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Activation Functions Comparison Experiment - Extended Training Dynamics Analysis
Compares Linear, Sigmoid, ReLU, Leaky ReLU, and GELU activation functions
on a deep neural network (10 hidden layers) for 1D non-linear regression.
NEW FEATURES:
- Gradient measurements at epochs 1, 100, and 200
- Training dynamics visualizations showing how activations evolve
- Gradient flow evolution over training
"""
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 - Training Dynamics Experiment")
print("=" * 70)
# ============================================================
# 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 and gradients 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 all layers when requested
if store_activations:
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 get_weight_stats(self):
"""Get weight statistics for each hidden layer."""
stats = []
for i, layer in enumerate(self.hidden_layers):
w = layer.weight.data
stats.append({
'mean': w.mean().item(),
'std': w.std().item(),
'min': w.min().item(),
'max': w.max().item()
})
return stats
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 with Extended Metrics
# ============================================================
def train_model(model, X_train, Y_train, X_eval, epochs=500, lr=0.001):
"""
Train a model and collect comprehensive metrics.
Returns:
- loss_history: List of losses per epoch
- gradient_history: Dict of gradient magnitudes at key epochs (1, 100, 200)
- activation_history: Activations at various epochs
- weight_history: Weight statistics over training
- prediction_history: Model predictions at key epochs
"""
optimizer = optim.Adam(model.parameters(), lr=lr)
criterion = nn.MSELoss()
loss_history = []
gradient_history = {} # Gradients at epochs 1, 100, 200
activation_history = {}
weight_history = {}
prediction_history = {}
# Key epochs for analysis
gradient_epochs = [1, 100, 200] # Epochs to measure gradients
activation_epochs = [0, 50, 100, 150, 200, 300, 400, 499] # Epochs to save activations
prediction_epochs = [0, 50, 100, 200, 300, 499] # Epochs to save predictions
for epoch in range(epochs):
model.train()
optimizer.zero_grad()
# Forward pass (store activations at specific epochs)
store_acts = epoch in activation_epochs
predictions = model(X_train, store_activations=store_acts)
# Compute loss
loss = criterion(predictions, Y_train)
# Backward pass
loss.backward()
# Capture gradient magnitudes at key epochs
if epoch in gradient_epochs:
gradient_history[epoch] = model.get_gradient_magnitudes()
print(f" [Gradient Capture] Epoch {epoch}: Layer 1={gradient_history[epoch][0]:.2e}, Layer 10={gradient_history[epoch][9]:.2e}")
# 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()
}
# Store weight statistics periodically
if epoch % 50 == 0:
weight_history[epoch] = model.get_weight_stats()
# Store predictions at key epochs
if epoch in prediction_epochs:
model.eval()
with torch.no_grad():
pred = model(X_eval)
prediction_history[epoch] = pred.numpy().flatten()
model.train()
# Print progress
if epoch % 100 == 0 or epoch == epochs - 1:
print(f" Epoch {epoch:4d}/{epochs}: Loss = {loss.item():.6f}")
return loss_history, gradient_history, activation_history, weight_history, prediction_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 with extended metrics...")
print("=" * 70)
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_history, act_history, weight_history, pred_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_history": grad_history, # Gradients at epochs 1, 100, 200
"activation_history": act_history,
"weight_history": weight_history,
"prediction_history": pred_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 Extended Data
# ============================================================
print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Saving extended data...")
# Save gradient magnitudes at all measured epochs
gradient_data = {}
for act_type in activation_types:
gradient_data[act_type] = {
str(epoch): grads for epoch, grads in results[act_type]["gradient_history"].items()
}
with open('activation_functions/gradient_magnitudes_epochs.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_epochs.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 at Epochs 1, 100, 200 ---
print(" Creating gradient_flow_epochs.png...")
fig, axes = plt.subplots(1, 3, figsize=(18, 6))
gradient_epochs = [1, 100, 200]
layer_indices = list(range(1, 11))
for idx, epoch in enumerate(gradient_epochs):
ax = axes[idx]
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_history"].get(epoch, [0]*10)
offset = (i - 2) * bar_width
bars = ax.bar(x_positions + offset, grad_mags, bar_width,
label=activation_labels[act_type] if idx == 0 else "",
color=colors[act_type], alpha=0.8)
ax.set_xlabel('Hidden Layer', fontsize=11)
ax.set_ylabel('Avg Gradient Magnitude', fontsize=11)
ax.set_title(f'Epoch {epoch}', fontsize=13, fontweight='bold')
ax.set_xticks(x_positions)
ax.set_xticklabels([f'L{i}' for i in layer_indices], fontsize=9)
ax.set_yscale('log')
ax.grid(True, alpha=0.3, axis='y')
ax.set_ylim(1e-12, 1e0)
# Add legend to first subplot
axes[0].legend(loc='upper right', fontsize=9)
fig.suptitle('Gradient Flow Analysis Across Training\n(Gradient Magnitude per Layer at Epochs 1, 100, 200)', fontsize=14, y=1.02)
plt.tight_layout()
plt.savefig('activation_functions/gradient_flow_epochs.png', dpi=150, bbox_inches='tight')
plt.close()
# --- Plot 4: Original Gradient Flow (Epoch 1 only for compatibility) ---
print(" Creating gradient_flow.png...")
