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 warp-level operations
- **Block reduction**: Two-level reduction (warp + shared memory)
- **Row-wise processing**: One CUDA block per row
- **Dynamic block sizing**: Adaptive thread block size
- **CUDA intrinsics**: `rsqrtf()` for reciprocal square root

## Mathematical Operations
- **Exponential**: `expf(x)` element-wise
- **L2 Normalization**: Compute and apply vector norms
- **Logarithm**: `logf(z)` where z = normalized exp(x)
- **Sum of squares**: Compute squared L2 norm
- **Reciprocal square root**: `rsqrtf()` for normalization factor

## Parallel Patterns
- **Two-pass algorithm**: First compute norm, then apply normalization
- **Row-level parallelism**: Each block processes one row
- **Efficient reduction**: Custom warp/block reduction functions
- **Grid-stride loops**: Threads process multiple columns per row

## Optimization Techniques
- **Fused operations**: exp + normalize + log 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 Mathematical Property
- **Composite function**: Computes log(exp(x)/||exp(x)||₂)
- **Numerical stability**: Handles large values via normalization
- **Softmax alternative**: Similar to log-softmax but with L2 norm
- **Row-wise normalization**: Each output row normalized independently

## Numerical Considerations
- **Overflow prevention**: Normalization stabilizes exp() computation
- **Epsilon protection**: Prevents division by zero
- **Log domain safety**: Ensures positive argument for log()
- **Adaptive block size**: Optimized for varying column 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, x):
        y = torch.exp(x)
        z = F.normalize(y, p=2.0, dim=-1, eps=1e-12)
        return torch.log(z)

batch_size = 1024
dim = 1024

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

def get_init_inputs():
    return []