import numpy as np import time from typing import Dict, List, Any class MockTrainer: def __init__(self): # More realistic base accuracy for DP-SGD on MNIST (should achieve 85-98% like research shows) self.base_accuracy = 0.98 # Non-private MNIST accuracy self.base_loss = 0.08 # Corresponding base loss def train(self, params: Dict[str, Any]) -> Dict[str, Any]: """ Simulate DP-SGD training with given parameters using realistic privacy trade-offs. Args: params: Dictionary containing training parameters: - clipping_norm: float - noise_multiplier: float - batch_size: int - learning_rate: float - epochs: int Returns: Dictionary containing training results and metrics """ # Extract parameters clipping_norm = params['clipping_norm'] noise_multiplier = params['noise_multiplier'] batch_size = params['batch_size'] learning_rate = params['learning_rate'] epochs = params['epochs'] # Calculate realistic privacy impact on performance privacy_factor = self._calculate_realistic_privacy_factor(clipping_norm, noise_multiplier, batch_size, epochs) # Generate epoch-wise data epochs_data = self._generate_epoch_data(epochs, privacy_factor) # Generate iteration-wise data (mock version for consistency) iterations_data = self._generate_iteration_data(epochs, privacy_factor, batch_size) # Calculate final metrics (must be consistent with epoch data) final_metrics = self._calculate_final_metrics(epochs_data, privacy_factor) # Generate recommendations recommendations = self._generate_recommendations(params, final_metrics) # Generate gradient information gradient_info = { 'before_clipping': self.generate_gradient_norms(clipping_norm), 'after_clipping': self.generate_clipped_gradients(clipping_norm) } # Calculate realistic privacy budget privacy_budget = self._calculate_mock_privacy_budget(params) return { 'epochs_data': epochs_data, 'iterations_data': iterations_data, 'final_metrics': final_metrics, 'recommendations': recommendations, 'gradient_info': gradient_info, 'privacy_budget': privacy_budget } def _calculate_mock_privacy_budget(self, params: Dict[str, Any]) -> float: """Calculate a realistic mock privacy budget based on DP-SGD theory.""" noise_multiplier = params['noise_multiplier'] epochs = params['epochs'] batch_size = params['batch_size'] # More realistic calculation based on DP-SGD research q = batch_size / 60000 # Sampling rate for MNIST steps = epochs * (60000 // batch_size) # Simplified but more accurate RDP calculation # Based on research: ε ≈ q*sqrt(steps*log(1/δ)) / σ for large σ import math delta = 1e-5 epsilon = (q * math.sqrt(steps * math.log(1/delta))) / noise_multiplier # Add some realistic variation epsilon *= (1 + np.random.normal(0, 0.1)) return max(0.1, min(50.0, epsilon)) def _calculate_realistic_privacy_factor(self, clipping_norm: float, noise_multiplier: float, batch_size: int, epochs: int) -> float: """Calculate realistic privacy impact based on DP-SGD research.""" # Research shows DP-SGD can achieve 85-98% accuracy with proper parameters # The privacy impact should be much less severe than previously modeled # Base degradation from noise (much less severe) if noise_multiplier <= 0.5: noise_degradation = 0.02 # Very little impact with low noise elif noise_multiplier <= 1.0: noise_degradation = 0.05 # Small impact with medium noise elif noise_multiplier <= 1.5: noise_degradation = 0.12 # Moderate impact else: noise_degradation = min(0.25, 0.1 + 0.05 * noise_multiplier) # Higher impact with very high noise # Clipping degradation (much less severe) if clipping_norm >= 2.0: clipping_degradation = 0.01 # Minimal impact with good clipping elif clipping_norm >= 1.0: clipping_degradation = 0.03 # Small impact else: clipping_degradation = min(0.15, 0.2 / clipping_norm) # More impact with very low clipping # Batch size effect (larger batches help significantly) if batch_size >= 256: batch_factor = -0.02 # Bonus for large batches elif batch_size >= 128: batch_factor = 0.01 # Small penalty else: batch_factor = min(0.08, 