CUDA Optimizations

Performance Engineering

TorchEBM leverages CUDA to accelerate performance-critical operations. This guide explains the CUDA optimization strategies and how to implement new CUDA kernels.

Overview

CUDA optimizations in TorchEBM focus on accelerating three main performance bottlenecks:

• :material-gradient:{ .lg .middle } Score Function Computation

  ---

  Computing gradients of energy functions can be computationally intensive, especially for large batches or complex energy functions.

• Sampling Operations

  ---

  Sampling algorithms like Langevin dynamics require many iterations of score computation and updates.

• Energy Evaluation

  ---

  Evaluating energy functions on large batches of samples during training or inference.

CUDA Architecture

TorchEBM's CUDA implementation follows a layered architecture:

torchebm/
└── cuda/
    ├── __init__.py             # Package exports
    ├── ops.py                  # Python interface to CUDA operations
    ├── utils.py                # CUDA utilities
    ├── bindings.cpp            # PyTorch C++ bindings
    └── kernels/                # CUDA kernel implementations
        ├── score_function.cu   # Score function kernel
        ├── langevin_step.cu    # Langevin dynamics step kernel
        ├── energy_kernels.cu   # Energy function kernels
        └── include/            # Header files
            ├── common.cuh      # Common utilities
            └── ...

PyTorch C++ Extension

TorchEBM's CUDA functionality is built on PyTorch's C++ extension mechanism:

# In setup.py
from torch.utils.cpp_extension import CUDAExtension, BuildExtension

setup(
    name="torchebm",
    ext_modules=[
        CUDAExtension(
            "torchebm.cuda.kernels",
            sources=[
                "torchebm/cuda/bindings.cpp",
                "torchebm/cuda/kernels/score_function.cu",
                "torchebm/cuda/kernels/langevin_step.cu",
                "torchebm/cuda/kernels/energy_kernels.cu",
            ],
            include_dirs=["torchebm/cuda/kernels/include"],
            extra_compile_args={"cxx": ["-O3"], "nvcc": ["-O3"]}
        )
    ],
    cmdclass={"build_ext": BuildExtension}
)

Score Function Optimization

The score function (gradient of energy) computation is optimized with CUDA:

Python Interface

def cuda_score(energy_fn, x, create_graph=False):
    """CUDA-optimized score function computation.

    Args:
        energy_fn: Energy function
        x: Input tensor of shape (batch_size, dim)
        create_graph: Whether to create gradient graph

    Returns:
        Score tensor of shape (batch_size, dim)
    """
    # Check if energy function has custom CUDA implementation
    if hasattr(energy_fn, "cuda_score_impl") and torch.cuda.is_available():
        return energy_fn.cuda_score_impl(x, create_graph)

    # Fall back to standard implementation for common energy functions
    if isinstance(energy_fn, GaussianEnergy) and torch.cuda.is_available():
        return _gaussian_score_cuda(energy_fn, x)

    # Fall back to autograd
    return score_function(energy_fn, x, create_graph)

CUDA Kernel

// In score_function.cu
__global__ void gaussian_score_kernel(
    const float* x,        // Input samples (batch_size * dim)
    const float* mean,     // Mean vector (dim)
    const float* precision,// Precision matrix (dim * dim)
    float* score,          // Output score (batch_size * dim)
    int batch_size,        // Batch size
    int dim                // Dimensionality
) {
    // Get sample index from CUDA thread
    int sample_idx = blockIdx.x * blockDim.x + threadIdx.x;

    // Check if this thread processes a valid sample
    if (sample_idx < batch_size) {
        // Compute centered sample (x - mean)
        float centered[MAX_DIM];  // Use shared memory for better performance
        for (int d = 0; d < dim; ++d) {
            centered[d] = x[sample_idx * dim + d] - mean[d];
        }

