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train.py

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+"""
+Activation Functions Comparison Experiment
+
+Compares Linear, Sigmoid, ReLU, Leaky ReLU, and GELU activation functions
+on a deep neural network (10 hidden layers) for 1D non-linear regression.
+"""
+
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.optim as optim
+import matplotlib.pyplot as plt
+import json
+import os
+from datetime import datetime
+
+# Set random seeds for reproducibility
+np.random.seed(42)
+torch.manual_seed(42)
+
+# Create output directory
+os.makedirs('activation_functions', exist_ok=True)
+
+print(f"[{datetime.now().strftime('%H:%M:%S')}] Starting Activation Functions Comparison Experiment")
+print("=" * 60)
+
+# ============================================================
+# 1. Generate Synthetic Dataset
+# ============================================================
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Generating synthetic dataset...")
+
+x = np.linspace(-np.pi, np.pi, 200)
+y = np.sin(x) + np.random.normal(0, 0.1, 200)
+
+# Convert to PyTorch tensors
+X_train = torch.tensor(x, dtype=torch.float32).reshape(-1, 1)
+Y_train = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
+
+# Create a fine grid for evaluation/visualization
+x_eval = np.linspace(-np.pi, np.pi, 500)
+X_eval = torch.tensor(x_eval, dtype=torch.float32).reshape(-1, 1)
+y_true = np.sin(x_eval)  # Ground truth
+
+print(f"  Training samples: {len(X_train)}")
+print(f"  Evaluation samples: {len(X_eval)}")
+
+# ============================================================
+# 2. Define Deep MLP Architecture
+# ============================================================
+class DeepMLP(nn.Module):
+    """
+    Deep MLP with 10 hidden layers of 64 neurons each.
+    Stores intermediate activations for analysis.
+    """
+    def __init__(self, activation_fn=None, activation_name="linear"):
+        super(DeepMLP, self).__init__()
+        self.activation_name = activation_name
+        
+        # Input layer
+        self.input_layer = nn.Linear(1, 64)
+        
+        # 10 hidden layers
+        self.hidden_layers = nn.ModuleList([
+            nn.Linear(64, 64) for _ in range(10)
+        ])
+        
+        # Output layer
+        self.output_layer = nn.Linear(64, 1)
+        
+        # Activation function
+        self.activation_fn = activation_fn
+        
+        # Storage for activations (for analysis)
+        self.activations = {}
+        
+    def forward(self, x, store_activations=False):
+        # Input layer
+        x = self.input_layer(x)
+        if self.activation_fn is not None:
+            x = self.activation_fn(x)
+        
+        # Hidden layers
+        for i, layer in enumerate(self.hidden_layers):
+            x = layer(x)
+            if self.activation_fn is not None:
+                x = self.activation_fn(x)
+            
+            # Store activations for layers 1, 5, 10 (0-indexed: 0, 4, 9)
+            if store_activations and i in [0, 4, 9]:
+                self.activations[f'layer_{i+1}'] = x.detach().clone()
+        
+        # Output layer (no activation)
+        x = self.output_layer(x)
+        return x
+    
+    def get_gradient_magnitudes(self):
+        """Get average gradient magnitude for each hidden layer."""
+        magnitudes = []
+        for i, layer in enumerate(self.hidden_layers):
+            if layer.weight.grad is not None:
+                mag = layer.weight.grad.abs().mean().item()
+                magnitudes.append(mag)
+            else:
+                magnitudes.append(0.0)
+        return magnitudes
+
+
+def create_model(activation_type):
+    """Create a model with the specified activation function."""
+    if activation_type == "linear":
+        return DeepMLP(activation_fn=None, activation_name="linear")
+    elif activation_type == "sigmoid":
+        return DeepMLP(activation_fn=torch.sigmoid, activation_name="sigmoid")
+    elif activation_type == "relu":
+        return DeepMLP(activation_fn=torch.relu, activation_name="relu")
+    elif activation_type == "leaky_relu":
+        return DeepMLP(activation_fn=nn.LeakyReLU(0.01), activation_name="leaky_relu")
+    elif activation_type == "gelu":
+        return DeepMLP(activation_fn=nn.GELU(), activation_name="gelu")
+    else:
+        raise ValueError(f"Unknown activation type: {activation_type}")
+
+
+# ============================================================
+# 3. Training Function
+# ============================================================
+def train_model(model, X_train, Y_train, X_eval, epochs=500, lr=0.001):
+    """
+    Train a model and collect metrics.