0.001 * (128 - batch_size)) # Epochs effect (more training helps overcome noise) if epochs >= 10: epoch_factor = -0.03 # Bonus for sufficient training elif epochs >= 5: epoch_factor = 0.01 # Small penalty else: epoch_factor = 0.05 # Penalty for insufficient training total_degradation = noise_degradation + clipping_degradation + batch_factor + epoch_factor privacy_factor = 1.0 - max(0, total_degradation) # Much less degradation overall return max(0.7, privacy_factor) # Ensure minimum 70% of original performance (can achieve 85%+ with good params) def _generate_iteration_data(self, epochs: int, privacy_factor: float, batch_size: int) -> List[Dict[str, float]]: """Generate realistic iteration-wise training metrics.""" iterations_data = [] # Simulate ~60,000 training samples, so iterations_per_epoch = 60000 / batch_size dataset_size = 60000 iterations_per_epoch = dataset_size // batch_size # Realistic base learning curve parameters base_accuracy = self.base_accuracy * privacy_factor base_loss = self.base_loss / privacy_factor current_iteration = 0 for epoch in range(1, epochs + 1): for iteration_in_epoch in range(0, iterations_per_epoch, 10): # Sample every 10th current_iteration += 10 # Overall progress through all training total_iterations = epochs * iterations_per_epoch overall_progress = current_iteration / total_iterations # More realistic learning curve: slower start, plateau effect learning_progress = 1 - np.exp(-3 * overall_progress) # Exponential approach to target # Add realistic variation (DP-SGD has more noise) noise_std = 0.08 if privacy_factor < 0.7 else 0.04 # More noise for high privacy noise = np.random.normal(0, noise_std) # Calculate realistic accuracy progression target_accuracy = base_accuracy * (0.4 + 0.6 * learning_progress) accuracy = target_accuracy + noise # Calculate corresponding loss target_loss = base_loss * (1.5 - 0.5 * learning_progress) loss = target_loss - noise * 0.3 # Loss inversely correlated with accuracy # Add some iteration-level oscillations (typical of SGD) oscillation = 0.015 * np.sin(current_iteration * 0.05) accuracy += oscillation loss -= oscillation * 0.5 iterations_data.append({ 'iteration': current_iteration, 'epoch': epoch, 'accuracy': max(5, min(95, accuracy * 100)), # Realistic bounds 'loss': max(0.05, loss), 'train_accuracy': max(5, min(95, (accuracy + np.random.normal(0, 0.02)) * 100)), 'train_loss': max(0.05, loss + np.random.normal(0, 0.1)) }) return iterations_data def _generate_epoch_data(self, epochs: int, privacy_factor: float) -> List[Dict[str, float]]: """Generate realistic training metrics for each epoch.""" epochs_data = [] # Realistic base learning curve parameters base_accuracy = self.base_accuracy * privacy_factor base_loss = self.base_loss / privacy_factor for epoch in range(1, epochs + 1): # Realistic learning curve: fast early improvement, then plateau progress = epoch / epochs learning_factor = 1 - np.exp(-2.5 * progress) # Exponential learning curve # Add realistic epoch-to-epoch variation noise_std = 0.03 if privacy_factor < 0.7 else 0.015 noise = np.random.normal(0, noise_std) # Calculate realistic metrics accuracy = base_accuracy * (0.4 + 0.6 * learning_factor) + noise loss = base_loss * (1.4 - 0.4 * learning_factor) - noise * 0.3 epochs_data.append({ 'epoch': epoch, 'accuracy': max(5, min(95, accuracy * 100)), # Convert to percentage with bounds 'loss': max(0.05, loss), 'train_accuracy': max(5, min(95, (accuracy + np.random.normal(0, 0.01)) * 100)), 'train_loss': max(0.05, loss + np.random.normal(0, 0.05)) }) return epochs_data def _calculate_final_metrics(self, epochs_data: List[Dict[str, float]], privacy_factor: float) -> Dict[str, float]: """Calculate final training metrics that are CONSISTENT with epoch data.""" if not epochs_data: return {'accuracy': 50.0, 'loss': 1.0, 'training_time': 1.0} # Use the LAST epoch's results as final metrics (consistency!) final_epoch = epochs_data[-1] # Training time should be realistic for DP-SGD (slower than normal) base_time = len(epochs_data) * 0.8 # Base time per epoch privacy_slowdown = (2.0 - privacy_factor) # DP-SGD is slower time_variation = 1.0 + np.random.normal(0, 0.1) return { 'accuracy': final_epoch['accuracy'], # Consistent with training progress! 