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.

Technologies Used :

PyTorch: Deep learning framework.

CUDA: GPU acceleration for parallel computing.

C++/CUDA C++: High-performance kernel programming.

Inline C++/CUDA Extension (torch.utils.cpp_extension.load_inline): Just-In-Time (JIT) compilation of custom operators.

Fused Kernel: Combines multiple operations (logarithm, division, squaring, addition) into a single GPU kernel to reduce memory bandwidth and launch overhead.

Element-wise Parallelism: Each GPU thread handles an independent element of the input tensors.

Grid-Stride Loop: Efficiently processes data of arbitrary size using a fixed number of threads.

Math Operations: logf, fmaxf (fast math with --use_fast_math flag).

Tensor Contiguity Check: Ensures memory layout optimization.

Reduction Operations (Mean/Sum): Aggregates loss values in the kernel's C++ wrapper.

Memory Access Patterns: Uses __restrict__ keyword to hint at non-aliasing pointers for compiler optimization.

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
import math

# -------------------------------------------------------------
# 常量定义
# -------------------------------------------------------------
N_BATCH = 128
N_FEATURES = 512

# 损失函数参数
FULL = False
EPS = 1e-6
REDUCTION = 'mean'


# -------------------------------------------------------------

class Model(nn.Module):
    """
    nn.GaussianNLLLoss 的纯 PyTorch 基准实现
    """

    def __init__(self, full=False, eps=1e-6, reduction='mean'):
        super().__init__()
        self.full = full
        self.eps = eps
        self.reduction = reduction

        if self.full:
            self.const_term = 0.5 * math.log(2 * math.pi)
        else:
            self.const_term = 0.0

    def forward(self, input: torch.Tensor, target: torch.Tensor, var: torch.Tensor) -> torch.Tensor:

        # 1. 确保 var > eps。
        #    torch.clamp(min=...) 等价于 max(var, eps)
        var_clamped = torch.clamp(var, min=self.eps)

        # 2. 计算两个主要项
        term1_log = torch.log(var_clamped)
        term2_sq_err = (input - target).pow(2) / var_clamped

        # 3. 组合
        # (N, *) 形状
        loss_unreduced = 0.5 * (term1_log + term2_sq_err) + self.const_term

        # 4. 应用 Reduciton
        if self.reduction == 'mean':
            return loss_unreduced.mean()
        elif self.reduction == 'sum':
            return loss_unreduced.sum()
        else:  # 'none'
            return loss_unreduced


def get_inputs():
    """
    生成 (N, D) 形状的输入
    """
    input = torch.randn(N_BATCH, N_FEATURES, dtype=torch.float32)
    target = torch.randn(N_BATCH, N_FEATURES, dtype=torch.float32)

    # Var 必须是正数
    var = torch.rand(N_BATCH, N_FEATURES, dtype=torch.float32) + EPS

    return [input, target, var]


def get_init_inputs():
    return [FULL, EPS, REDUCTION]

