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 (gamma_divergence_kernel)

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

Parallel Reduction: Tree-based reduction with multiple accumulators

Shared Memory: Using __shared__ with triple-buffer pattern (s_p, s_pq, s_q)

Block-Level Parallelism: One CUDA block per batch element

Thread-Level Parallelism: Parallel reduction across class dimensions

Mathematical Components
Gamma Divergence: Information-geometric divergence measure

Logarithmic Terms: Three logarithmic terms with different denominators

Power Computations: Multiple powf() calls with (1 + gamma) exponent

Normalization: Gamma parameter scaling in denominator terms

Statistical Distance: Measures difference between probability distributions

Memory & Parallelism Patterns
Triple Shared Memory Buffers: Separate buffers for p, pq, and q summations

Batch-Level Parallelism: Each batch element processed by separate CUDA block

Class-Level Parallelism: Threads parallelize across class dimensions

Hierarchical Reduction: Two-level parallel reduction within blocks

Optimization Techniques
Shared Memory Optimization: Efficient triple-buffer layout

Coalesced Memory Access: Sequential memory access patterns

Fused Computation: Complete divergence calculation per batch element

Logarithm Post-processing: Log operations after reduction (numerically stable)

Performance Features
Massive Parallelization: GPU acceleration for divergence computation

Numerical Stability: Log operations performed after summation

Memory Efficiency: Shared memory reuse across multiple reductions

Batch Independence: Parallel processing of batch elements

Host-Device Coordination: Final mean computation on CPU

Unique Implementation Aspects
Per-Batch Block Assignment: One CUDA block per batch element

Triple Reduction Pattern: Simultaneous reduction of three different sums

Logarithmic Normalization: Log operations in final divergence formula

Gamma Parameter Scaling: Parameter appears in all three denominator terms




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

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

        sum_p_pow = torch.sum(p_prob.pow(1.0 + self.gamma), dim=1)
        sum_pq_pow = torch.sum(p_prob * q_prob.pow(self.gamma), dim=1)
        sum_q_pow = torch.sum(q_prob.pow(1.0 + self.gamma), dim=1)

        term1 = torch.log(sum_p_pow) / (self.gamma * (1.0 + self.gamma))
        term2 = torch.log(sum_pq_pow) / self.gamma
        term3 = torch.log(sum_q_pow) / (1.0 + self.gamma)

        loss = term1 - term2 + term3
        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]