You write custom CUDA kernels to replace the PyTorch operators in the given EvoNorm 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 normalization+affine_transform+nonlinear_gating), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.

Technical Overview: CUDA-Optimized Cosine Embedding Loss
This implementation provides a high-performance CUDA kernel for computing cosine embedding loss, designed for deep learning applications with optimized memory access and parallel computation.
Key Features:
Architecture:
Custom CUDA kernel with inline compilation using PyTorch C++ extensions
Optimized for NVIDIA GPUs with warp-level parallelism and shared memory utilization
Supports 4-element vectorization (float4) for memory coalescing
Performance Optimizations:
Vectorized Memory Access: Uses float4 data type to load 4 elements per instruction
Instruction-Level Parallelism (ILP): Processes 4 vectors simultaneously per thread
Warp Reduction: Efficient warp-level reduction operations using __shfl_down_sync
Shared Memory: Intermediate results stored in shared memory for block-level reduction
Memory Coalescing: Contiguous memory access patterns for optimal bandwidth utilization
Kernel Specifications:
Block size: 256 threads
Warp size: 32 threads
Grid dimension: N (batch size)
Input requirement: C×H×W must be divisible by 4 for vectorization


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


N, C, H, W = 32, 64, 56, 56
EPS = 1e-8

class CosineEmbeddingLossCustom(nn.Module):

    def __init__(self, margin=0.0, reduction='mean', eps=1e-8):
        super().__init__()
        self.margin = margin
        self.reduction = reduction
        self.eps = eps

    def forward(self, x1: torch.Tensor, x2: torch.Tensor, target: torch.Tensor) -> torch.Tensor:


        dot_product = torch.sum(x1 * x2, dim=1)
        norm_x1 = torch.norm(x1, p=2, dim=1)
        norm_x2 = torch.norm(x2, p=2, dim=1)

        cos_sim = dot_product / (norm_x1 * norm_x2 + self.eps)



        loss_pos = 1.0 - cos_sim
        loss_neg = F.relu(cos_sim - self.margin)


        loss = torch.where(target == 1, loss_pos, loss_neg)


        if self.reduction == 'mean':
            return loss.mean()
        elif self.reduction == 'sum':
            return loss.sum()
        else:
            return loss

class Model(nn.Module):
    def __init__(self, margin=0.5):
        super().__init__()
        self.op = CosineEmbeddingLossCustom(margin=margin, reduction='mean', eps=EPS)

    def forward(self, x1: torch.Tensor, x2: torch.Tensor, target: torch.Tensor) -> torch.Tensor:

        x1_flat = x1.view(x1.size(0), -1)
        x2_flat = x2.view(x2.size(0), -1)
        return self.op(x1_flat, x2_flat, target)

def get_inputs():

    x1 = torch.randn(N, C, H, W, dtype=torch.float32)
    x2 = torch.randn(N, C, H, W, dtype=torch.float32)


    target = torch.randint(0, 2, (N,), dtype=torch.float32) # 0 or 1
    target = torch.where(target == 0, torch.tensor(-1.0), torch.tensor(1.0))

    return [x1, x2, target]

def get_init_inputs():
    return [0.5] # margin