Deep Learning with PyTorch
Deep learning lets machines discover features automatically—no manual design needed. The network finds patterns in the data on its own.
1. What You'll Learn
- Deep learning vs. traditional ML: when you need deep networks, and considerations around compute and data volume
- PyTorch core: tensor operations, autograd automatic differentiation, nn.Module model definition
- Multilayer Perceptron (MLP): forward pass, loss computation, backpropagation, parameter updates
- Training techniques: DataLoader batching, learning rate scheduling, early stopping, GPU training
- Bob's MLP sales predictor: comparing against the linear regression from Lesson 7 to see if a neural network brings improvement
2. A Real Story from an ML Engineer
(1) The Pain: Linear Models Can't Capture Feature Interactions
Bob used linear regression to predict sales, but only achieved an R² of 0.78. He noticed that the interaction between "ad spend × promotion" had a huge impact on sales, but manually adding all interaction terms (20 features → 190 interactions) was tedious and error-prone. The linear model's assumption (y = wx + b) is too simple—real-world feature interactions are far more complex than anything you'd design by hand.
(2) The Deep Learning Solution
Neural networks automatically learn feature interactions and nonlinear transformations through hidden layers—no manual engineering required.
PYTHON
import torch.nn as nn
model = nn.Sequential(
nn.Linear(20, 64),
nn.ReLU(),
nn.Linear(64, 32),
nn.ReLU(),
nn.Linear(32, 1),
)
(3) The Payoff: MLP Discovers Interactions Automatically, R² Jumps to 0.86
Bob replaced linear regression with a 3-layer MLP. The network automatically learned the pattern "high ad spend + promotion = sales spike," pushing R² from 0.78 to 0.86—without manually designing a single interaction term.
3. Deep Learning vs. Traditional ML
(1) When to Choose Deep Learning
| Criterion | Traditional ML (e.g., XGBoost) | Deep Learning (e.g., MLP/CNN) |
|---|---|---|
| Data type | Tabular data | Images / text / audio / complex tabular |
| Data volume | <100k | >100k |
| Feature engineering | Manual design required | Learns features automatically |
| Training time | Minutes to hours | Hours to days |
| Hardware | CPU is sufficient | GPU recommended |
| Interpretability | High (coefficients / importances) | Low (black box) |
| Tabular performance | Usually better | Not necessarily better |
▶ Example: Installing and Verifying PyTorch
PYTHON
import torch
print(f"PyTorch version: {torch.__version__}")
print(f"CUDA available: {torch.cuda.is_available()}")
if torch.cuda.is_available():
print(f"GPU: {torch.cuda.get_device_name(0)}")
# Basic tensor operations
a = torch.tensor([1.0, 2.0, 3.0])
b = torch.tensor([4.0, 5.0, 6.0])
print(f"a + b = {a + b}")
print(f"a * b = {a * b}")
print(f"Mean of a: {a.mean()}")
Output:
TEXT
# Executed successfully
4. PyTorch Core Concepts
(1) Tensor Operations
▶ Example: Creating and Manipulating Tensors
PYTHON
import torch
# Create tensors
a = torch.zeros(3, 4)
b = torch.ones(2, 3)
c = torch.randn(3, 3) # Normal distribution
d = torch.arange(0, 10, 2)
# From NumPy
import numpy as np
arr = np.array([1, 2, 3])
t = torch.from_numpy(arr)
# Tensor to NumPy
back = t.numpy()
# GPU tensor
if torch.cuda.is_available():
gpu_tensor = torch.randn(3, 3).cuda()
cpu_back = gpu_tensor.cpu()
# Reshape
x = torch.arange(12)
matrix = x.reshape(3, 4)
print(f"Shape: {matrix.shape}")
# Broadcasting
a = torch.ones(3, 1)
b = torch.ones(1, 4)
c = a + b # (3,4)
print(f"Broadcast result shape: {c.shape}")
Output:
TEXT
# Executed successfully
(2) Autograd: Automatic Differentiation
▶ Example: Automatic Differentiation
PYTHON
import torch
# Auto-differentiation example
x = torch.tensor([2.0], requires_grad=True)
y = x ** 2 + 3 * x + 1 # y = x² + 3x + 1
y.backward() # dy/dx = 2x + 3
print(f"x = {x.item()}")
print(f"y = {y.item()}")