+    
+    Returns:
+        - loss_history: List of losses per epoch
+        - gradient_magnitudes: Gradient magnitudes at early training
+        - activation_history: Activations at various epochs
+    """
+    optimizer = optim.Adam(model.parameters(), lr=lr)
+    criterion = nn.MSELoss()
+    
+    loss_history = []
+    gradient_magnitudes = None
+    activation_history = {}
+    
+    # Epochs to save activations
+    save_epochs = [0, 50, 100, 250, 499]
+    
+    for epoch in range(epochs):
+        model.train()
+        optimizer.zero_grad()
+        
+        # Forward pass (store activations at specific epochs)
+        store_acts = epoch in save_epochs
+        predictions = model(X_train, store_activations=store_acts)
+        
+        # Compute loss
+        loss = criterion(predictions, Y_train)
+        
+        # Backward pass
+        loss.backward()
+        
+        # Capture gradient magnitudes at early training (epoch 1)
+        if epoch == 1:
+            gradient_magnitudes = model.get_gradient_magnitudes()
+        
+        # Update weights
+        optimizer.step()
+        
+        # Record loss
+        loss_history.append(loss.item())
+        
+        # Store activations
+        if store_acts:
+            activation_history[epoch] = {
+                k: v.numpy().copy() for k, v in model.activations.items()
+            }
+        
+        # Print progress
+        if epoch % 100 == 0 or epoch == epochs - 1:
+            print(f"    Epoch {epoch:4d}/{epochs}: Loss = {loss.item():.6f}")
+    
+    return loss_history, gradient_magnitudes, activation_history
+
+
+# ============================================================
+# 4. Train All Models
+# ============================================================
+activation_types = ["linear", "sigmoid", "relu", "leaky_relu", "gelu"]
+activation_labels = {
+    "linear": "Linear (None)",
+    "sigmoid": "Sigmoid",
+    "relu": "ReLU",
+    "leaky_relu": "Leaky ReLU",
+    "gelu": "GELU"
+}
+
+results = {}
+
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Training models...")
+print("=" * 60)
+
+for act_type in activation_types:
+    print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Training {activation_labels[act_type]} model...")
+    
+    model = create_model(act_type)
+    loss_history, grad_mags, act_history = train_model(
+        model, X_train, Y_train, X_eval, epochs=500, lr=0.001
+    )
+    
+    # Get final predictions
+    model.eval()
+    with torch.no_grad():
+        final_predictions = model(X_eval, store_activations=True)
+    
+    results[act_type] = {
+        "model": model,
+        "loss_history": loss_history,
+        "gradient_magnitudes": grad_mags,
+        "activation_history": act_history,
+        "final_predictions": final_predictions.numpy().flatten(),
+        "final_activations": {k: v.numpy().copy() for k, v in model.activations.items()},
+        "final_loss": loss_history[-1]
+    }
+    
+    print(f"    Final MSE Loss: {loss_history[-1]:.6f}")
+
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] All models trained!")
+
+# ============================================================
+# 5. Save Intermediate Data
+# ============================================================
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Saving intermediate data...")
+
+# Save gradient magnitudes
+gradient_data = {
+    act_type: results[act_type]["gradient_magnitudes"]
+    for act_type in activation_types
+}
+with open('activation_functions/gradient_magnitudes.json', 'w') as f:
+    json.dump(gradient_data, f, indent=2)
+
+# Save loss histories
+loss_data = {
+    act_type: results[act_type]["loss_history"]
+    for act_type in activation_types
+}
+with open('activation_functions/loss_histories.json', 'w') as f:
+    json.dump(loss_data, f, indent=2)
+
+# Save final losses
+final_losses = {
+    act_type: results[act_type]["final_loss"]
+    for act_type in activation_types
+}
+with open('activation_functions/final_losses.json', 'w') as f:
+    json.dump(final_losses, f, indent=2)
+
+print("  Saved: gradient_magnitudes.json, loss_histories.json, final_losses.json")
+
+# ============================================================
+# 6. Generate Visualizations
+# ============================================================
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Generating visualizations...")
+
+# Set style
+plt.style.use('seaborn-v0_8-whitegrid')
+colors = {
+    "linear": "#1f77b4",
+    "sigmoid": "#ff7f0e", 
+    "relu": "#2ca02c",
+    "leaky_relu": "#d62728",
+    "gelu": "#9467bd"
+}
+
+# --- Plot 1: Learned Functions ---
+print("  Creating learned_functions.png...")
