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.

This CUDA kernel implements optimized LogMeanExp (Logarithm of Mean of Exponentials) with:

Memory Optimization:

Vectorized memory access using float4 for 4x bandwidth

Contiguous tensor inputs for coalesced memory access

Shared memory for reduction buffers and maximum value storage

Numerical Stability:

Numerically stable LogMeanExp using max subtraction

Formula: Max + log(Sum(exp(x - Max))) - log(N)

Prevents overflow in exponential calculations

Parallel Reduction:

Two-stage reduction: warp-level then block-level

Efficient max and sum reductions using warp shuffles

Shared memory for inter-warp communication

Vectorized max and sum computations

Work Distribution:

One block per batch sample with 256 threads

Vectorized processing of 4 elements per thread via float4

Thread 0 handles remaining elements (feature_dim % 4)

Final computation by thread 0 only

Computational Optimization:

Fast math compilation flags for optimized expf() and logf()

Efficient reduction patterns for max and sum operations

Balanced workload distribution across threads

The implementation provides numerical stability while maximizing throughput through vectorization and efficient parallel reductions.






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):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # LogMeanExp(x) = log(mean(exp(x))) = LogSumExp(x) - log(N)
        return torch.logsumexp(x, dim=-1) - torch.log(torch.tensor(x.size(-1), dtype=x.dtype, device=x.device))

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 []