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 code implements Chebyshev polynomial + absolute value + square with CUDA optimizations:

Element-wise parallelism - Each thread processes one element independently (no reduction needed).

FMA (fused multiply-add) optimization - Uses fmaf() for efficient polynomial evaluation: 16x⁴ - 20x² + 5.

Chebyshev polynomial T₅(x) - Computes 5th-order Chebyshev polynomial: T₅(x) = 16x⁵ - 20x³ + 5x.

Fused operations - Combines polynomial evaluation, absolute value, and squaring in one kernel.

Memory coalescing - Contiguous tensor access patterns.

Grid-stride mapping - Standard 1D grid/block mapping for element-wise operations.

No shared memory - Simple element-wise kernel avoids synchronization overhead.

CUDA math functions - Uses fmaf() and fabsf() for hardware-accelerated operations.

Efficient polynomial computation - Uses Horner-like scheme with FMA for numerical stability.





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(Model, self).__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x2 = x * x
        x3 = x2 * x
        x5 = x3 * x2
        t5 = 16.0 * x5 - 20.0 * x3 + 5.0 * x
        return torch.square(torch.abs(t5))

batch_size = 128
input_dim = 1024

def get_inputs():
    x = torch.randn(batch_size, input_dim)
    return [x]

def get_init_inputs():
    return []