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):
“”"
Cosine Similarity implementation.
Computes the cosine similarity between two sets of vectors.
“”"
def init(self):
super(Model, self).init()

def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:  
    """  
    Compute cosine similarity between x and y.  

    Args:  
        x (torch.Tensor): First set of vectors [batch_size, feature_dim]  
        y (torch.Tensor): Second set of vectors [batch_size, feature_dim]  

    Returns:  
        torch.Tensor: Cosine similarities [batch_size]  
    """  
    # Compute L2 norms  
    norm_x = torch.sqrt(torch.sum(x * x, dim=1, keepdim=True))  
    norm_y = torch.sqrt(torch.sum(y * y, dim=1, keepdim=True))  
      
    # Compute dot product  
    dot_product = torch.sum(x * y, dim=1, keepdim=True)  
      
    # Compute cosine similarity with epsilon to avoid division by zero  
    cosine_sim = dot_product / (norm_x * norm_y + 1e-8)  
      
    return cosine_sim.squeeze(1)  
batch_size = 1024
feature_dim = 512

def get_inputs():
# Generate two sets of vectors
x = torch.randn(batch_size, feature_dim)
y = torch.randn(batch_size, feature_dim)
return [x, y]

def get_init_inputs():
return [] # No special initialization inputs needed
IMPORTANT: The cosine similarity computation involves multiple PyTorch operations (element-wise multiplication, reduction, square root, division) that can be fused into a single CUDA kernel for significant performance improvements. Consider algorithmic innovations like sampling-based approximation with statistical correction to achieve both high performance and accuracy. Focus on creating a novel approach that differs from traditional block-wise or vectorization optimizations.
