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

Adaptive Piecewise Linear (APL) Function

Computes APL(x) = max(0,x) + Σ_s α_s * max(0, β_s - x)

Learnable parameters: α_s (slopes), β_s (breakpoints)

S-shaped piecewise linear approximation

Loop Optimization

Outer loop over vector elements

Inner loop over S parameters

Accumulates contributions from each learnable piece

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Grid-stride loop for arbitrary sizes

Efficient parameter loading

Performance Optimization

Compiler flags: -O3, --use_fast_math

Efficient kernel launch configuration

Block count limited to 65535

Uses fmaxf for ReLU operations

Mathematical Efficiency

Vectorized operations for 4 elements simultaneously

Accumulates S parameter contributions efficiently

Simple arithmetic operations only

Key Innovation: Vectorized Adaptive Piecewise Linear activation with learnable parameters, optimized for efficient computation of multiple piecewise linear components in parallel.



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, S=1, a_init=-0.2, b_init=0.4):
        super().__init__()
        self.S = S

        self.alpha = nn.Parameter(torch.full((S,), a_init, dtype=torch.float32))

        self.beta = nn.Parameter(torch.full((S,), b_init, dtype=torch.float32))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        output = F.relu(x)

        for s in range(self.S):
            output += self.alpha[s] * F.relu(-x + self.beta[s])

        return output


batch_size = 128
feature_dim = 512


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


def get_init_inputs():
    return [1, -0.2, 0.4]