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.

This CUDA kernel implements a Combo Loss function combining Dice Loss and Focal Loss with advanced parallel reduction techniques:

Key Optimizations:
Numerically Stable Sigmoid: Implements stable sigmoid for both positive and negative inputs using exp(-|x|) to avoid overflow.

Stable Log-Sigmoid: Uses different formulas for positive/negative inputs to maintain numerical precision.

Parallel Reduction with Shared Memory: Each thread block processes one batch sample, using shared memory reduction to sum across feature dimensions:

Local accumulation in registers

Store to shared memory arrays

Tree reduction (for (int s = blockDim.x / 2; s > 0; s >>= 1))

Thread 0 writes final reduced values

Computational Components (per batch sample):
Dice Loss Components:

inter = Σ(p * y) (intersection)

sum_inputs = Σ(p)

sum_targets = Σ(y)

Later computed as: dice = (2*inter + smooth) / (sum_inputs + sum_targets + smooth)

Focal Loss Components:

Computes BCE loss with focal weighting: focal_weight * bce

pt = exp(-bce) (probability of correct classification)

focal_weight = (1 - pt)^gamma

Performance Characteristics:
Double Precision: Uses double for higher numerical accuracy

Batch-Level Parallelism: Each block processes one batch element independently

Feature-Level Parallel Reduction: Threads within block sum across feature dimensions

Multiple Outputs: Computes 4 intermediate values per batch sample concurrently

Final Loss Computation:
L = α * dice_loss + (1 - α) * focal_loss

Where:

dice_loss = 1 - mean(dice) (averaged across batch)

focal_loss = sum(focal_out) / (batch_size * feature_dim)

Advantages:
Avoids intermediate tensor creation between reductions

Fuses multiple loss computations into single kernel

Efficient shared memory utilization for reductions



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


class Model(nn.Module):
    def __init__(self, alpha_combo=0.5, gamma_focal=2.0, smooth=1.0):
        super().__init__()
        self.alpha_combo = alpha_combo
        self.gamma_focal = gamma_focal
        self.smooth = smooth

    def _dice_loss(self, inputs, targets) -> torch.Tensor:
        inputs = inputs.sigmoid()
        inputs = inputs.flatten(1)
        targets = targets.flatten(1)

        intersection = (inputs * targets).sum(dim=1)
        dice = (2.0 * intersection + self.smooth) / (inputs.sum(dim=1) + targets.sum(dim=1) + self.smooth)

        return 1.0 - dice.mean()

    def _focal_loss(self, inputs, targets) -> torch.Tensor:
        BCE_loss = F.binary_cross_entropy_with_logits(inputs, targets, reduction='none')
        pt = torch.exp(-BCE_loss)

        focal_loss = ((1.0 - pt) ** self.gamma_focal) * BCE_loss
        return focal_loss.mean()

    def forward(self, logits: torch.Tensor, targets: torch.Tensor) -> torch.Tensor:
        targets_f = targets.float()

        dice_loss = self._dice_loss(logits, targets_f)

        focal_loss = self._focal_loss(logits, targets_f)

        return self.alpha_combo * dice_loss + (1.0 - self.alpha_combo) * focal_loss


batch_size = 512
feature_dim = 128


def get_inputs():
    logits = torch.randn(batch_size, feature_dim, dtype=torch.float64)
    targets = torch.randint(0, 2, (batch_size, feature_dim), dtype=torch.float64)
    return [logits, targets]


def get_init_inputs():
    return [0.5, 2.0, 1.0]