Performance Optimization Guide¶
This comprehensive guide covers performance optimization strategies for Entropic AI, including computational efficiency, memory management, GPU acceleration, and scalability considerations.
Performance Philosophy¶
Entropic AI performance optimization is guided by several key principles:
- Thermodynamic Efficiency: Optimize along natural energy gradients
- Adaptive Scaling: Performance that scales with problem complexity
- Resource Awareness: Efficient use of computational resources
- Real-time Capability: Support for time-critical applications
- Sustainable Computing: Energy-efficient algorithmic design
Performance Architecture¶
Computational Layers¶
┌─────────────────────────────────────────────────────────────┐
│ Application Layer │
│ ┌─────────────────┐ ┌─────────────────┐ ┌────────────────┐ │
│ │ Optimization │ │ Discovery │ │ Design │ │
│ │ Applications │ │ Applications │ │ Applications │ │
│ └─────────────────┘ └─────────────────┘ └────────────────┘ │
└─────────────────────────────────────────────────────────────┘
│
┌─────────────────────────────────────────────────────────────┐
│ Algorithmic Layer │
│ ┌─────────────────┐ ┌─────────────────┐ ┌────────────────┐ │
│ │ Thermodynamic │ │ Entropy │ │ Evolution │ │
│ │ Networks │ │ Diffusion │ │ Operators │ │
│ └─────────────────┘ └─────────────────┘ └────────────────┘ │
└─────────────────────────────────────────────────────────────┘
│
┌─────────────────────────────────────────────────────────────┐
│ Computational Layer │
│ ┌─────────────────┐ ┌─────────────────┐ ┌────────────────┐ │
│ │ Tensor │ │ Parallel │ │ Memory │ │
│ │ Operations │ │ Processing │ │ Management │ │
│ └─────────────────┘ └─────────────────┘ └────────────────┘ │
└─────────────────────────────────────────────────────────────┘
│
┌─────────────────────────────────────────────────────────────┐
│ Hardware Layer │
│ ┌─────────────────┐ ┌─────────────────┐ ┌────────────────┐ │
│ │ CPU │ │ GPU │ │ Distributed │ │
│ │ Execution │ │ Acceleration │ │ Compute │ │
│ └─────────────────┘ └─────────────────┘ └────────────────┘ │
└─────────────────────────────────────────────────────────────┘
Computational Optimization¶
Tensor Operations Optimization¶
Efficient Energy Computations¶
import torch
import torch.nn.functional as F
from typing import Optional, Tuple
import numpy as np
class OptimizedEnergyComputation:
"""Optimized energy computation with various acceleration techniques."""
def __init__(self, device: Optional[torch.device] = None):
self.device = device or torch.device('cuda' if torch.cuda.is_available() else 'cpu')
self.compiled_functions = {}
@torch.compile(mode="max-autotune")
def batched_energy_computation(self, states: torch.Tensor,
energy_params: torch.Tensor) -> torch.Tensor:
"""Compute energies for batch of states with compilation optimization."""
# Vectorized energy computation
# E = Σᵢ αᵢ φᵢ(x) where φᵢ are basis functions
batch_size, state_dim = states.shape
# Use fused operations for better performance
squared_states = torch.square(states) # φ₁(x) = x²
quartic_states = torch.square(squared_states) # φ₂(x) = x⁴
# Stack basis functions efficiently
basis_functions = torch.stack([
torch.ones_like(states[:, 0]), # φ₀ = 1
torch.sum(states, dim=1), # φ₁ = Σx
torch.sum(squared_states, dim=1), # φ₂ = Σx²
torch.sum(quartic_states, dim=1), # φ₃ = Σx⁴
], dim=1)
# Matrix multiplication for all energies at once
energies = torch.matmul(basis_functions, energy_params)
return energies
def memory_efficient_large_batch(self, states: torch.Tensor,
energy_params: torch.Tensor,
chunk_size: int = 1000) -> torch.Tensor:
"""Process large batches in chunks to manage memory."""
batch_size = states.shape[0]
energies = torch.empty(batch_size, device=self.device)
for start_idx in range(0, batch_size, chunk_size):
end_idx = min(start_idx + chunk_size, batch_size)
chunk = states[start_idx:end_idx]
with torch.cuda.amp.autocast(enabled=self.device.type == 'cuda'):
chunk_energies = self.batched_energy_computation(chunk, energy_params)
energies[start_idx:end_idx] = chunk_energies
return energies
def sparse_energy_computation(self, sparse_states: torch.sparse.FloatTensor,
energy_matrix: torch.Tensor) -> torch.Tensor:
"""Optimized computation for sparse state representations."""
