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

Covariance/Variance Calculation: Statistical measure of joint variability between two variables

Vectorized Memory Access (float4): Uses 128-bit wide loads (4 floats) to improve memory bandwidth utilization

Instruction-Level Parallelism (ILP): Processes multiple float4 elements per loop iteration to hide instruction latency

Warp-Level Primitives: Uses __shfl_down_sync for efficient intra-warp reduction

Two-Stage Parallel Reduction: Combines warp-level reduction with shared memory and block-level reduction

Multi-Dimensional Grid Layout: Uses dim3(splits, N) for parallel processing across splits and batches

Five-Statistic Computation: Simultaneously calculates sum_x, sum_y, sum_xx, sum_yy, sum_xy in fused kernel

Dynamic Kernel Configuration: Calculates optimal split count based on GPU SM count and data size

Temporary Buffer Strategy: Uses pre-allocated buffer [N, 5] to store intermediate statistical results

Constant Memory/__ldg: Uses read-only data cache for improved memory access patterns

Atomic Operations (atomicAdd): Safely accumulates results from multiple thread blocks to temporary buffer

Fast Math Operations: Uses --use_fast_math compiler flag for optimized mathematical functions

Memory Coalescing: Optimized memory access patterns through contiguous tensor layout

Pointer Chasing Loop: Efficient main loop with ILP-unrolled memory access patterns

Tail Processing: Handles remaining elements after main vectorized loop

Covariance Formula Implementation: Computes covariance using computational formula: cov = sum_xy - nmean_xmean_y

Bias Correction: Supports both unbiased (n-1 divisor) and biased (n divisor) variance estimation

Numerical Stability: Handles zero divisor case to prevent division by zero

Buffer Zeroing: Clears temporary buffer before each forward pass

Device Query API: Uses cudaGetDevice and cudaDeviceGetAttribute for optimal kernel configuration

Shared Memory for Warp Results: Uses separate shared memory arrays for each statistical variable

Boundary Checking: Handles data size variations and split boundaries safely

Automatic Device Placement: Ensures tensors are on CUDA device

Statistical Flexibility: Can compute both covariance (between x and y) and variance (when x=y)

Efficient Mean Calculation: Computes means from accumulated sums for covariance computation

Comprehensive Statistical Infrastructure: Reuses Pearson correlation kernel for efficient covariance calculation

Batch Processing: Handles multiple samples concurrently with independent covariance calculations




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

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


class Covariance(nn.Module):


    def __init__(self, eps=1e-8, unbiased=True):
        super().__init__()
        self.unbiased = unbiased

    def forward(self, x, y):
        # 扁平化 x 和 y 从 (N, C, H, W) 到 (N, D)
        x_flat = x.reshape(x.size(0), -1)
        y_flat = y.reshape(y.size(0), -1)

        # 元素总数 D = C * H * W
        D = x_flat.size(1)

        # 1. 计算均值 (Mean)
        x_mean = x_flat.mean(dim=1, keepdim=True)
        y_mean = y_flat.mean(dim=1, keepdim=True)

        # 2. 居中化 (Centering)
        x_centered = x_flat - x_mean
        y_centered = y_flat - y_mean

        # 3. 计算协方差和 (Covariance Sum)
        # 结果维度: (N,)
        cov_sum = (x_centered * y_centered).sum(dim=1)

        # 4. 计算协方差 (除以 D 或 D-1)
        if self.unbiased:
            # 样本协方差
            divisor = D - 1
        else:
            # 总体协方差
            divisor = D

        if divisor <= 0:
            return cov_sum * 0.0

        return cov_sum / divisor


class Model(nn.Module):
    def __init__(self, unbiased=True):
        super().__init__()
        self.op = Covariance(unbiased=unbiased)

    def forward(self, x, y):
        return self.op(x, y)


def get_inputs():
    x = torch.randn(N, C, H, W, dtype=torch.float32)
    y = torch.randn(N, C, H, W, dtype=torch.float32)
    return [x, y]


def get_init_inputs():
    return []