You write custom CUDA kernels to replace the pytorch operators in the given 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 matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.  
  
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
python
import torch
import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
def init(self) -> None:
super().init()

def forward(self, a, b):
    return a + b
def get_inputs():
# randomly generate input tensors based on the model architecture
a = torch.randn(1, 128).cuda()
b = torch.randn(1, 128).cuda()
return [a, b]

def get_init_inputs():
# randomly generate tensors required for initialization based on the model architecture
return []


  
The example new arch with custom CUDA kernels looks like this:   
python
import torch
import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
def init(self) -> None:
super().init()

def forward(self, a, b):
    return a + b
def get_inputs():
# randomly generate input tensors based on the model architecture
a = torch.randn(1, 128).cuda()
b = torch.randn(1, 128).cuda()
return [a, b]

def get_init_inputs():
# randomly generate tensors required for initialization based on the model architecture
return []  

You are given the following architecture:   

python
import torch
import torch.nn as nn

class Model(nn.Module):
“”"
Simple model that performs RMSNorm.
“”"
def init(self, dim, eps=1e-6):
super(Model, self).init()
self.eps = eps
self.weight = torch.nn.Parameter(torch.ones(dim))

def forward(self, x: torch.Tensor) -> torch.Tensor:  
    """  
    Applies RMSNorm activation to the input tensor.  

    Args:  
        x (torch.Tensor): Input tensor of shape (B, L, D).  

    Returns:  
        torch.Tensor: Output tensor with RMSNorm applied, same shape as input.  
    """  
    dtype = x.dtype  
    x = x.float()  
    variance = x.pow(2).mean(-1, keepdim=True)  
    x = x * torch.rsqrt(variance + self.eps)  
    return (x * self.weight).to(dtype)  
batch_size = 16
seq_len = 512
dim = 4096

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

def get_init_inputs():
return [dim]