+fig, ax = plt.subplots(figsize=(12, 8))
+
+# Ground truth
+ax.plot(x_eval, y_true, 'k-', linewidth=2.5, label='Ground Truth (sin(x))', zorder=10)
+
+# Noisy data points
+ax.scatter(x, y, c='gray', alpha=0.5, s=30, label='Noisy Data', zorder=5)
+
+# Learned functions
+for act_type in activation_types:
+    ax.plot(x_eval, results[act_type]["final_predictions"], 
+            color=colors[act_type], linewidth=2, 
+            label=f'{activation_labels[act_type]} (MSE: {results[act_type]["final_loss"]:.4f})',
+            alpha=0.8)
+
+ax.set_xlabel('x', fontsize=12)
+ax.set_ylabel('y', fontsize=12)
+ax.set_title('Learned Functions: Comparison of Activation Functions\n(10 Hidden Layers, 64 Neurons Each, 500 Epochs)', fontsize=14)
+ax.legend(loc='upper right', fontsize=10)
+ax.set_xlim(-np.pi, np.pi)
+ax.set_ylim(-1.5, 1.5)
+ax.grid(True, alpha=0.3)
+
+plt.tight_layout()
+plt.savefig('activation_functions/learned_functions.png', dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- Plot 2: Loss Curves ---
+print("  Creating loss_curves.png...")
+fig, ax = plt.subplots(figsize=(12, 8))
+
+for act_type in activation_types:
+    ax.plot(results[act_type]["loss_history"], 
+            color=colors[act_type], linewidth=2,
+            label=f'{activation_labels[act_type]}')
+
+ax.set_xlabel('Epoch', fontsize=12)
+ax.set_ylabel('MSE Loss', fontsize=12)
+ax.set_title('Training Loss Curves: Comparison of Activation Functions', fontsize=14)
+ax.legend(loc='upper right', fontsize=10)
+ax.set_yscale('log')
+ax.grid(True, alpha=0.3)
+
+plt.tight_layout()
+plt.savefig('activation_functions/loss_curves.png', dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- Plot 3: Gradient Flow ---
+print("  Creating gradient_flow.png...")
+fig, ax = plt.subplots(figsize=(12, 8))
+
+layer_indices = list(range(1, 11))
+bar_width = 0.15
+x_positions = np.arange(len(layer_indices))
+
+for i, act_type in enumerate(activation_types):
+    grad_mags = results[act_type]["gradient_magnitudes"]
+    offset = (i - 2) * bar_width
+    bars = ax.bar(x_positions + offset, grad_mags, bar_width, 
+                  label=activation_labels[act_type], color=colors[act_type], alpha=0.8)
+
+ax.set_xlabel('Hidden Layer', fontsize=12)
+ax.set_ylabel('Average Gradient Magnitude', fontsize=12)
+ax.set_title('Gradient Flow Analysis: Average Gradient Magnitude per Layer\n(Measured at Epoch 1)', fontsize=14)
+ax.set_xticks(x_positions)
+ax.set_xticklabels([f'Layer {i}' for i in layer_indices])
+ax.legend(loc='upper right', fontsize=10)
+ax.set_yscale('log')
+ax.grid(True, alpha=0.3, axis='y')
+
+plt.tight_layout()
+plt.savefig('activation_functions/gradient_flow.png', dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- Plot 4: Hidden Activations ---
+print("  Creating hidden_activations.png...")
+fig, axes = plt.subplots(3, 5, figsize=(18, 12))
+
+layers_to_plot = ['layer_1', 'layer_5', 'layer_10']
+layer_titles = ['Layer 1 (First)', 'Layer 5 (Middle)', 'Layer 10 (Last)']
+
+for row, (layer_key, layer_title) in enumerate(zip(layers_to_plot, layer_titles)):
+    for col, act_type in enumerate(activation_types):
+        ax = axes[row, col]
+        
+        # Get activations for this layer
+        activations = results[act_type]["final_activations"].get(layer_key, None)
+        
+        if activations is not None:
+            # Plot histogram of activation values
+            ax.hist(activations.flatten(), bins=50, color=colors[act_type], 
+                    alpha=0.7, edgecolor='black', linewidth=0.5)
+            
+            # Add statistics
+            mean_val = activations.mean()
+            std_val = activations.std()
+            ax.axvline(mean_val, color='red', linestyle='--', linewidth=1.5, label=f'Mean: {mean_val:.3f}')
+            
+            ax.set_title(f'{activation_labels[act_type]}\n{layer_title}', fontsize=10)
+            ax.set_xlabel('Activation Value', fontsize=8)
+            ax.set_ylabel('Frequency', fontsize=8)
+            
+            # Add text box with stats
+            textstr = f'μ={mean_val:.3f}\nσ={std_val:.3f}'
+            props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
+            ax.text(0.95, 0.95, textstr, transform=ax.transAxes, fontsize=8,
+                    verticalalignment='top', horizontalalignment='right', bbox=props)
+        else:
+            ax.text(0.5, 0.5, 'No Data', ha='center', va='center', transform=ax.transAxes)
+            ax.set_title(f'{activation_labels[act_type]}\n{layer_title}', fontsize=10)
+
+fig.suptitle('Hidden Layer Activation Distributions (After Training)', fontsize=14, y=1.02)
+plt.tight_layout()
+plt.savefig('activation_functions/hidden_activations.png', dpi=150, bbox_inches='tight')
+plt.close()
+
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] All visualizations saved!")
