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):
“”"
Weighted Sum implementation.
Computes the weighted sum of values using corresponding weights.
“”"
def init(self):
super(Model, self).init()

def forward(self, values: torch.Tensor, weights: torch.Tensor) -> torch.Tensor:  
    """  
    Compute weighted sum of values.  

    Args:  
        values (torch.Tensor): Input values [batch_size, feature_dim]  
        weights (torch.Tensor): Corresponding weights [batch_size, feature_dim]  

    Returns:  
        torch.Tensor: Weighted sums [batch_size]  
    """  
    # Element-wise multiplication  
    elementwise_product = values * weights  
      
    # Sum along feature dimension  
    result = torch.sum(elementwise_product, dim=1)  
      
    return result  
batch_size = 256
feature_dim = 512

def get_inputs():
# Generate values and corresponding weights
values = torch.randn(batch_size, feature_dim)
weights = torch.rand(batch_size, feature_dim) # Random weights between 0 and 1
return [values, weights]

def get_init_inputs():
return [] # No special initialization inputs needed

IMPORTANT: The weighted sum computation involves two separate PyTorch operations (element-wise multiplication and reduction) that can be fused into a single CUDA kernel for significant performance improvements. Consider warp-level optimizations and efficient reduction techniques to achieve both high performance and accuracy. Focus on creating a robust implementation that maintains perfect precision while delivering consistent speedups.