fig, ax = plt.subplots(figsize=(12, 8))
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_history"].get(1, [0]*10)
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 5: 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)
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()
# --- NEW Plot 6: Training Dynamics - Function Learning Over Time ---
print(" Creating training_dynamics_functions.png...")
fig, axes = plt.subplots(2, 3, figsize=(16, 10))
axes = axes.flatten()
# Show how each activation learns the function over epochs
prediction_epochs = [0, 50, 100, 200, 300, 499]
epoch_colors = plt.cm.viridis(np.linspace(0, 1, len(prediction_epochs)))
for idx, act_type in enumerate(activation_types):
ax = axes[idx]
# Ground truth
ax.plot(x_eval, y_true, 'k--', linewidth=2, label='Ground Truth', alpha=0.7)
# Predictions at different epochs
for ep_idx, epoch in enumerate(prediction_epochs):
if epoch in results[act_type]["prediction_history"]:
pred = results[act_type]["prediction_history"][epoch]
ax.plot(x_eval, pred, color=epoch_colors[ep_idx], linewidth=1.5,
label=f'Epoch {epoch}', alpha=0.8)
ax.set_xlabel('x', fontsize=10)
ax.set_ylabel('y', fontsize=10)
ax.set_title(f'{activation_labels[act_type]}', fontsize=12, fontweight='bold')
ax.set_xlim(-np.pi, np.pi)
ax.set_ylim(-2, 2)
ax.grid(True, alpha=0.3)
ax.legend(loc='upper right', fontsize=7)
# Hide the 6th subplot (we have 5 activations)
axes[5].axis('off')
fig.suptitle('Training Dynamics: How Each Activation Learns the Function Over Time', fontsize=14, y=1.02)
plt.tight_layout()
plt.savefig('activation_functions/training_dynamics_functions.png', dpi=150, bbox_inches='tight')
plt.close()
# --- NEW Plot 7: Gradient Evolution Over Training ---
print(" Creating gradient_evolution.png...")
fig, axes = plt.subplots(1, 2, figsize=(14, 6))
# Left plot: Gradient ratio (Layer 10 / Layer 1) evolution
ax1 = axes[0]
gradient_epochs = [1, 100, 200]
x_pos = np.arange(len(gradient_epochs))
bar_width = 0.15
for i, act_type in enumerate(activation_types):
ratios = []
for epoch in gradient_epochs:
grads = results[act_type]["gradient_history"].get(epoch, [1e-10]*10)
# Avoid division by zero
if grads[0] > 1e-15:
ratio = grads[9] / grads[0] # Layer 10 / Layer 1
else:
ratio = 1e10 # Very large ratio indicates vanishing gradients
ratios.append(ratio)
offset = (i - 2) * bar_width
ax1.bar(x_pos + offset, ratios, bar_width, label=activation_labels[act_type],
color=colors[act_type], alpha=0.8)
ax1.set_xlabel('Epoch', fontsize=12)
ax1.set_ylabel('Gradient Ratio (Layer 10 / Layer 1)', fontsize=12)
ax1.set_title('Gradient Ratio Evolution\n(Higher = More Vanishing)', fontsize=13)
ax1.set_xticks(x_pos)
ax1.set_xticklabels([f'Epoch {e}' for e in gradient_epochs])
ax1.set_yscale('log')
ax1.axhline(y=1, color='black', linestyle='--', linewidth=1, label='Ideal (ratio=1)')
ax1.legend(loc='upper left', fontsize=9)
ax1.grid(True, alpha=0.3, axis='y')
# Right plot: Layer 1 gradient magnitude over epochs
ax2 = axes[1]
for act_type in activation_types:
layer1_grads = []
for epoch in gradient_epochs:
grads = results[act_type]["gradient_history"].get(epoch, [0]*10)
layer1_grads.append(grads[0])
ax2.plot(gradient_epochs, layer1_grads, 'o-', color=colors[act_type],
linewidth=2, markersize=8, label=activation_labels[act_type])
ax2.set_xlabel('Epoch', fontsize=12)
ax2.set_ylabel('Layer 1 Gradient Magnitude', fontsize=12)
ax2.set_title('First Layer Gradient Over Training\n(Key Indicator of Learning)', fontsize=13)
ax2.set_yscale('log')
ax2.legend(loc='upper right', fontsize=9)
ax2.grid(True, alpha=0.3)
fig.suptitle('Activation Effect on Gradient Dynamics During Training', fontsize=14, y=1.02)
plt.tight_layout()
plt.savefig('activation_functions/gradient_evolution.png', dpi=150, bbox_inches='tight')
plt.close()
# --- NEW Plot 8: Activation Distribution Evolution ---
print(" Creating activation_evolution.png...")