# Use sparse matrix operations for systems with sparse connectivity
return torch.sparse.mm(sparse_states, energy_matrix)
Entropy Diffusion Optimization¶
class OptimizedEntropyDiffusion:
"""Optimized entropy diffusion with GPU acceleration."""
def __init__(self, diffusion_steps: int = 1000):
self.diffusion_steps = diffusion_steps
self.cached_schedules = {}
def get_noise_schedule(self, steps: int, schedule_type: str = 'cosine') -> torch.Tensor:
"""Get cached or compute noise schedule."""
cache_key = (steps, schedule_type)
if cache_key not in self.cached_schedules:
if schedule_type == 'cosine':
self.cached_schedules[cache_key] = self._cosine_schedule(steps)
elif schedule_type == 'linear':
self.cached_schedules[cache_key] = self._linear_schedule(steps)
else:
raise ValueError(f"Unknown schedule type: {schedule_type}")
return self.cached_schedules[cache_key]
def _cosine_schedule(self, steps: int) -> torch.Tensor:
"""Cosine noise schedule for better sampling quality."""
s = 0.008
t = torch.linspace(0, 1, steps + 1)
f_t = torch.cos((t + s) / (1 + s) * torch.pi / 2) ** 2
alpha_bar = f_t / f_t[0]
betas = 1 - alpha_bar[1:] / alpha_bar[:-1]
return torch.clamp(betas, 0, 0.999)
@torch.compile(mode="reduce-overhead")
def forward_diffusion_step(self, x: torch.Tensor, t: torch.Tensor,
noise: Optional[torch.Tensor] = None) -> Tuple[torch.Tensor, torch.Tensor]:
"""Single forward diffusion step with compilation."""
if noise is None:
noise = torch.randn_like(x)
schedule = self.get_noise_schedule(self.diffusion_steps)
alpha_bar = torch.cumprod(1 - schedule, dim=0)
alpha_bar_t = alpha_bar[t].reshape(-1, 1)
# q(x_t | x_0) = N(√α̅_t x_0, (1-α̅_t)I)
mean = torch.sqrt(alpha_bar_t) * x
variance = 1 - alpha_bar_t
x_t = mean + torch.sqrt(variance) * noise
return x_t, noise
@torch.no_grad()
def reverse_diffusion_batch(self, x_t: torch.Tensor,
denoising_network: torch.nn.Module,
timesteps: Optional[torch.Tensor] = None) -> torch.Tensor:
"""Efficient batched reverse diffusion."""
if timesteps is None:
timesteps = torch.arange(self.diffusion_steps - 1, -1, -1, device=x_t.device)
schedule = self.get_noise_schedule(self.diffusion_steps).to(x_t.device)
alpha = 1 - schedule
alpha_bar = torch.cumprod(alpha, dim=0)
for t in timesteps:
t_batch = torch.full((x_t.shape[0],), t, device=x_t.device, dtype=torch.long)
# Predict noise
with torch.cuda.amp.autocast(enabled=x_t.device.type == 'cuda'):
predicted_noise = denoising_network(x_t, t_batch)
# Compute coefficients
alpha_t = alpha[t]
alpha_bar_t = alpha_bar[t]
alpha_bar_prev = alpha_bar[t - 1] if t > 0 else torch.tensor(1.0)
# Compute mean of reverse distribution
coeff1 = 1 / torch.sqrt(alpha_t)
coeff2 = (1 - alpha_t) / torch.sqrt(1 - alpha_bar_t)
x_t_mean = coeff1 * (x_t - coeff2 * predicted_noise)
if t > 0:
# Add noise for non-final steps
posterior_variance = (1 - alpha_bar_prev) / (1 - alpha_bar_t) * (1 - alpha_t)
noise = torch.randn_like(x_t)
x_t = x_t_mean + torch.sqrt(posterior_variance) * noise
else:
x_t = x_t_mean
return x_t
Network Architecture Optimization¶
Efficient Thermodynamic Networks¶
class OptimizedThermodynamicNetwork(torch.nn.Module):
"""Memory and computation optimized thermodynamic network."""