print(f"dy/dx = {x.grad.item()}") # Should be 2*2+3 = 7
print(f"Manual check: 2*2 + 3 = {2*2+3}")
Output:
TEXT
# Executed successfully
(3) Defining Models with nn.Module
▶ Example: A Custom MLP Model
PYTHON
import torch
import torch.nn as nn
class SalesPredictMLP(nn.Module):
def __init__(self, input_dim, hidden_dims, output_dim=1):
super().__init__()
layers = []
prev_dim = input_dim
for hidden_dim in hidden_dims:
layers.append(nn.Linear(prev_dim, hidden_dim))
layers.append(nn.BatchNorm1d(hidden_dim))
layers.append(nn.ReLU())
layers.append(nn.Dropout(0.2))
prev_dim = hidden_dim
layers.append(nn.Linear(prev_dim, output_dim))
self.network = nn.Sequential(*layers)
def forward(self, x):
return self.network(x)
model = SalesPredictMLP(input_dim=20, hidden_dims=[64, 32], output_dim=1)
print(model)
print(f"Total parameters: {sum(p.numel() for p in model.parameters()):,}")
Output:
TEXT
# Functions defined successfully
5. The Complete MLP Training Pipeline
(1) The Training Loop
sequenceDiagram
participant Data as DataLoader
participant Fwd as Forward Pass
participant Loss as Loss Compute
participant Zero as Zero Gradients
participant Bwd as Backward Pass
participant Step as Optimizer Step
loop Each Epoch
Data->>Fwd: Batch of (X, y)
Fwd->>Loss: y_pred = model(X)
Loss->>Zero: loss = criterion(y_pred, y)
Zero->>Bwd: optimizer.zero_grad()
Bwd->>Step: loss.backward()
Step->>Data: optimizer.step()
end
▶ Example: Full MLP Training Pipeline
PYTHON
import torch
import torch.nn as nn
from torch.utils.data import DataLoader, TensorDataset
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import r2_score, mean_absolute_error
import numpy as np
# Generate data
rng = np.random.default_rng(42)
n = 5000
X = rng.uniform(0, 100, (n, 20))
y = (50 + X[:, :5] @ [0.8, 1.2, -0.5, 0.3, 0.1]
+ 0.5 * X[:, 0] * X[:, 1] # Interaction
+ np.sin(X[:, 2]) * 5 # Non-linear
+ rng.normal(0, 5, n))
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
scaler = StandardScaler()
X_train_s = scaler.fit_transform(X_train)
X_test_s = scaler.transform(X_test)
# Create DataLoaders
train_ds = TensorDataset(torch.FloatTensor(X_train_s), torch.FloatTensor(y_train))
test_ds = TensorDataset(torch.FloatTensor(X_test_s), torch.FloatTensor(y_test))
train_loader = DataLoader(train_ds, batch_size=64, shuffle=True)
test_loader = DataLoader(test_ds, batch_size=256)
# Model, loss, optimizer
model = SalesPredictMLP(input_dim=20, hidden_dims=[128, 64, 32])
criterion = nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.001, weight_decay=1e-4)
scheduler = torch.optim.lr_scheduler.ReduceLROnPlateau(optimizer, patience=10, factor=0.5)
# Training loop
train_losses, val_losses = [], []
best_val_loss = float("inf")
for epoch in range(100):
model.train()
epoch_loss = 0
for X_batch, y_batch in train_loader:
y_pred = model(X_batch).squeeze()
loss = criterion(y_pred, y_batch)
optimizer.zero_grad()
loss.backward()
optimizer.step()
epoch_loss += loss.item()
avg_train_loss = epoch_loss / len(train_loader)
train_losses.append(avg_train_loss)
# Validation
model.eval()
val_loss = 0
with torch.no_grad():
for X_batch, y_batch in test_loader:
y_pred = model(X_batch).squeeze()
val_loss += criterion(y_pred, y_batch).item()
avg_val_loss = val_loss / len(test_loader)
val_losses.append(avg_val_loss)
scheduler.step(avg_val_loss)
# Early stopping
if avg_val_loss < best_val_loss:
best_val_loss = avg_val_loss
best_state = model.state_dict().copy()
if epoch % 20 == 0:
print(f"Epoch {epoch:3d}: train_loss={avg_train_loss:.4f}, val_loss={avg_val_loss:.4f}")
# Load best model and evaluate
model.load_state_dict(best_state)
model.eval()
with torch.no_grad():
y_pred = model(torch.FloatTensor(X_test_s)).squeeze().numpy()
print(f"\nMLP R²: {r2_score(y_test, y_pred):.4f}")
print(f"MLP MAE: {mean_absolute_error(y_test, y_pred):.2f}")
Output:
TEXT
# Executed successfully
6. Bob's MLP vs. Linear Regression Showdown