'loss': final_epoch['loss'], 'training_time': base_time * privacy_slowdown * time_variation } def _generate_recommendations(self, params: Dict[str, Any], metrics: Dict[str, float]) -> List[Dict[str, str]]: """Generate realistic recommendations based on DP-SGD best practices.""" recommendations = [] # Noise multiplier recommendations (critical for DP-SGD) if params['noise_multiplier'] < 0.5: recommendations.append({ 'icon': '🔒', 'text': 'Very low noise provides minimal privacy. Consider σ ≥ 0.8 for meaningful privacy.' }) elif params['noise_multiplier'] > 2.0: recommendations.append({ 'icon': '⚠️', 'text': 'High noise (σ > 2.0) significantly degrades accuracy. Try reducing to 0.8-1.5.' }) elif params['noise_multiplier'] > 1.5: recommendations.append({ 'icon': '💡', 'text': 'Consider reducing noise multiplier to 0.8-1.2 for better utility-privacy trade-off.' }) # Clipping norm recommendations if params['clipping_norm'] < 0.5: recommendations.append({ 'icon': '⚠️', 'text': 'Very low clipping norm can prevent learning. Try C = 1.0-2.0.' }) elif params['clipping_norm'] > 3.0: recommendations.append({ 'icon': '🔒', 'text': 'Large clipping norm reduces privacy protection. Consider C ≤ 2.0.' }) # Batch size recommendations (important for DP-SGD) if params['batch_size'] < 64: recommendations.append({ 'icon': '⚡', 'text': 'Small batch sizes amplify noise effects. Try batch size ≥ 128 for better stability.' }) elif params['batch_size'] > 512: recommendations.append({ 'icon': '💾', 'text': 'Very large batch sizes may require more memory and longer training time.' }) # Learning rate recommendations if params['learning_rate'] > 0.05: recommendations.append({ 'icon': '⚠️', 'text': 'High learning rate with noise can destabilize training. Try ≤ 0.02.' }) elif params['learning_rate'] < 0.005: recommendations.append({ 'icon': '⏳', 'text': 'Very low learning rate may require more epochs for convergence.' }) # Epochs recommendations if params['epochs'] < 5: recommendations.append({ 'icon': '📈', 'text': 'Few epochs may not be enough to overcome noise. Try 8-15 epochs.' }) elif params['epochs'] > 20: recommendations.append({ 'icon': '🔒', 'text': 'Many epochs increase privacy cost. Consider early stopping around 10-15 epochs.' }) # Accuracy-based recommendations if metrics['accuracy'] < 60: recommendations.append({ 'icon': '📉', 'text': 'Low accuracy suggests too much noise. Reduce σ or increase C for better utility.' }) elif metrics['accuracy'] > 85: recommendations.append({ 'icon': '🎯', 'text': 'Good accuracy! This is a well-balanced privacy-utility trade-off.' }) return recommendations def generate_gradient_norms(self, clipping_norm: float) -> List[Dict[str, float]]: """Generate realistic gradient norms following a log-normal distribution.""" num_points = 100 gradients = [] # Parameters for log-normal distribution mu = np.log(clipping_norm) - 0.5 sigma = 0.8 for _ in range(num_points): # Generate log-normal distributed gradient norms u1, u2 = np.random.random(2) z = np.sqrt(-2.0 * np.log(u1)) * np.cos(2.0 * np.pi * u2) norm = np.exp(mu + sigma * z) # Calculate density using kernel density estimation density = np.exp(-(np.power(np.log(norm) - mu, 2) / (2 * sigma * sigma))) / (norm * sigma * np.sqrt(2 * np.pi)) density = 0.2 + 0.8 * (density / 0.8) + 0.1 * (np.random.random() - 0.5) gradients.append({'x': float(norm), 'y': float(density)}) return sorted(gradients, key=lambda x: x['x']) def generate_clipped_gradients(self, clipping_norm: float) -> List[Dict[str, float]]: """Generate clipped versions of the gradient norms.""" original_gradients = self.generate_gradient_norms(clipping_norm) return [{'x': min(g['x'], clipping_norm), 'y': g['y']} for g in original_gradients]