def __init__(self, input_dim: int, hidden_dims: list, output_dim: int,
use_checkpointing: bool = False, activation_memory_efficient: bool = True):
super().__init__()
self.use_checkpointing = use_checkpointing
self.activation_memory_efficient = activation_memory_efficient
# Build layers with efficient initialization
layers = []
prev_dim = input_dim
for hidden_dim in hidden_dims:
# Use efficient linear layers
layer = torch.nn.Linear(prev_dim, hidden_dim, bias=False)
# Initialize with proper scaling for thermodynamic networks
with torch.no_grad():
torch.nn.init.normal_(layer.weight, 0, np.sqrt(2.0 / prev_dim))
layers.append(layer)
layers.append(torch.nn.LayerNorm(hidden_dim)) # More stable than BatchNorm
if self.activation_memory_efficient:
layers.append(torch.nn.SiLU(inplace=True)) # Memory efficient activation
else:
layers.append(torch.nn.SiLU())
prev_dim = hidden_dim
# Output layer
layers.append(torch.nn.Linear(prev_dim, output_dim, bias=False))
self.network = torch.nn.Sequential(*layers)
# Compile for better performance
if hasattr(torch, 'compile'):
self.network = torch.compile(self.network, mode="max-autotune")
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""Forward pass with optional gradient checkpointing."""
if self.use_checkpointing and self.training:
return torch.utils.checkpoint.checkpoint(self.network, x, use_reentrant=False)
else:
return self.network(x)
def compute_energy_efficient(self, states: torch.Tensor) -> torch.Tensor:
"""Memory-efficient energy computation."""
# Use mixed precision for forward pass
with torch.cuda.amp.autocast(enabled=states.device.type == 'cuda'):
features = self.forward(states)
# Energy is sum of squared features (positive definite)
energies = torch.sum(features ** 2, dim=-1)
return energies
def parallel_energy_gradients(self, states: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
"""Compute energies and gradients in parallel."""
states.requires_grad_(True)
energies = self.compute_energy_efficient(states)
# Efficient gradient computation
gradients = torch.autograd.grad(
outputs=energies.sum(),
inputs=states,
create_graph=False,
retain_graph=False,
only_inputs=True
)[0]
return energies, gradients
Adaptive Precision Training¶
class AdaptivePrecisionTrainer:
"""Training with adaptive precision for optimal performance."""
def __init__(self, model: torch.nn.Module,
use_amp: bool = True,
use_compile: bool = True):
self.model = model
self.use_amp = use_amp and torch.cuda.is_available()
if use_compile and hasattr(torch, 'compile'):
self.model = torch.compile(model, mode="max-autotune")
# Initialize mixed precision training
if self.use_amp:
self.scaler = torch.cuda.amp.GradScaler()
def training_step(self, batch: dict, optimizer: torch.optim.Optimizer) -> dict:
"""Optimized training step with mixed precision."""
states = batch['states']
targets = batch['targets']
optimizer.zero_grad(set_to_none=True) # More efficient than zero_grad()
if self.use_amp:
with torch.cuda.amp.autocast():
outputs = self.model(states)
loss = F.mse_loss(outputs, targets)
# Scale loss and backward pass
self.scaler.scale(loss).backward()
# Unscale gradients and check for infs/NaNs
self.scaler.unscale_(optimizer)
torch.nn.utils.clip_grad_norm_(self.model.parameters(), max_norm=1.0)
# Update weights
self.scaler.step(optimizer)
self.scaler.update()
else:
outputs = self.model(states)
loss = F.mse_loss(outputs, targets)
loss.backward()
torch.nn.utils.clip_grad_norm_(self.model.parameters(), max_norm=1.0)
optimizer.step()
return {
'loss': loss.item(),
'outputs': outputs.detach()
}
Memory Management¶
Efficient Memory Patterns¶
class MemoryEfficientEvolution:
"""Memory-optimized evolution algorithms."""
