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.

Core Optimization Techniques:

Performance Optimizations

Vectorized Processing - Uses float4 for 4-element vectorized loads/stores

Fast Math Compilation - --use_fast_math flag with -O3 for maximum speed

Efficient Grid Sizing - Optimized grid calculation using bit-shift operations

Read-Only Cache - Uses __ldg() intrinsic for cached memory access

Memory Optimizations

Vectorized Memory Access - Processes 4 elements per operation via float4

Memory Coalescing - Ensures contiguous memory access patterns

Minimal Memory Allocation - Only allocates necessary output tensors

Numerical Optimizations

Fast Math Operations - Uses __expf, __fmul_rn for optimized floating-point math

Pre-computed Constants - Calculates k = -1.0f / (beta * beta) once on host

Efficient Welsch Formula - Optimized computation: 1.0f - expf(d*d*k)

Kernel Design

Two-Phase Processing - Vectorized main loop + scalar remainder handling

Efficient Reduction - Warp-level and block-level reduction with shared memory

Flexible Output - Supports both element-wise and reduced outputs

Key Features

High Throughput - Vectorized processing maximizes memory bandwidth

Fast Exponential - Optimized Welsch loss computation using fast math

Efficient Reduction - Minimal synchronization in reduction steps

Remainder Handling - Properly processes non-multiple-of-4 elements

This implementation provides extremely efficient Welsch loss computation through extensive vectorization and fast math optimizations.



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

# 定义用于测试的假设常量
N, C, H, W = 32, 64, 56, 56


class WelschLoss(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.reduction = reduction
        self.beta = float(beta)
        self.beta_sq = self.beta * self.beta
        if reduction not in ['none', 'mean', 'sum']:
            raise ValueError("Invalid reduction mode")

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        # Calculate squared difference: (x - y)^2
        diff_sq = (input - target) ** 2

        # Calculate loss: 1 - exp(-(diff^2 / beta^2))
        loss = 1.0 - torch.exp(-diff_sq / self.beta_sq)

        if self.reduction == 'mean':
            return loss.mean()
        elif self.reduction == 'sum':
            return loss.sum()
        else:
            return loss


class Model(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.op = WelschLoss(reduction, beta)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        # 适应 benchmark 输入格式 (如果输入是列表)
        if isinstance(input, (list, tuple)): input = input[0]
        if isinstance(target, (list, tuple)): target = target[0]

        return self.op(input, target)


def get_inputs():
    input = torch.randn(N, C, H, W, dtype=torch.float32)
    target = torch.randn(N, C, H, W, dtype=torch.float32)
    return [input, target]


def get_init_inputs():
    return ['mean', 1.0]