul(h, self.W) + self.v_bias)
        return v_prob, torch.bernoulli(v_prob)

    def train(self, data, lr=0.1, k=1):
        for epoch in range(k):
            v0 = data
            h0, h0_sample = self.sample_h(v0)
            v1, v1_sample = self.sample_v(h0_sample)
            h1, _ = self.sample_h(v1_sample)

            # Update
            self.W += lr * (torch.matmul(h0_sample.t(), v0) - torch.matmul(h1.t(), v1_sample)) / data.size(0)
            self.h_bias += lr * (h0_sample.mean(0) - h1.mean(0))
            self.v_bias += lr * (v0.mean(0) - v1.mean(0))

2.3 Building DBN by Stacking Multiple RBMs

class DBN:
    def __init__(self, layer_sizes):
        self.RBMs = []
        for i in range(len(layer_sizes) - 1):
            self.RBMs.append(RBM(layer_sizes[i], layer_sizes[i + 1]))

    def fit(self, data, lr=0.1, k=1):
        for rbm in self.RBMs:
            rbm.train(data, lr=lr, k=k)
            data, _ = rbm.sample_h(data)

    def transform(self, data):
        for rbm in self.RBMs:
            _, data = rbm.sample_h(data)
        return data

2.4 Training the DBN Model

# Training DBN
dbn = DBN(layer_sizes=[784, 256, 128])
for batch_idx, (data, target) in enumerate(train_loader):
    dbn.fit(data.view(-1, 784), lr=0.1, k=10)  # Perform K-learning 10 times

2.5 Transforming and Evaluating on Test Dataset

test_data = next(iter(test_loader))[0].view(-1, 784)
transformed_data = dbn.transform(test_data)
print(transformed_data)
# Here, transformed_data can be used for subsequent models.

3. Conclusion

In this tutorial, we have explored the fundamental concepts and principles of Deep Belief Networks and how to implement them with PyTorch. DBNs are very useful models for learning the latent structure of complex data. Using PyTorch, these deep learning models can be effectively implemented.

For deeper learning and utilization, we recommend referring to the official PyTorch documentation and various examples. Welcome to the world of deep learning!