def __init__(self, population_size: int, state_dim: int,
device: torch.device, use_memory_pool: bool = True):
self.population_size = population_size
self.state_dim = state_dim
self.device = device
if use_memory_pool:
self._setup_memory_pool()
def _setup_memory_pool(self):
"""Pre-allocate memory pools for frequent operations."""
self.population_pool = torch.empty(
self.population_size, self.state_dim,
device=self.device, dtype=torch.float32
)
self.fitness_pool = torch.empty(
self.population_size,
device=self.device, dtype=torch.float32
)
self.temp_pool = torch.empty(
self.population_size, self.state_dim,
device=self.device, dtype=torch.float32
)
@torch.no_grad()
def evolve_population_efficient(self, population: torch.Tensor,
fitness_function: callable,
mutation_strength: float = 0.1) -> torch.Tensor:
"""Memory-efficient population evolution."""
# Reuse pre-allocated memory
current_pop = self.population_pool[:population.shape[0]]
current_pop.copy_(population)
# Compute fitness in chunks to manage memory
chunk_size = min(1000, self.population_size)
fitness = self.fitness_pool[:population.shape[0]]
for i in range(0, population.shape[0], chunk_size):
end_idx = min(i + chunk_size, population.shape[0])
chunk_fitness = fitness_function(current_pop[i:end_idx])
fitness[i:end_idx] = chunk_fitness
# Selection and mutation using in-place operations
sorted_indices = torch.argsort(fitness, descending=True)
elite_size = self.population_size // 4
elite_indices = sorted_indices[:elite_size]
# Generate new population in-place
new_pop = self.temp_pool[:population.shape[0]]
new_pop[:elite_size] = current_pop[elite_indices]
# Fill rest with mutations of elite
for i in range(elite_size, population.shape[0]):
parent_idx = elite_indices[i % elite_size]
mutation = mutation_strength * torch.randn_like(current_pop[parent_idx])
new_pop[i] = current_pop[parent_idx] + mutation
return new_pop.clone() # Return copy to avoid memory issues
def cleanup_memory(self):
"""Explicit memory cleanup."""
if hasattr(self, 'population_pool'):
del self.population_pool
if hasattr(self, 'fitness_pool'):
del self.fitness_pool
if hasattr(self, 'temp_pool'):
del self.temp_pool
# Force garbage collection
if torch.cuda.is_available():
torch.cuda.empty_cache()
Memory Monitoring¶
import psutil
import time
from typing import Dict, Any
class MemoryProfiler:
"""Monitor and profile memory usage during computation."""
def __init__(self):
self.peak_memory = 0
self.memory_timeline = []
self.gpu_memory_timeline = []
def start_profiling(self):
"""Start memory profiling."""
self.start_time = time.time()
self.initial_memory = self.get_current_memory()
self.memory_timeline = [self.initial_memory]
if torch.cuda.is_available():
self.initial_gpu_memory = torch.cuda.memory_allocated()
self.gpu_memory_timeline = [self.initial_gpu_memory]
def get_current_memory(self) -> Dict[str, float]:
"""Get current memory usage."""
process = psutil.Process()
memory_info = process.memory_info()
result = {
'rss': memory_info.rss / 1024**3, # GB
'vms': memory_info.vms / 1024**3, # GB
'percent': process.memory_percent()
}
if torch.cuda.is_available():
result['gpu_allocated'] = torch.cuda.memory_allocated() / 1024**3
result['gpu_reserved'] = torch.cuda.memory_reserved() / 1024**3
return result
def checkpoint(self, label: str = ""):
"""Record memory checkpoint."""
current_memory = self.get_current_memory()
current_time = time.time() - self.start_time
checkpoint_data = {
'time': current_time,
'label': label,
'memory': current_memory
}
self.memory_timeline.append(checkpoint_data)
# Track peak memory
current_peak = current_memory['rss']
if current_peak > self.peak_memory:
self.peak_memory = current_peak
def get_memory_report(self) -> Dict[str, Any]:
"""Generate comprehensive memory report."""