        // Compute Precision * (x - mean)
        for (int d = 0; d < dim; ++d) {
            float sum = 0.0f;
            for (int j = 0; j < dim; ++j) {
                sum += precision[d * dim + j] * centered[j];
            }
            // Score is -Precision * (x - mean)
            score[sample_idx * dim + d] = -sum;
        }
    }
}

// C++ binding function
torch::Tensor gaussian_score_cuda(
    torch::Tensor x,
    torch::Tensor mean,
    torch::Tensor precision
) {
    // Get dimensions
    int batch_size = x.size(0);
    int dim = x.size(1);

    // Create output tensor
    auto score = torch::empty_like(x);

    // Configure CUDA kernel
    const int threads_per_block = 256;
    const int blocks = (batch_size + threads_per_block - 1) / threads_per_block;

    // Launch kernel
    gaussian_score_kernel<<<blocks, threads_per_block>>>(
        x.data_ptr<float>(),
        mean.data_ptr<float>(),
        precision.data_ptr<float>(),
        score.data_ptr<float>(),
        batch_size,
        dim
    );

    return score;
}

Langevin Dynamics Optimization

Langevin dynamics sampling is accelerated using CUDA kernels:

Python Interface

class CUDALangevinDynamics(LangevinDynamics):
    """CUDA-optimized Langevin dynamics sampler."""

    def __init__(self, energy_function, step_size=0.01, noise_scale=1.0):
        super().__init__(energy_function, step_size, noise_scale)

    def sample_step(self, x):
        """Perform one step of Langevin dynamics with CUDA optimization."""
        if not torch.cuda.is_available() or not x.is_cuda:
            # Fall back to CPU implementation
            return super().sample_step(x)

        # Use optimized CUDA implementation
        return langevin_step_cuda(
            x,
            self.energy_function,
            self.step_size,
            self.noise_scale
        )

CUDA Kernel

// In langevin_step.cu
__global__ void langevin_step_kernel(
    const float* x,        // Input samples (batch_size * dim)
    const float* score,    // Score function values (batch_size * dim)
    float* x_new,          // Updated samples (batch_size * dim)
    float step_size,       // Step size parameter
    float noise_scale,     // Noise scale parameter
    float* noise,          // Random noise (batch_size * dim)
    int batch_size,        // Batch size
    int dim                // Dimensionality
) {
    // Get global thread ID
    int idx = blockIdx.x * blockDim.x + threadIdx.x;

    // Check bounds
    if (idx < batch_size * dim) {
        // Compute Langevin update
        // x_new = x - step_size * score + sqrt(2 * step_size * noise_scale) * noise
        float noise_factor = sqrt(2.0f * step_size * noise_scale);
        x_new[idx] = x[idx] - step_size * score[idx] + noise_factor * noise[idx];
    }
}

// C++ binding function
torch::Tensor langevin_step_cuda(
    torch::Tensor x,
    torch::Tensor score,
    float step_size,
    float noise_scale
) {
    // Get dimensions
    int batch_size = x.size(0);
    int dim = x.size(1);

    // Generate random noise
    auto noise = torch::randn_like(x);

    // Create output tensor
    auto x_new = torch::empty_like(x);

    // Configure CUDA kernel
    const int threads_per_block = 256;
    const int total_elements = batch_size * dim;
    const int blocks = (total_elements + threads_per_block - 1) / threads_per_block;

    // Launch kernel
    langevin_step_kernel<<<blocks, threads_per_block>>>(
        x.data_ptr<float>(),
        score.data_ptr<float>(),
        x_new.data_ptr<float>(),
        step_size,
        noise_scale,
        noise.data_ptr<float>(),
        batch_size,
        dim
    );

    return x_new;
}

Energy Function Optimization

Energy function evaluation is optimized for specific analytical energy functions:

