You write custom CUDA kernels to replace the pytorch operators in the given GeGLU architecture to get speedups.

You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.
Technologies Used in This Code
Core Libraries & Frameworks
PyTorch: Deep learning framework

CUDA: NVIDIA's parallel computing platform for GPU acceleration

C++: For high-performance kernel implementation

PyTorch Specific Components
torch.nn.Module: Base class for neural network modules

torch.nn.functional.F.softmax: Softmax activation function

torch.utils.cpp_extension.load_inline: For inline compilation of CUDA/C++ extensions

PyTorch Tensors: Multi-dimensional arrays with automatic differentiation

CUDA/C++ Implementation Details
CUDA Kernels: Custom GPU kernel (renyi_divergence_kernel)

CUDA Math Functions: powf() for exponentiation, logf() for logarithms

Parallel Reduction: Tree-based reduction within shared memory

Shared Memory: Using __shared__ for inter-thread communication

Block-Level Parallelism: One CUDA block per batch element

Grid-Stride Loops: Efficient memory access within each row

Mathematical Components
Rényi Divergence: Information-theoretic alpha-divergence family

Power Operations: powf(p, alpha) * powf(q, 1-alpha) calculation

Logarithmic Scaling: log(sum) / (alpha - 1) normalization

Statistical Distance: Measures difference between probability distributions

Alpha Parameter: Controls divergence sensitivity (alpha ≠ 1)

Memory & Parallelism Patterns
Per-Batch Block Assignment: One CUDA block processes one batch element

Shared Memory Reduction: Efficient sum reduction within blocks

Row-Wise Processing: Each thread processes elements from one probability distribution row

Final Log Operation: Applied after reduction for numerical stability

Optimization Techniques
Grid-Stride Loops: Threads process multiple elements within their assigned row

Shared Memory Efficiency: Single buffer for intermediate sums

Log After Sum: More numerically stable than summing logs

Batch Independence: Parallel processing of batch elements

Fused Computation: Complete Rényi divergence calculation per batch element

Performance Features
Massive Parallelization: GPU acceleration for divergence computation

Numerical Stability: Log operation performed after summation

Memory Coalescing: Sequential memory access within rows

Scalable Design: Efficient for varying batch sizes and class counts

Minimal Synchronization: Single __syncthreads() call per reduction

Unique Implementation Aspects
Alpha Parameter Handling: Special case for alpha ≠ 1 requirement

Power Product Computation: P^alpha * Q^(1-alpha) formulation

Logarithmic Normalization: Standard Rényi divergence formula implementation

Per-Sample Output: Each batch element gets its own divergence value

Batch Mean Finalization: Average across batch on CPU




Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:
import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self, alpha=0.5):
        super(Model, self).__init__()
        self.alpha = alpha

    def forward(self, p, q):
        p_prob = F.softmax(p, dim=1)
        q_prob = F.softmax(q, dim=1)

        # sum(P^alpha * Q^(1-alpha))
        sum_term = torch.sum((p_prob ** self.alpha) * (q_prob ** (1.0 - self.alpha)), dim=1)

        # 1/(alpha-1) * log(sum)
        loss = torch.log(sum_term) / (self.alpha - 1.0)

        return loss.mean()


batch_size = 32
num_classes = 1000


def get_inputs():
    p = torch.randn(batch_size, num_classes, requires_grad=True)
    q = torch.randn(batch_size, num_classes)
    return [p, q]


def get_init_inputs():
    return [0.5]