if not self.memory_timeline:
return {}
final_memory = self.memory_timeline[-1]['memory']
memory_growth = final_memory['rss'] - self.initial_memory['rss']
report = {
'initial_memory_gb': self.initial_memory['rss'],
'final_memory_gb': final_memory['rss'],
'peak_memory_gb': self.peak_memory,
'memory_growth_gb': memory_growth,
'timeline': self.memory_timeline
}
if torch.cuda.is_available():
gpu_growth = (final_memory['gpu_allocated'] -
self.initial_gpu_memory / 1024**3)
report['gpu_memory_growth_gb'] = gpu_growth
return report
GPU Acceleration¶
CUDA Optimization¶
class CUDAOptimizedOperations:
"""CUDA-optimized operations for thermodynamic computing."""
def __init__(self, device_id: int = 0):
if not torch.cuda.is_available():
raise RuntimeError("CUDA not available")
self.device = torch.device(f'cuda:{device_id}')
torch.cuda.set_device(device_id)
# Optimize CUDA settings
torch.backends.cudnn.benchmark = True
torch.backends.cudnn.deterministic = False
def create_cuda_streams(self, num_streams: int = 4) -> list:
"""Create CUDA streams for parallel execution."""
return [torch.cuda.Stream() for _ in range(num_streams)]
def parallel_energy_computation(self, state_batches: list,
energy_function: callable,
streams: list) -> list:
"""Compute energies in parallel using CUDA streams."""
results = []
for i, (batch, stream) in enumerate(zip(state_batches, streams)):
with torch.cuda.stream(stream):
# Move data to GPU asynchronously
batch_gpu = batch.to(self.device, non_blocking=True)
# Compute energy
energy = energy_function(batch_gpu)
results.append(energy)
# Synchronize all streams
for stream in streams:
stream.synchronize()
return results
def fused_thermodynamic_update(self, states: torch.Tensor,
gradients: torch.Tensor,
temperature: float,
dt: float) -> torch.Tensor:
"""Fused CUDA kernel for thermodynamic updates."""
# Use custom CUDA kernel for maximum performance
# This would typically be implemented in C++/CUDA
# For now, use optimized PyTorch operations
noise = torch.randn_like(states)
# Langevin dynamics update: dx = -∇E dt + √(2kT dt) η
deterministic_term = -gradients * dt
stochastic_term = np.sqrt(2 * temperature * dt) * noise
# Fused update
new_states = states + deterministic_term + stochastic_term
return new_states
@torch.jit.script
def optimized_distance_matrix(self, points: torch.Tensor) -> torch.Tensor:
"""JIT-compiled distance matrix computation."""
n = points.shape[0]
distances = torch.empty(n, n, device=points.device)
# Compute pairwise distances efficiently
for i in range(n):
diff = points - points[i:i+1]
distances[i] = torch.sum(diff * diff, dim=1)
return torch.sqrt(distances)
Multi-GPU Scaling¶
class MultiGPUEvolution:
"""Multi-GPU parallel evolution for large-scale problems."""
def __init__(self, gpu_ids: list = None):
if gpu_ids is None:
gpu_ids = list(range(torch.cuda.device_count()))
self.gpu_ids = gpu_ids
self.num_gpus = len(gpu_ids)
if self.num_gpus == 0:
raise RuntimeError("No GPUs available")
def distribute_population(self, population: torch.Tensor) -> list:
"""Distribute population across GPUs."""
population_size = population.shape[0]
chunk_size = population_size // self.num_gpus
distributed_pop = []
for i, gpu_id in enumerate(self.gpu_ids):
start_idx = i * chunk_size
if i == self.num_gpus - 1: # Last GPU gets remainder
end_idx = population_size
else:
end_idx = (i + 1) * chunk_size
chunk = population[start_idx:end_idx].to(f'cuda:{gpu_id}')
distributed_pop.append(chunk)
return distributed_pop
def parallel_evolution_step(self, distributed_population: list,
fitness_function: callable) -> list:
"""Perform evolution step in parallel across GPUs."""