fig, axes = plt.subplots(5, 4, figsize=(16, 18))
# Show activation distributions at epochs 0, 100, 200, 499 for layer 5
epochs_to_show = [0, 100, 200, 499]
for row, act_type in enumerate(activation_types):
for col, epoch in enumerate(epochs_to_show):
ax = axes[row, col]
if epoch in results[act_type]["activation_history"]:
activations = results[act_type]["activation_history"][epoch].get('layer_5', None)
if activations is not None:
# Clean data for histogram
acts_clean = activations.flatten()
acts_clean = acts_clean[np.isfinite(acts_clean)]
if len(acts_clean) > 0:
ax.hist(acts_clean, bins=50, color=colors[act_type],
alpha=0.7, edgecolor='black', linewidth=0.5)
mean_val = np.nanmean(acts_clean)
std_val = np.nanstd(acts_clean)
ax.axvline(mean_val, color='red', linestyle='--', linewidth=1.5)
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)
if row == 0:
ax.set_title(f'Epoch {epoch}', fontsize=11, fontweight='bold')
if col == 0:
ax.set_ylabel(f'{activation_labels[act_type]}', fontsize=10)
fig.suptitle('Activation Distribution Evolution (Layer 5 - Middle Layer)\nHow Activations Change During Training', fontsize=14, y=1.01)
plt.tight_layout()
plt.savefig('activation_functions/activation_evolution.png', dpi=150, bbox_inches='tight')
plt.close()
# --- NEW Plot 9: Comprehensive Training Dynamics Summary ---
print(" Creating training_dynamics_summary.png...")
fig = plt.figure(figsize=(20, 16))
# Create grid layout
gs = fig.add_gridspec(3, 3, hspace=0.3, wspace=0.3)
# Panel 1: Loss curves (top-left)
ax1 = fig.add_subplot(gs[0, 0])
for act_type in activation_types:
ax1.plot(results[act_type]["loss_history"],
color=colors[act_type], linewidth=2, label=activation_labels[act_type])
ax1.set_xlabel('Epoch', fontsize=11)
ax1.set_ylabel('MSE Loss', fontsize=11)
ax1.set_title('A. Training Loss Curves', fontsize=12, fontweight='bold')
ax1.set_yscale('log')
ax1.legend(loc='upper right', fontsize=8)
ax1.grid(True, alpha=0.3)
# Panel 2: Gradient ratio evolution (top-middle)
ax2 = fig.add_subplot(gs[0, 1])
for act_type in activation_types:
ratios = []
for epoch in [1, 100, 200]:
grads = results[act_type]["gradient_history"].get(epoch, [1e-10]*10)
if grads[0] > 1e-15:
ratio = grads[9] / grads[0]
else:
ratio = 1e10
ratios.append(ratio)
ax2.plot([1, 100, 200], ratios, 'o-', color=colors[act_type],
linewidth=2, markersize=8, label=activation_labels[act_type])
ax2.set_xlabel('Epoch', fontsize=11)
ax2.set_ylabel('Gradient Ratio (L10/L1)', fontsize=11)
ax2.set_title('B. Gradient Ratio Over Training', fontsize=12, fontweight='bold')
ax2.set_yscale('log')
ax2.axhline(y=1, color='black', linestyle='--', linewidth=1, alpha=0.5)
ax2.legend(loc='upper left', fontsize=8)
ax2.grid(True, alpha=0.3)
# Panel 3: Final learned functions (top-right)
ax3 = fig.add_subplot(gs[0, 2])
ax3.plot(x_eval, y_true, 'k--', linewidth=2, label='Ground Truth', alpha=0.7)
for act_type in activation_types:
ax3.plot(x_eval, results[act_type]["final_predictions"],
color=colors[act_type], linewidth=1.5, label=activation_labels[act_type], alpha=0.8)
ax3.set_xlabel('x', fontsize=11)
ax3.set_ylabel('y', fontsize=11)
ax3.set_title('C. Final Learned Functions', fontsize=12, fontweight='bold')
ax3.legend(loc='upper right', fontsize=8)
ax3.grid(True, alpha=0.3)