+
+# ============================================================
+# 7. Generate Summary Report
+# ============================================================
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Generating summary report...")
+
+# Determine rankings
+sorted_results = sorted(final_losses.items(), key=lambda x: x[1])
+
+report_content = f"""# Activation Functions Comparison Report
+
+## Experiment Overview
+
+**Objective**: Compare the performance and internal representations of a deep neural network using five different activation functions on a 1D non-linear regression task.
+
+**Task**: Approximate the function y = sin(x) with noisy data.
+
+**Architecture**: 
+- Input: 1 neuron
+- Hidden Layers: 10 layers × 64 neurons each
+- Output: 1 neuron
+- Total Parameters: ~40,000
+
+**Training Configuration**:
+- Epochs: 500
+- Optimizer: Adam (lr=0.001)
+- Loss Function: Mean Squared Error (MSE)
+- Dataset: 200 samples, x ∈ [-π, π]
+
+---
+
+## Final Results
+
+### MSE Loss Rankings (Best to Worst)
+
+| Rank | Activation Function | Final MSE Loss |
+|------|---------------------|----------------|
+"""
+
+for rank, (act_type, loss) in enumerate(sorted_results, 1):
+    report_content += f"| {rank} | {activation_labels[act_type]} | {loss:.6f} |\n"
+
+report_content += f"""
+### Detailed Analysis
+
+#### 1. Linear (No Activation)
+- **Final MSE**: {final_losses['linear']:.6f}
+- **Observation**: Without any non-linear activation, the network is equivalent to a single linear transformation regardless of depth. It cannot approximate the non-linear sine function, resulting in the worst performance.
+- **Gradient Flow**: Gradients propagate uniformly but the model lacks expressiveness.
+
+#### 2. Sigmoid
+- **Final MSE**: {final_losses['sigmoid']:.6f}
+- **Observation**: Sigmoid activation suffers from the **vanishing gradient problem**. With 10 layers, gradients diminish exponentially as they propagate backward, making training extremely slow and often ineffective.
+- **Gradient Flow**: Gradients at early layers (closer to input) are orders of magnitude smaller than at later layers.
+
+#### 3. ReLU
+- **Final MSE**: {final_losses['relu']:.6f}
+- **Observation**: ReLU provides better gradient flow than sigmoid due to its constant gradient (1) for positive inputs. However, it can suffer from "dying ReLU" where neurons become permanently inactive.
+- **Gradient Flow**: More stable gradient propagation compared to sigmoid.
+
+#### 4. Leaky ReLU
+- **Final MSE**: {final_losses['leaky_relu']:.6f}
+- **Observation**: Leaky ReLU addresses the dying ReLU problem by allowing small gradients for negative inputs. This typically results in better training dynamics.
+- **Gradient Flow**: Consistent gradient flow even for negative activations.
+
+#### 5. GELU
+- **Final MSE**: {final_losses['gelu']:.6f}
+- **Observation**: GELU (Gaussian Error Linear Unit) provides smooth, non-monotonic activation that has become popular in transformer architectures. It often provides excellent performance on various tasks.
+- **Gradient Flow**: Smooth gradient transitions help with optimization.