from concurrent.futures import ThreadPoolExecutor, as_completed
def evolve_chunk(chunk_data):
chunk, gpu_id = chunk_data
device = f'cuda:{gpu_id}'
with torch.cuda.device(device):
# Compute fitness
fitness = fitness_function(chunk)
# Local evolution operations
# Selection, crossover, mutation
evolved_chunk = self._local_evolution(chunk, fitness)
return evolved_chunk
# Execute in parallel
with ThreadPoolExecutor(max_workers=self.num_gpus) as executor:
future_to_gpu = {
executor.submit(evolve_chunk, (chunk, gpu_id)): gpu_id
for chunk, gpu_id in zip(distributed_population, self.gpu_ids)
}
evolved_chunks = [None] * self.num_gpus
for future in as_completed(future_to_gpu):
gpu_id = future_to_gpu[future]
gpu_index = self.gpu_ids.index(gpu_id)
evolved_chunks[gpu_index] = future.result()
return evolved_chunks
def gather_and_migrate(self, evolved_chunks: list,
migration_rate: float = 0.1) -> list:
"""Gather results and perform inter-GPU migration."""
# Collect best individuals from each GPU
migrants = []
for chunk in evolved_chunks:
chunk_size = chunk.shape[0]
num_migrants = int(chunk_size * migration_rate)
# Select best individuals (assuming fitness is stored)
# This is simplified - would need actual fitness values
best_indices = torch.randperm(chunk_size)[:num_migrants]
migrants.append(chunk[best_indices])
# Redistribute migrants across GPUs
all_migrants = torch.cat(migrants, dim=0)
migrant_chunks = self.distribute_population(all_migrants)
# Replace worst individuals in each chunk with migrants
for i, (chunk, migrant_chunk) in enumerate(zip(evolved_chunks, migrant_chunks)):
chunk_size = chunk.shape[0]
num_migrants = migrant_chunk.shape[0]
# Replace worst individuals (simplified)
worst_indices = torch.randperm(chunk_size)[:num_migrants]
chunk[worst_indices] = migrant_chunk
return evolved_chunks
def _local_evolution(self, population: torch.Tensor,
fitness: torch.Tensor) -> torch.Tensor:
"""Local evolution operations on single GPU."""
# Selection
sorted_indices = torch.argsort(fitness, descending=True)
elite_size = population.shape[0] // 4
elite = population[sorted_indices[:elite_size]]
# Generate offspring through mutation
offspring = []
for i in range(population.shape[0] - elite_size):
parent = elite[i % elite_size]
mutation = 0.1 * torch.randn_like(parent)
child = parent + mutation
offspring.append(child)
offspring = torch.stack(offspring)
new_population = torch.cat([elite, offspring], dim=0)
return new_population
Scalability Optimization¶
Adaptive Algorithm Selection¶
class AdaptiveAlgorithmSelector:
"""Automatically select optimal algorithms based on problem characteristics."""
def __init__(self):
self.algorithm_profiles = {
'small_dense': {
'population_size': lambda n: min(100, 10 * n),
'mutation_rate': 0.1,
'use_gpu': False,
'memory_efficient': False
},
'large_dense': {
'population_size': lambda n: min(1000, int(np.sqrt(n) * 50)),
'mutation_rate': 0.05,
'use_gpu': True,
'memory_efficient': True
},
'sparse': {
'population_size': lambda n: min(500, 20 * int(np.log(n))),
'mutation_rate': 0.15,
'use_gpu': True,
'memory_efficient': True,
'use_sparse_ops': True
}
}
def analyze_problem(self, problem_data: dict) -> dict:
"""Analyze problem characteristics."""
n_variables = problem_data.get('n_variables', 0)
n_constraints = problem_data.get('n_constraints', 0)
sparsity = problem_data.get('sparsity', 0.0)
# Estimate computational complexity
complexity = n_variables * n_constraints
# Determine problem category
if sparsity > 0.7:
category = 'sparse'
elif complexity < 10000:
category = 'small_dense'
else:
category = 'large_dense'
return {
'category': category,
'complexity': complexity,
'recommended_profile': self.algorithm_profiles[category]
}
def get_optimal_parameters(self, problem_analysis: dict) -> dict:
"""Get optimal parameters for the problem."""
