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:

Vectorized Memory Access

Uses float4 for 4-element vector loads/stores

__ldg() for read-only caching through texture memory

Bit shifts for division (>> 2, << 2) for efficiency

Precomputed Constants

Precomputes inv_denom = 1.0f / (edge1 - edge0) outside kernel

Avoids repeated division in loop

Improves arithmetic intensity

Smoothstep Function

Computes t = clamp((x-edge0)/(edge1-edge0), 0, 1)

Applies cubic polynomial: t² * (3 - 2t)

Uses fminf and fmaxf for clamping

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Grid-stride loop for arbitrary sizes

Performance Optimization

Compiler flags: -O3, --use_fast_math

Efficient kernel launch configuration

Block count limited to 65535

Mathematical Efficiency

Single inv_denom multiplication per element

Optimized cubic polynomial evaluation

Vectorized operations for 4 elements simultaneously

Key Innovation: Vectorized smoothstep activation with precomputed scaling factor, optimized for differentiable clamping operations in neural networks.

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, edge0=0.0, edge1=1.0):
        super().__init__()
        self.edge0 = edge0
        self.edge1 = edge1
        # 預計算分母倒數，避免除法
        self.inv_denom = 1.0 / (edge1 - edge0) if edge1 != edge0 else 1.0

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # GLSL 規範實現
        t = torch.clamp((x - self.edge0) * self.inv_denom, 0.0, 1.0)
        return t * t * (3.0 - 2.0 * t)


batch_size = 1024
feature_dim = 1024


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


def get_init_inputs():
    return [0.0, 1.0]