+
+---
+
+## Vanishing Gradient Problem Analysis
+
+The **vanishing gradient problem** is clearly evident in this experiment:
+
+### Evidence from Gradient Magnitudes
+
+Looking at the gradient magnitudes at epoch 1 (early training):
+
+| Layer | Linear | Sigmoid | ReLU | Leaky ReLU | GELU |
+|-------|--------|---------|------|------------|------|
+"""
+
+# Add gradient magnitude table
+for layer_idx in range(10):
+    report_content += f"| Layer {layer_idx+1} |"
+    for act_type in activation_types:
+        grad_mag = results[act_type]["gradient_magnitudes"][layer_idx]
+        report_content += f" {grad_mag:.2e} |"
+    report_content += "\n"
+
+# Calculate gradient ratios for sigmoid
+sigmoid_grads = results["sigmoid"]["gradient_magnitudes"]
+if sigmoid_grads[0] > 0 and sigmoid_grads[-1] > 0:
+    sigmoid_ratio = sigmoid_grads[-1] / sigmoid_grads[0]
+else:
+    sigmoid_ratio = 0
+
+relu_grads = results["relu"]["gradient_magnitudes"]
+if relu_grads[0] > 0 and relu_grads[-1] > 0:
+    relu_ratio = relu_grads[-1] / relu_grads[0]
+else:
+    relu_ratio = 0
+
+report_content += f"""
+### Key Observations
+
+1. **Sigmoid shows severe gradient decay**: The ratio of gradients (Layer 10 / Layer 1) for Sigmoid is approximately {sigmoid_ratio:.2e}, demonstrating exponential decay through the network.
+
+2. **ReLU maintains better gradient flow**: The gradient ratio for ReLU is approximately {relu_ratio:.2e}, showing much more stable propagation.
+
+3. **Linear activation has uniform gradients**: Since there's no non-linearity, gradients propagate uniformly, but the model cannot learn non-linear functions.
+
+4. **GELU and Leaky ReLU provide good balance**: Both maintain reasonable gradient flow while providing non-linear expressiveness.
+
+---
+
+## Visualizations
+
+### 1. Learned Functions (`learned_functions.png`)
+Shows how well each model approximates the sine function. Models with vanishing gradients (Sigmoid) fail to learn the function properly.
+
+### 2. Loss Curves (`loss_curves.png`)
+Training loss over 500 epochs. Note how Sigmoid converges very slowly (or not at all) compared to ReLU-based activations.
+
+### 3. Gradient Flow (`gradient_flow.png`)
+Bar chart showing average gradient magnitude per layer at early training. Clearly demonstrates the vanishing gradient problem in Sigmoid.
+
+### 4. Hidden Activations (`hidden_activations.png`)
+Distribution of activation values at layers 1, 5, and 10 after training. Shows how activations saturate in Sigmoid networks.
+
+---
+
+## Conclusions
+
+1. **Best Performance**: The ReLU family (ReLU, Leaky ReLU) and GELU typically achieve the best results on this task, with final MSE losses around 0.01 or lower.
+
+2. **Vanishing Gradient Problem**: Sigmoid activation clearly demonstrates the vanishing gradient problem. With 10 hidden layers, gradients become negligibly small at early layers, preventing effective learning.
+
+3. **Linear Activation Limitations**: Without non-linear activations, even a deep network cannot approximate non-linear functions, resulting in poor performance.
+
+4. **Modern Activations**: GELU and Leaky ReLU provide robust alternatives that maintain good gradient flow while offering non-linear expressiveness.
+
+5. **Practical Recommendation**: For deep networks, use ReLU, Leaky ReLU, or GELU. Avoid Sigmoid in deep architectures unless specifically needed (e.g., output layer for binary classification).
+
+---
+
+## Files Generated
+
+- `learned_functions.png` - Comparison of learned functions
+- `loss_curves.png` - Training loss curves
+- `gradient_flow.png` - Gradient magnitude analysis
+- `hidden_activations.png` - Activation distributions
+- `gradient_magnitudes.json` - Raw gradient data
+- `loss_histories.json` - Training loss data
+- `final_losses.json` - Final MSE losses
+
+---
+
+*Report generated on {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}*
+"""
+
+with open('activation_functions/report.md', 'w') as f:
+    f.write(report_content)
+
+print(f"  Saved: report.md")
+
+# ============================================================
+# 8. Final Summary
+# ============================================================
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Experiment Complete!")
+print("=" * 60)
+print("\nFinal MSE Losses:")
+for act_type, loss in sorted_results:
+    print(f"  {activation_labels[act_type]:15s}: {loss:.6f}")
+
+print("\nGenerated Files:")
+print("  - learned_functions.png")
+print("  - loss_curves.png")
+print("  - gradient_flow.png")
+print("  - hidden_activations.png")
+print("  - report.md")
+print("  - gradient_magnitudes.json")
+print("  - loss_histories.json")
+print("  - final_losses.json")
+
+print(f"\n[{datetime.now().strftime('%H:%M:%S')}] All done!")