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
- **PyTorch**: Deep learning framework
- **CUDA**: NVIDIA GPU parallel computing
- **C++**: Kernel implementation

## Advanced CUDA Features
- **Warp reduction**: `__shfl_down_sync()` for efficient warp-level operations
- **Block-level parallelism**: One CUDA block per batch sample
- **Two-level reduction**: Warp shuffles + shared memory for statistics
- **Dynamic parallelism**: Threads process multiple elements per row

## Statistical Operations
- **Mean computation**: Calculate per-row average
- **Variance calculation**: Compute per-row variance
- **Standard deviation**: sqrt(variance) for normalization
- **Z-score normalization**: (x - mean) / (std + eps)

## Clipping/Normalization
- **Value clipping**: Hard limits with min_val and max_val
- **Batch normalization**: Per-sample standardization
- **Numerical stability**: Epsilon to prevent division by zero
- **Conditional clamping**: Branch-based clipping logic

## Parallel Patterns
- **Row-wise processing**: Each block processes one batch sample
- **Two-pass statistics**: First compute mean, then variance
- **Shared memory coordination**: Broadcast mean/std to all threads
- **Warp-level optimization**: Efficient reduction using warp shuffles

## Optimization Techniques
- **Fused operations**: Statistics + normalization + clipping in single kernel
- **Efficient reduction**: Custom warp/block reduction functions
- **Memory coalescing**: Row-major access patterns
- **Numerical safety**: Epsilon protection and Bessel's correction (dim-1)

## Performance Features
- **Massive parallelism**: Batch-level and element-level parallelism
- **Minimal synchronization**: Shared memory for statistic broadcasting
- **Statistical accuracy**: Proper variance calculation with Bessel's correction
- **Adaptive design**: Works for any batch size and dimension

## Unique Aspects
- **Complete pipeline**: Statistics → normalization → clipping
- **Per-sample normalization**: Independent normalization per batch element
- **Warp-aware reduction**: Optimized for GPU warp architecture (32 threads)
- **Robust statistics**: Handles edge cases with eps protection

## Numerical Considerations
- **Bessel's correction**: Uses (dim-1) for unbiased variance
- **Clipping range**: User-defined min_val and max_val
- **Epsilon selection**: Prevents division by near-zero std
- **Floating-point stability**: Careful order of operations



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, min_val, max_val, eps=1e-5):
        super(Model, self).__init__()
        self.min_val = min_val
        self.max_val = max_val
        self.eps = eps

    def forward(self, x):
        mean = x.mean(dim=-1, keepdim=True)
        std = x.std(dim=-1, keepdim=True)

        norm = (x - mean) / (std + self.eps)
        return torch.clamp(norm, self.min_val, self.max_val)


batch_size = 16
dim = 256
min_val = -1.0
max_val = 1.0


def get_inputs():
    x = torch.randn(batch_size, dim) * 10.0
    return [x]


def get_init_inputs():
    return [min_val, max_val]