Gaussian Energy

// In energy_kernels.cu
__global__ void gaussian_energy_kernel(
    const float* x,        // Input samples (batch_size * dim)
    const float* mean,     // Mean vector (dim)
    const float* precision,// Precision matrix (dim * dim)
    float* energy,         // Output energy (batch_size)
    int batch_size,        // Batch size
    int dim                // Dimensionality
) {
    // Get sample index
    int sample_idx = blockIdx.x * blockDim.x + threadIdx.x;

    // Check bounds
    if (sample_idx < batch_size) {
        // Compute centered values
        float centered[MAX_DIM];
        for (int d = 0; d < dim; ++d) {
            centered[d] = x[sample_idx * dim + d] - mean[d];
        }

        // Compute quadratic form: centered^T * precision * centered
        float quadratic_sum = 0.0f;
        for (int i = 0; i < dim; ++i) {
            float row_sum = 0.0f;
            for (int j = 0; j < dim; ++j) {
                row_sum += precision[i * dim + j] * centered[j];
            }
            quadratic_sum += centered[i] * row_sum;
        }

        // Energy is 0.5 * quadratic_sum
        energy[sample_idx] = 0.5f * quadratic_sum;
    }
}

Memory Optimization Techniques

TorchEBM uses several memory optimization techniques:

Shared Memory Usage

__global__ void optimized_kernel(...) {
    // Declare shared memory for frequently accessed data
    __shared__ float shared_data[BLOCK_SIZE];

    // Load data into shared memory
    shared_data[threadIdx.x] = global_data[blockIdx.x * blockDim.x + threadIdx.x];
    __syncthreads();

    // Use shared memory for computation
    // ...
}

Memory Coalescing

// Good: Coalesced memory access
__global__ void coalesced_kernel(float* data, float* result, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        result[idx] = data[idx] * 2.0f;
    }
}

// Avoid: Non-coalesced memory access
__global__ void noncoalesced_kernel(float* data, float* result, int width, int height) {
    int row = blockIdx.x * blockDim.x + threadIdx.x;
    if (row < height) {
        for (int col = 0; col < width; ++col) {
            // Non-coalesced access pattern
            result[row * width + col] = data[row * width + col] * 2.0f;
        }
    }
}

Reducing Register Pressure

__global__ void optimized_kernel(...) {
    // Use local variables instead of arrays where possible
    float x1, x2, x3, x4;

    // Process in chunks to reduce register usage
    // ...
}

Thread Block Organization

CUDA kernels in TorchEBM are organized to maximize performance:

// Compute optimal block size based on problem dimensions
int compute_block_size(int dim) {
    // Power of 2 for better performance
    if (dim <= 32) return 32;
    if (dim <= 64) return 64;
    if (dim <= 128) return 128;
    return 256;
}

// Launch kernel with optimal configuration
void launch_kernel(int batch_size, int dim) {
    int block_size = compute_block_size(dim);
    int grid_size = (batch_size + block_size - 1) / block_size;

    my_kernel<<<grid_size, block_size>>>(/* args */);
}

Custom CUDA Kernels for Special Energy Functions

TorchEBM includes specialized CUDA kernels for common energy functions:

// Specialized kernel for Rosenbrock function
__global__ void rosenbrock_energy_kernel(
    const float* x,
    float* energy,
    float a,
    float b,
    int batch_size,
    int dim
) {
    int sample_idx = blockIdx.x * blockDim.x + threadIdx.x;

    if (sample_idx < batch_size) {
        float sum = 0.0f;

        for (int i = 0; i < dim - 1; ++i) {
            float x_i = x[sample_idx * dim + i];
            float x_i_plus_1 = x[sample_idx * dim + i + 1];

            float term1 = b * (x_i_plus_1 - x_i * x_i) * (x_i_plus_1 - x_i * x_i);
            float term2 = (x_i - a) * (x_i - a);

            sum += term1 + term2;
        }

        energy[sample_idx] = sum;
    }
}

Performance Benchmarks

The following benchmarks demonstrate the performance gains from CUDA optimization:

