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):
“”"
合理优化的PyTorch BCE Loss实现
使用PyTorch内置函数，避免重复的数值处理
“”"
def init(self):
super(Model, self).init()

def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:  
    """  
    使用PyTorch内置的binary_cross_entropy函数  
    让PyTorch自己处理数值稳定性  

    Args:  
        input (torch.Tensor): 预测概率 (0-1之间)  
        target (torch.Tensor): 真实标签 (0或1)  

    Returns:  
        torch.Tensor: BCE Loss标量值  
    """  
    # 直接使用内置函数，让PyTorch处理数值稳定性  
    return torch.nn.functional.binary_cross_entropy(  
        input,  
        target,  
        reduction='sum'  
    )  
batch_size = 128
num_features = 2000

def get_inputs():
“”"
生成合理的测试数据
“”"
input_probs = torch.sigmoid(torch.randn(batch_size, num_features))
target_labels = torch.randint(0, 2, (batch_size, num_features)).float()
return [input_probs, target_labels]

def get_init_inputs():
return [] # 没有特殊的初始化输入需求
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):
“”"
合理优化的PyTorch BCE Loss实现
使用PyTorch内置函数，避免重复的数值处理
“”"
def init(self):
super(Model, self).init()

def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:  
    """  
    使用PyTorch内置的binary_cross_entropy函数  
    让PyTorch自己处理数值稳定性  

    Args:  
        input (torch.Tensor): 预测概率 (0-1之间)  
        target (torch.Tensor): 真实标签 (0或1)  

    Returns:  
        torch.Tensor: BCE Loss标量值  
    """  
    # 直接使用内置函数，让PyTorch处理数值稳定性  
    return torch.nn.functional.binary_cross_entropy(  
        input,  
        target,  
        reduction='sum'  
    )  
batch_size = 128
num_features = 2000

def get_inputs():
“”"
生成合理的测试数据
“”"
input_probs = torch.sigmoid(torch.randn(batch_size, num_features))
target_labels = torch.randint(0, 2, (batch_size, num_features)).float()
return [input_probs, target_labels]

def get_init_inputs():
return [] # 没有特殊的初始化输入需求