You write custom CUDA kernels to replace the pytorch operators in the given GeGLU 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 chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.

Here are the key optimization techniques implemented in this CUDA Dice Loss code, suitable for AI-generated code recognition:

Performance Optimizations:

Custom CUDA Kernel Implementation - Full forward/backward passes implemented in CUDA for maximum performance

Warp-Level Reduction - Uses warp_reduce_sum_double with __shfl_down_sync for efficient intra-warp reductions

Block-Level Reduction - Implements block_reduce_sum_double using shared memory for inter-warp reductions

Memory Coalescing - Ensures contiguous memory access patterns through contiguous() calls

Grid Size Optimization - Limits grid size to MAX_GRID_SIZE (4096) to prevent excessive resource usage

Compiler Optimizations - Uses -O3 flag for aggressive CUDA compiler optimization

Inline Compilation - Compiles CUDA code directly within Python using load_inline

Memory Optimizations:

Double Precision for Accumulation - Uses double for intermediate sums to maintain numerical precision

Shared Memory Utilization - Employs shared memory (s_data[3]) for block-level reductions

Intermediate Storage - Stores intersection and sum terms (hp_terms) during forward pass for backward reuse

In-Place Operations - Avoids unnecessary memory allocations in backward pass

Numerical Stability:

Epsilon Handling - Adds small epsilon (1e-6) to denominators to prevent division by zero

Sigmoid Stabilization - Computes sigmoid via 1.0f/(1.0f + expf(-p_logit)) for numerical stability

Gradient Scaling - Properly scales gradients based on reduction type in backward pass

Parallelization Strategy:

NC Parallelization - Processes each (batch, channel) combination in parallel in forward pass

Element-Wise Parallelization - Parallelizes over all elements in backward pass

Block Configuration - Uses BLOCK_SIZE=256 threads per block for optimal occupancy

API Design Optimizations:

Reduction Flexibility - Supports 'none', 'mean', and 'sum' reduction types

Type Safety - Automatically handles dtype conversion between input and target

Gradient Computation - Computes gradients for both input and target tensors

These optimizations collectively provide high-performance Dice loss computation suitable for training segmentation models with large batch sizes and high-resolution inputs.


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, 1, 64, 64


class DiceLoss(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.reduction = reduction
        self.epsilon = 1e-6

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

        probs = torch.sigmoid(input)

        dims = tuple(range(2, input.dim()))

        intersection = (probs * target).sum(dim=dims)
        denominator = probs.sum(dim=dims) + target.sum(dim=dims)

        dice_coeff = (2. * intersection + self.epsilon) / (denominator + self.epsilon)

        loss = 1. - dice_coeff

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


class Model(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.op = DiceLoss(reduction, beta)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        if isinstance(input, (list, tuple)) and len(input) > 0:
            input = input[0]
            target = target[0] if len(target) > 0 else target

        return self.op(input, target)


def get_inputs():
    input = torch.randn(N, C, H, W, dtype=torch.float32)
    target = torch.randint(0, 2, (N, C, H, W), dtype=torch.float32)
    return [input, target]


def get_init_inputs():
    return ['mean', 1.0]
