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:

Numerical Stability Optimization

Threshold protection: Returns x directly when x > 20.0f

Prevents expf(2*x) overflow in float32 (avoids e^88 overflow)

Algebraic reformulation for better numerical behavior

Vectorized Memory Access + ILP

Uses float4 for 4-element vector loads/stores

Instruction-Level Parallelism (ILP): Processes 2 vectors (8 elements) per loop iteration

Increases computational density and hides memory latency

Algebraic Reformulation

Optimized Mish computation: x * (e*(2+e)) / (2 + 2*e + e*e)

Avoids separate tanh and softplus computations

Reduces mathematical operations

Grid-Stride Loop

Processes elements with grid-stride pattern

Handles arbitrary tensor sizes efficiently

Better GPU utilization

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Coalesced memory access patterns

Performance Tuning

Fixed 256 threads per block

Block count capped at 65535

Compiler flags: -O3, --use_fast_math

Key Innovation: Algebraic reformulation with numerical stability protection prevents overflow while maintaining mathematical equivalence, combined with ILP for performance.





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):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return x * torch.tanh(F.softplus(x))

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 []