profile = problem_analysis['recommended_profile']
n_vars = problem_analysis.get('n_variables', 100)
return {
'population_size': profile['population_size'](n_vars),
'mutation_rate': profile['mutation_rate'],
'use_gpu': profile['use_gpu'],
'memory_efficient': profile['memory_efficient'],
'use_sparse_ops': profile.get('use_sparse_ops', False)
}
Dynamic Resource Allocation¶
class DynamicResourceManager:
"""Manage computational resources dynamically during optimization."""
def __init__(self, max_memory_gb: float = 16.0):
self.max_memory_gb = max_memory_gb
self.memory_monitor = MemoryProfiler()
self.performance_history = []
def monitor_performance(self, iteration: int, metrics: dict):
"""Monitor performance and adjust resources."""
current_memory = self.memory_monitor.get_current_memory()
performance_data = {
'iteration': iteration,
'memory_usage': current_memory['rss'],
'convergence_rate': metrics.get('convergence_rate', 0),
'computation_time': metrics.get('computation_time', 0)
}
self.performance_history.append(performance_data)
# Trigger adjustments if needed
if current_memory['rss'] > 0.8 * self.max_memory_gb:
return self._reduce_memory_usage()
elif len(self.performance_history) > 10:
return self._optimize_for_convergence()
return {}
def _reduce_memory_usage(self) -> dict:
"""Reduce memory usage by adjusting algorithm parameters."""
return {
'batch_size_multiplier': 0.7,
'population_size_multiplier': 0.8,
'use_gradient_checkpointing': True,
'memory_efficient_attention': True
}
def _optimize_for_convergence(self) -> dict:
"""Optimize parameters for better convergence."""
recent_performance = self.performance_history[-10:]
# Check convergence trend
convergence_rates = [p['convergence_rate'] for p in recent_performance]
avg_convergence = np.mean(convergence_rates)
if avg_convergence < 0.01: # Slow convergence
return {
'temperature_multiplier': 1.2,
'mutation_rate_multiplier': 1.1,
'exploration_bonus': 0.1
}
elif avg_convergence > 0.1: # Too fast, might miss optima
return {
'temperature_multiplier': 0.9,
'mutation_rate_multiplier': 0.9,
'exploitation_bonus': 0.1
}
return {}
Performance Benchmarking¶
Comprehensive Benchmarks¶
class PerformanceBenchmarker:
"""Comprehensive performance benchmarking suite."""
def __init__(self):
self.benchmark_results = {}
def run_optimization_benchmarks(self) -> dict:
"""Run optimization performance benchmarks."""
benchmarks = {
'sphere_function': self._benchmark_sphere,
'rosenbrock_function': self._benchmark_rosenbrock,
'rastrigin_function': self._benchmark_rastrigin,
'ackley_function': self._benchmark_ackley
}
results = {}
for name, benchmark_func in benchmarks.items():
print(f"Running benchmark: {name}")
# Test different problem sizes
for dim in [10, 50, 100, 500]:
result = benchmark_func(dim)
results[f"{name}_{dim}d"] = result
return results
def _benchmark_sphere(self, dim: int) -> dict:
"""Benchmark sphere function optimization."""
from entropic-ai.optimization import ThermodynamicOptimizer
def sphere_function(x):
return torch.sum(x**2)
bounds = (torch.tensor([-5.0] * dim), torch.tensor([5.0] * dim))
optimizer = ThermodynamicOptimizer()
start_time = time.time()
result = optimizer.optimize(sphere_function, bounds, max_iterations=1000)
end_time = time.time()
return {
'dimension': dim,
'final_error': result.final_energy,
'convergence_time': end_time - start_time,
'iterations_to_convergence': result.convergence_iteration,
'function_evaluations': result.function_evaluations
}
def benchmark_memory_scaling(self) -> dict:
"""Benchmark memory usage scaling."""
