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

torch.tensor(): Tensor creation from Python scalar

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

CUDA Math Functions: powf() for floating-point exponentiation

Parallel Reduction: Tree-based reduction using shared memory

Shared Memory: Using __shared__ for inter-thread communication

Atomic Operations: atomicAdd for thread-safe global updates

Grid-Stride Loops: Efficient memory access pattern

Mathematical Components
Beta Divergence: Information-theoretic divergence measure

Polynomial Computation: Three-term calculation with power functions

Exponential Operations: Multiple powf() calls with different exponents

Normalization: Scaling by (beta * (beta - 1.0f))

Statistical Distance: Measures difference between probability distributions

Optimization Techniques
Shared Memory Reduction: Parallel tree reduction within thread blocks

Grid-Stride Loops: Efficient handling of arbitrary tensor sizes

Fused Computation: Complete divergence calculation in single kernel

Batch Processing: Mean computation across batch dimension

Intermediate Terms: Precomputed terms to reduce redundant calculations

Performance Features
Massive Parallelization: GPU acceleration for divergence computation

Memory Efficiency: Shared memory for intermediate reduction results

Numerical Precision: Proper handling of beta parameter constraints

Host-Device Coordination: CPU post-processing of GPU results

Vectorized Operations: Parallel computation across all distribution elements

Additional Notes
Parameter Sensitivity: The beta parameter controls the divergence behavior

Probability Inputs: Expects softmax-normalized probability distributions

Batch-Averaged Loss: Returns mean divergence across batch dimension






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, beta=0.5):
        super(Model, self).__init__()
        self.beta = beta

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

        term1 = p_prob.pow(self.beta)
        term2 = (self.beta - 1) * q_prob.pow(self.beta)
        term3 = self.beta * p_prob * q_prob.pow(self.beta - 1)

        sum_val = torch.sum(term1 + term2 - term3, dim=1)
        loss = sum_val / (self.beta * (self.beta - 1))

        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]