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

SERLU Activation Function

Scaled Exponential ReLU: λ * x if x ≥ 0 else λ * α * (exp(x) - 1)

Combination of SELU and ELU concepts

Default parameters: λ=1.0507, α=1.67326

Numerical Precision

Uses expm1f(x) for exp(x) - 1 in negative region

Higher accuracy for small x values

Precomputed neg_scale = λ * α constant

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

Branch for positive/negative condition

Mathematical Efficiency

Vectorized operations for 4 elements simultaneously

Minimal conditional branching

Precomputed scaling constants

Key Innovation: Vectorized SERLU activation with high-precision expm1f for the negative region, combining SELU scaling with ELU's exponential decay.



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


class Model(nn.Module):
    def __init__(self, lambd=1.0507, alpha=1.67326):
        super().__init__()
        self.lambd = lambd
        self.alpha = alpha

    def forward(self, x: torch.Tensor) -> torch.Tensor:

        return torch.where(
            x >= 0,
            self.lambd * x,
            self.lambd * self.alpha * torch.expm1(x)
        )


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 [1.0507, 1.67326]