You write custom CUDA kernels to replace the PyTorch operators in the given Pairwise Euclidean Distance 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 the combined broadcasting subtraction and L2 norm operators with a custom CUDA kernel (considering operator fusion opportunities to combine the element-wise difference calculation, sum of squares, and square root into a single kernel) or adjust algorithms for better performance. You are only limited by your imagination.

Here's an example to show you the syntax of inline embedding custom CUDA operators in PyTorch (for reference of code structure, not functional alignment):
The example given architecture (fma structure):
import torch
import torch.nn as nn

class Model(nn.Module):

    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, a: torch.Tensor, b: torch.Tensor, c: torch.Tensor, activation: str = 'relu') -> torch.Tensor:

        fma_out = a * b + c
        if activation == 'relu':
            output = torch.relu(fma_out)
        elif activation == 'sigmoid':
            output = torch.sigmoid(fma_out)
        else:
            raise ValueError("Unsupported activation. Use 'relu' or 'sigmoid'")
        return output

N = 2048  # Rows
M = 2048  # Columns

def get_inputs():
    a = torch.randn(N, M)
    b = torch.randn(N, M)
    c = torch.randn(N, M)
    return [a, b, c]

def get_init_inputs():
    return []


The example new arch with custom CUDA kernels (sample structure):
import torch
from torch.utils.cpp_extension import load_inline

# CUDA source for fused FMA + Activation
fma_activation_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <math.h>

__global__ void fma_relu_kernel(
    const float* __restrict__ a,
    const float* __restrict__ b,
    const float* __restrict__ c,
    float* __restrict__ output,
    int total_elements
) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (idx < total_elements) {
        // Fused multiply-add with ReLU activation
        float fma_result = a[idx] * b[idx] + c[idx];
        output[idx] = fmaxf(0.0f, fma_result);  // ReLU
    }
}

// Kernel for fused FMA + Sigmoid
__global__ void fma_sigmoid_kernel(
    const float* __restrict__ a,
    const float* __restrict__ b,
    const float* __restrict__ c,
    float* __restrict__ output,
    int total_elements
) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (idx < total_elements) {
        // Fused multiply-add with Sigmoid activation
        float fma_result = a[idx] * b[idx] + c[idx];
        // Fast sigmoid approximation: 1 / (1 + exp(-x))
        output[idx] = 1.0f / (1.0f + expf(-fma_result));
    }
}

torch::Tensor fma_activation_cuda(
    torch::Tensor a,
    torch::Tensor b,
    torch::Tensor c,
    std::string activation = "relu"
) {
    TORCH_CHECK(a.is_cuda() && a.is_contiguous());
    TORCH_CHECK(b.is_cuda() && b.is_contiguous());
    TORCH_CHECK(c.is_cuda() && c.is_contiguous());
    TORCH_CHECK(a.sizes() == b.sizes() && a.sizes() == c.sizes());
    TORCH_CHECK(a.dim() == 2);

    int N = a.size(0);
    int M = a.size(1);
    int total_elements = N * M;
    
    auto output = torch::empty_like(a);

    // Use 1D grid for element-wise operations
    int block_size = 256;
    int grid_size = (total_elements + block_size - 1) / block_size;

    if (activation == "relu") {
        fma_relu_kernel<<<grid_size, block_size>>>(
            a.data_ptr<float>(),
            b.data_ptr<float>(),
            c.data_ptr<float>(),
            output.data_ptr<float>(),
            total_elements
        );
    } else if (activation == "sigmoid") {
        fma_sigmoid_kernel<<<grid_size, block_size>>>(
            a.data_ptr<float>(),
            b.data_ptr<float>(),
            c.data_ptr<float>(),
            output.data_ptr<float>(),
            total_elements
        );
    } else {
        TORCH_CHECK(false, "Unsupported activation. Use 'relu' or 'sigmoid'");
    }
    
    return output;
}
"""

fma_activation_cpp_source = """
torch::Tensor fma_activation_cuda(
    torch::Tensor a,
    torch::Tensor b,
    torch::Tensor c,
    std::string activation = "relu"
);
"""

# Compile module
fma_activation_module = load_inline(
    name="fma_activation",
    cpp_sources=fma_activation_cpp_source,
    cuda_sources=fma_activation_source,
    functions=["fma_activation_cuda"],
    verbose=True,
    extra_cuda_cflags=["-O3", "--use_fast_math"]
)

class ModelNew(torch.nn.Module):
    def __init__(self):
        super(ModelNew, self).__init__()
        self.fma_activation = fma_activation_module

    def forward(self, a, b, c, activation='relu'):
        if not a.is_contiguous(): a = a.contiguous()
        if not b.is_contiguous(): b = b.contiguous()
        if not c.is_contiguous(): c = b.contiguous()
        return self.fma_activation.fma_activation_cuda(a, b, c, activation)