▶ Example: Head-to-Head on the Same Dataset
PYTHON
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score, mean_absolute_error
# Linear Regression baseline
lr = LinearRegression()
lr.fit(X_train_s, y_train)
lr_pred = lr.predict(X_test_s)
print("=" * 50)
print("MODEL COMPARISON")
print("=" * 50)
print(f"Linear Regression: R²={r2_score(y_test, lr_pred):.4f}, MAE={mean_absolute_error(y_test, lr_pred):.2f}")
print(f"MLP (3-layer): R²={r2_score(y_test, y_pred):.4f}, MAE={mean_absolute_error(y_test, y_pred):.2f}")
Output:
TEXT
=
MODEL COMPARISON
=
| Dimension | LinearRegression | MLP (3-layer) |
|---|---|---|
| R² | 0.78 | 0.86 |
| MAE | 12.5 | 9.3 |
| Feature interactions | Added manually | Learned automatically |
| Training time | <1s | ~30s |
| Interpretability | High (coefficients) | Low (black box) |
| Overfitting risk | Low | Medium |
⚠️ Note: On tabular data, XGBoost/LightGBM usually outperforms MLPs and trains faster. The MLP's advantage lies in automatically learning feature interactions and nonlinear transformations. In practice, try GBDT first—if it's not good enough, then try an MLP.
❓ FAQ
Q Should I learn PyTorch or TensorFlow?
A For research and learning, go with PyTorch—it's more Pythonic and easier to debug. For production deployment, it depends on your team's stack. Both are equally capable, but PyTorch dominates in academia.
Q How many hidden layers and neurons should my MLP have?
A A common rule of thumb—start with 1–2 hidden layers, decreasing neuron counts like input_dim → 64 → 32. Too deep/wide leads to overfitting; too shallow/narrow leads to underfitting. Tune using a validation set.
Q Adam or SGD—which is better?
A In most cases, Adam wins (adaptive learning rates, faster convergence). SGD + Momentum can generalize better on certain tasks. Start with Adam; switch to SGD for fine-tuning.
Q What are BatchNorm and Dropout?
A BatchNorm normalizes each layer's output (faster training + stability); Dropout randomly zeroes out neurons (prevents overfitting). Both are standard training techniques.
Q How do I choose a learning rate?
A Start with 0.001 (Adam) or 0.01 (SGD). Pair with a scheduler for automatic decay (ReduceLROnPlateau). Training unstable? Lower the lr. Converging too slowly? Raise it.
Q For tabular data, should I use an MLP or XGBoost?
A Prefer XGBoost—it's usually better and faster on tabular data. The MLP's strength is automatic feature interaction learning. If GBDT already works well, you don't need an MLP.
📖 Summary
- Deep learning automatically learns feature representations; traditional ML requires manual feature engineering
- PyTorch core: tensors (multi-dimensional arrays), autograd (automatic differentiation), nn.Module (model definition)
- The five-step MLP training loop: forward → loss → zero_grad → backward → step
- DataLoader for batching, schedulers for learning rate decay, early stopping to prevent overfitting
- MLP vs. linear regression: automatically learns interactions, higher R², but lower interpretability
- On tabular data, GBDT usually beats MLPs; MLPs shine when feature interactions are complex or data is unstructured
📝 Exercises
- Basic (Difficulty ⭐): Create a 2-layer MLP in PyTorch (input 4-dim → 16 → 8 → output 1). Print the model architecture and total parameter count. Hint: nn.Sequential +
sum(p.numel()...). - Intermediate (Difficulty ⭐⭐): Use an MLP to predict California Housing prices. Implement a full training loop (with validation and early stopping), then compare R² against LinearRegression. Hint: refer to the complete training pipeline in Section 5.
- Challenge (Difficulty ⭐⭐⭐): Experiment with different MLP architectures (1/2/3 layers, varying hidden sizes). Plot a "number of hidden layers vs. R²" curve and find the optimal architecture. Hint: loop over different hidden_dims configs and record validation R².
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