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

CoLU Activation Function

Computes CoLU(x) = x / (1 - x * exp(-x))

Novel activation with smooth monotonic properties

Denominator has minimum value ~0.632 (no division by zero)

Numerical Stability

Uses expf(-x) for exponential decay

No explicit division check (mathematically safe)

Well-behaved for all real inputs

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

Inline function for CoLU computation

Mathematical Efficiency

Vectorized operations for 4 elements simultaneously

Single division and exponential per element

No conditional branching

Key Innovation: Vectorized CoLU (Continuous Linear Unit) activation with mathematical guarantees of numerical stability and smooth monotonic behavior.


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__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return x / (1.0 - x * torch.exp(-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 []