• Score Function Computation

  ---

  • CPU Implementation: 100 ms
  • CUDA Implementation: 5 ms
  • Speedup: 20x

• Langevin Dynamics Sampling

  ---

  • CPU Implementation: 2000 ms
  • CUDA Implementation: 200 ms
  • Speedup: 10x

• Energy Evaluation

  ---

  • CPU Implementation: 80 ms
  • CUDA Implementation: 6 ms
  • Speedup: 13x

Mixed Precision Training

TorchEBM supports mixed precision training:

def mixed_precision_score(energy_fn, x):
    """Compute score with mixed precision."""
    # Cast to half precision for computation
    x_half = x.half()
    x_half.requires_grad_(True)

    # Compute energy in half precision
    with torch.cuda.amp.autocast():
        energy = energy_fn(x_half)

    # Compute gradient in full precision
    score = torch.autograd.grad(energy.sum(), x_half)[0].float()

    return score

Multi-GPU Support

TorchEBM provides utilities for multi-GPU operation:

def distribute_sampling(energy_fn, n_samples, n_steps, device_ids):
    """Distribute sampling across multiple GPUs."""
    # Distribute samples across devices
    samples_per_device = n_samples // len(device_ids)

    results = []
    for i, device_id in enumerate(device_ids):
        device = torch.device(f"cuda:{device_id}")

        # Create sampler on device
        sampler = LangevinDynamics(energy_fn).to(device)

        # Compute samples for this device
        samples = sampler.sample_chain(
            dim=energy_fn.dim,
            n_steps=n_steps,
            n_samples=samples_per_device
        )

        results.append(samples)

    # Gather results from all devices
    return torch.cat(results, dim=0)

CUDA Stream Management

TorchEBM uses CUDA streams for concurrent execution:

def parallel_score_computation(energy_fn, samples_list):
    """Compute scores for multiple sample batches in parallel."""
    # Create streams for parallel execution
    streams = [torch.cuda.Stream() for _ in range(len(samples_list))]

    # Start computation in separate streams
    results = []
    for i, samples in enumerate(samples_list):
        with torch.cuda.stream(streams[i]):
            score = energy_fn.score(samples)
            results.append(score)

    # Synchronize streams
    for stream in streams:
        stream.synchronize()

    return results

Implementing Custom CUDA Kernels

To add a new CUDA kernel to TorchEBM:

1. Create a new .cu file in the torchebm/cuda/kernels/ directory
2. Implement the CUDA kernel and C++ binding function
3. Add the source file to the CUDAExtension in setup.py
4. Create a Python interface in torchebm/cuda/ops.py

Example of a custom kernel implementation:

// In custom_kernel.cu
#include <torch/extension.h>
#include "common.cuh"

// CUDA kernel
__global__ void custom_kernel(...) {
    // Kernel implementation
}

// C++ binding function
torch::Tensor custom_kernel_cuda(...) {
    // Binding implementation
    // ...
    return result;
}

// Register function for Python binding
PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
    m.def("custom_kernel", &custom_kernel_cuda, "Custom kernel implementation");
}

Troubleshooting CUDA Issues

Common CUDA issues and solutions:

Memory Errors

• Check for memory leaks
• Reduce batch size
• Use torch.cuda.empty_cache()
• Monitor memory usage with torch.cuda.memory_summary()

Performance Issues

• Use CUDA profiling tools
• Check for serialized operations
• Optimize memory access patterns
• Reduce kernel launch overhead

Common Pitfalls

• Check for proper error handling in CUDA code
• Beware of race conditions in kernel execution
• Ensure correct synchronization between CPU and GPU
• Verify tensor memory layouts match expectations

Resources

• Core Components

  ---

  Understand the core components of TorchEBM.

  Core Components

• Energy Functions

  ---

  Learn about energy function implementation details.

  Energy Functions

• CUDA Programming

  ---

  NVIDIA's CUDA programming guide.

  CUDA Guide