# Panels 4-6: Gradient flow at epochs 1, 100, 200 (middle row)
for idx, epoch in enumerate([1, 100, 200]):
ax = fig.add_subplot(gs[1, idx])
bar_width = 0.15
x_positions = np.arange(10)
for i, act_type in enumerate(activation_types):
grad_mags = results[act_type]["gradient_history"].get(epoch, [0]*10)
offset = (i - 2) * bar_width
ax.bar(x_positions + offset, grad_mags, bar_width,
color=colors[act_type], alpha=0.8)
ax.set_xlabel('Layer', fontsize=10)
ax.set_ylabel('Gradient Magnitude', fontsize=10)
ax.set_title(f'D{idx+1}. Gradient Flow - Epoch {epoch}', fontsize=12, fontweight='bold')
ax.set_xticks(x_positions)
ax.set_xticklabels([f'{i+1}' for i in range(10)], fontsize=8)
ax.set_yscale('log')
ax.set_ylim(1e-12, 1e0)
ax.grid(True, alpha=0.3, axis='y')
# Panels 7-9: Function learning at epochs 50, 200, 499 (bottom row)
for idx, epoch in enumerate([50, 200, 499]):
ax = fig.add_subplot(gs[2, idx])
ax.plot(x_eval, y_true, 'k--', linewidth=2, label='Ground Truth', alpha=0.7)
for act_type in activation_types:
if epoch in results[act_type]["prediction_history"]:
pred = results[act_type]["prediction_history"][epoch]
ax.plot(x_eval, pred, color=colors[act_type], linewidth=1.5,
label=activation_labels[act_type], alpha=0.8)
ax.set_xlabel('x', fontsize=10)
ax.set_ylabel('y', fontsize=10)
ax.set_title(f'E{idx+1}. Predictions at Epoch {epoch}', fontsize=12, fontweight='bold')
ax.set_xlim(-np.pi, np.pi)
ax.set_ylim(-2, 2)
ax.grid(True, alpha=0.3)
if idx == 2:
ax.legend(loc='upper right', fontsize=7)
fig.suptitle('Comprehensive Training Dynamics Analysis: Activation Functions in Deep Networks\n(10 Layers × 64 Neurons, 500 Epochs, Adam Optimizer)', fontsize=16, y=1.01)
plt.savefig('activation_functions/training_dynamics_summary.png', dpi=150, bbox_inches='tight')
plt.close()
print(f"\n[{datetime.now().strftime('%H:%M:%S')}] All visualizations saved!")
print(" - learned_functions.png")
print(" - loss_curves.png")
print(" - gradient_flow.png")
print(" - gradient_flow_epochs.png (NEW)")
print(" - hidden_activations.png")
print(" - training_dynamics_functions.png (NEW)")
print(" - gradient_evolution.png (NEW)")
print(" - activation_evolution.png (NEW)")
print(" - training_dynamics_summary.png (NEW)")
# ============================================================
# 7. Print Summary Statistics
# ============================================================
print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Summary Statistics")
print("=" * 70)
print("\n### Gradient Magnitudes at Key Epochs ###")
print("-" * 70)
print(f"{'Activation':<15} {'Epoch':<8} {'Layer 1':<12} {'Layer 5':<12} {'Layer 10':<12} {'Ratio (L10/L1)':<15}")
print("-" * 70)
for act_type in activation_types:
for epoch in [1, 100, 200]:
grads = results[act_type]["gradient_history"].get(epoch, [0]*10)
if grads[0] > 1e-15:
ratio = grads[9] / grads[0]
else:
ratio = float('inf')
print(f"{activation_labels[act_type]:<15} {epoch:<8} {grads[0]:<12.2e} {grads[4]:<12.2e} {grads[9]:<12.2e} {ratio:<15.2e}")
print("\n### Final MSE Losses ###")
print("-" * 40)
sorted_losses = sorted(final_losses.items(), key=lambda x: x[1])
for act_type, loss in sorted_losses:
print(f"{activation_labels[act_type]:<20}: {loss:.6f}")
print(f"\n[{datetime.now().strftime('%H:%M:%S')}] Experiment complete!")
print("=" * 70)
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