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.

CUDA Optimization Strategies:

Numerical Stability

Max Subtraction: Computes exp(-alpha * x - max) to prevent overflow

Uses -FLT_MAX for initial max value

Final result: -(1/alpha) * (log(sum) + max)

Mathematical Transformation

Smooth Minimum: Uses identity smoothmin(x) = -smoothmax(-x)

Computes max(-alpha * x) for numerical stability

Efficient transformation avoids redundant computation

Two-Pass Reduction

Pass 1: Find maximum of -alpha * x using parallel reduction

Pass 2: Compute sum of exponentials using parallel reduction

Shared memory for broadcasting max value

Vectorized Memory Access

Uses float4 for 4-element vector loads

Reduces memory instructions by 4x

Better memory bandwidth utilization

Parallel Reduction

Dual Reduction: Separate max and sum reductions

Warp shuffle operations with #pragma unroll

Shared memory for block-level results

Kernel Design

One block per batch sample (row)

256 threads per block for feature processing

Vectorized main loop + scalar tail handling

Performance Optimization

Compiler flags: -O3, --use_fast_math

Single thread handles remainder elements

Precomputes neg_alpha = -alpha outside loop

Key Innovation: Mathematical transformation from Smooth Minimum to Smooth Maximum with proper sign handling, maintaining numerical stability through max subtraction technique.



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

class Model(nn.Module):
    def __init__(self, alpha=1.0):
        super().__init__()
        self.alpha = alpha

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return -(1.0 / self.alpha) * torch.logsumexp(-self.alpha * x, dim=-1)

batch_size = 1024
feature_dim = 4096

def get_inputs():
    x = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    return [x]

def get_init_inputs():
    return [1.0]