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:

cuBLAS Integration

Uses cublasGemmEx for matrix multiplication

Falls back to cublasSgemm if TF32 fails

Enables Tensor Cores with CUBLAS_TENSOR_OP_MATH

Memory Access

contiguous() for all tensors

Coalesced memory access patterns

__restrict__ pointers for alias analysis

Parallel Reduction

Warp-level reduction with __shfl_down_sync

Block-level reduction using shared memory

Double precision for numerical accuracy

Kernel Design

Dedicated sub_mean_kernel for element-wise ops

reduction_kernel per batch for dot products

Fixed 256 threads, auto grid calculation

Numerical Optimization

TF32 precision for Ampere+ GPUs

sqrtf and max for stability

Compiler flag: -O3

Resource Management

Static cuBLAS handle with lazy initialization

Efficient shared memory usage






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, feature_dim):
        super().__init__()
        self.register_buffer("mean", torch.zeros(feature_dim))
        self.register_buffer("inv_cov", torch.eye(feature_dim))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        diff = x - self.mean
        temp = torch.mm(diff, self.inv_cov)
        dist_sq = (temp * diff).sum(dim=1)
        return torch.sqrt(dist_sq)

batch_size = 512
feature_dim = 256

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

def get_init_inputs():
    return [feature_dim]