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 Pade Activation Unit (PAU) with:

Memory Optimization:

Vectorized memory access using float4 for 4x bandwidth

Contiguous tensor inputs for coalesced memory access

Direct computation without temporary storage

Numerical Precision:

Double precision for rational function computation

Absolute value for denominator stability

Parameter conversion to double for accuracy

Parallelization Strategy:

Grid-stride loop for efficient workload distribution

256 threads per block optimal configuration

Automatic grid size calculation with 65535 block limit

Computational Optimization:

Inline rational function: (a0 + a1*x + a2*x²) / (1 + b1*|x| + b2*x²)

Efficient computation reuse: val_sq = val * val

Branchless absolute value calculation

Work Distribution:

Each thread processes 4 elements via float4

Independent PAU computation per element

No shared memory needed (pure element-wise)

The implementation balances numerical accuracy with performance through double precision computation and vectorized memory access.




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__()
        self.a0 = nn.Parameter(torch.tensor(0.0))
        self.a1 = nn.Parameter(torch.tensor(1.0))
        self.a2 = nn.Parameter(torch.tensor(0.0))
        self.b1 = nn.Parameter(torch.tensor(0.0))
        self.b2 = nn.Parameter(torch.tensor(0.0))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x_sq = x * x
        abs_x = torch.abs(x)

        num = self.a0 + self.a1 * x + self.a2 * x_sq
        den = 1.0 + torch.abs(self.b1) * abs_x + torch.abs(self.b2) * x_sq

        return num / den

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 []