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.
Technologies Used in This Code
Core Libraries & Frameworks
PyTorch: Deep learning framework

CUDA: NVIDIA's parallel computing platform

C++: For high-performance kernel implementation

CUDA/C++ Advanced Features
Warp Reduction: __shfl_down_sync() for warp-level operations

Block Reduction: Two-level reduction (warp + shared memory)

CUDA Intrinsics: rsqrtf() for reciprocal square root

Dynamic Block Sizing: Adaptive thread block size based on columns

Row-Level Parallelism: One CUDA block per row

Mathematical Operations
Gated Blending: g*a + (1-g)*b (element-wise gating)

L2 Normalization: Compute and apply vector norms

Reciprocal Square Root: Efficient 1/sqrt(x) computation

Sum of Squares: Compute squared L2 norm

Parallel Patterns
Row-Based Processing: Each block processes one row

Two-Pass Algorithm: First compute norm, then normalize

Efficient Reduction: Warp shuffles + shared memory

Grid-Stride Loops: Within each row for column processing

Optimization Techniques
Fused Operations: Blend and normalize in single kernel

Numerical Stability: Epsilon (1e-12) for division safety

Memory Coalescing: Row-major access patterns

Adaptive Block Size: Dynamically adjusted for column count

Performance Features
Massive Parallelism: Row-level and column-level parallelism

Low Synchronization: Minimal __syncthreads() usage

Efficient Math: Use of rsqrtf() intrinsic

Memory Efficiency: Shared memory for reduction results

Unique Aspects
Three-Input Gating: Uses gate tensor to blend two inputs

Per-Row Normalization: Each output row has unit L2 norm

Advanced Reduction: Custom two-level reduction functions

Auto-tuning: Block size adapts to input dimensions




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(Model, self).__init__()

    def forward(self, a, b, gate):
        blended = gate * a + (1 - gate) * b
        return F.normalize(blended, p=2.0, dim=-1, eps=1e-12)

batch_size = 1024
dim = 1024

def get_inputs():
    a = torch.randn(batch_size, dim)
    b = torch.randn(batch_size, dim)
    gate = torch.rand(batch_size, dim)
    return [a, b, gate]

def get_init_inputs():
    return []