from entropic-ai.core import ThermodynamicNetwork
results = {}
for network_size in [100, 500, 1000, 2000, 5000]:
memory_before = self._get_memory_usage()
# Create network
network = ThermodynamicNetwork(
input_dim=network_size,
hidden_dims=[network_size, network_size],
output_dim=network_size
)
# Perform operations
batch_size = 64
input_data = torch.randn(batch_size, network_size)
start_time = time.time()
for _ in range(100):
output = network(input_data)
loss = torch.sum(output**2)
loss.backward()
network.zero_grad()
end_time = time.time()
memory_after = self._get_memory_usage()
results[network_size] = {
'memory_used_gb': (memory_after - memory_before) / 1024**3,
'forward_backward_time': end_time - start_time,
'throughput_samples_per_sec': (100 * batch_size) / (end_time - start_time)
}
# Cleanup
del network, input_data, output, loss
torch.cuda.empty_cache() if torch.cuda.is_available() else None
return results
def _get_memory_usage(self) -> float:
"""Get current memory usage in bytes."""
if torch.cuda.is_available():
return torch.cuda.memory_allocated()
else:
process = psutil.Process()
return process.memory_info().rss
def generate_performance_report(self, results: dict) -> str:
"""Generate comprehensive performance report."""
report = []
report.append("# Entropic AI Performance Report\n")
# Optimization benchmarks
report.append("## Optimization Benchmarks\n")
for benchmark_name, result in results.items():
if 'dimension' in result:
report.append(f"### {benchmark_name}")
report.append(f"- Dimension: {result['dimension']}")
report.append(f"- Final Error: {result['final_error']:.2e}")
report.append(f"- Convergence Time: {result['convergence_time']:.2f}s")
report.append(f"- Iterations: {result['iterations_to_convergence']}")
report.append("")
# Memory scaling
if 'memory_scaling' in results:
report.append("## Memory Scaling\n")
for size, metrics in results['memory_scaling'].items():
report.append(f"### Network Size: {size}")
report.append(f"- Memory Used: {metrics['memory_used_gb']:.2f} GB")
report.append(f"- Throughput: {metrics['throughput_samples_per_sec']:.0f} samples/sec")
report.append("")
return "\n".join(report)
Real-time Performance Optimization¶
Low-latency Applications¶
class RealTimeOptimizer:
"""Optimized for real-time applications with strict latency requirements."""
def __init__(self, max_latency_ms: float = 10.0):
self.max_latency_ms = max_latency_ms
self.precomputed_schedules = {}
self.warm_start_solutions = {}
def precompute_resources(self, problem_types: list):
"""Precompute resources for faster real-time execution."""
for problem_type in problem_types:
# Precompute noise schedules
schedule = self._generate_optimal_schedule(problem_type)
self.precomputed_schedules[problem_type] = schedule
# Generate warm-start solutions
warm_starts = self._generate_warm_starts(problem_type)
self.warm_start_solutions[problem_type] = warm_starts
@torch.jit.script
def fast_single_step(self, state: torch.Tensor,
gradient: torch.Tensor,
temperature: float) -> torch.Tensor:
"""JIT-compiled single optimization step."""
# Simplified Langevin step for minimal latency
noise = torch.randn_like(state)
dt = 0.01
# Update: x_{t+1} = x_t - η∇E + √(2ηkT) ε
new_state = state - 0.01 * gradient + 0.1 * temperature * noise
return new_state
def real_time_optimize(self, objective_function: callable,
initial_state: torch.Tensor,
problem_type: str = 'default') -> torch.Tensor:
"""Real-time optimization with latency constraints."""
start_time = time.time()
# Use warm start if available
if problem_type in self.warm_start_solutions:
current_state = self.warm_start_solutions[problem_type].clone()
else:
current_state = initial_state
current_state.requires_grad_(True)
max_iterations = 100 # Safety limit
for iteration in range(max_iterations):
# Check latency constraint
elapsed_ms = (time.time() - start_time) * 1000
if elapsed_ms > self.max_latency_ms:
break
# Compute gradient
energy = objective_function(current_state)
gradient = torch.autograd.grad(energy, current_state)[0]
# Fast update step
current_state = self.fast_single_step(
current_state.detach(),
gradient,
temperature=1.0
)
current_state.requires_grad_(True)
return current_state.detach()
This comprehensive performance optimization guide provides the foundation for building highly efficient, scalable, and real-time capable thermodynamic AI systems. The optimizations cover all aspects from low-level tensor operations to high-level algorithmic choices, ensuring optimal performance across different hardware configurations and problem scales.