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 an Angular Loss function with shared memory parallel reduction, similar to the Combo Loss but with different mathematical components:

Key Optimizations:
Numerically Stable Sigmoid & Log-Sigmoid: Same stable implementations as Combo Loss using exp(-|x|) to avoid overflow.

Parallel Reduction with Shared Memory: Each thread block processes one batch sample using tree reduction in shared memory:

Local accumulation in registers

Shared memory arrays for three values: inter, union, bce

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

Thread 0 writes final reduced values

Computational Components (per batch sample):
Intersection: inter = Σ(p * y) where p = sigmoid(z)

Union: union = Σ(p + y) (sum of predictions and targets)

BCE Loss: bce = -[y*log(p) + (1-y)*log(1-p)] using stable log-sigmoid

Angular Loss Computation (in Python forward):
Angle Metric: angle = 1 - (2*inter + smooth) / (union + smooth)

Similar to Dice but with different normalization

Angular Loss: angular_loss = mean(angle * (1 - angle))

Quadratic penalty that peaks at angle=0.5

BCE Loss: bce_loss = sum(bce) / (batch_size * feature_dim)

Final Loss:
L = α * angular_loss + (1 - α) * bce_loss

Performance Characteristics:
Double Precision: Uses double for numerical accuracy in angle calculations

Batch-Level Parallelism: Each block processes one batch element

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

Three Concurrent Reductions: Computes intersection, union, and BCE simultaneously

Advantages:
Avoids intermediate tensor creation

Fuses multiple computations into single kernel

Efficient shared memory utilization

Numerically stable operations for extreme values


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=0.5, smooth=1e-6):
        super().__init__()
        self.alpha = alpha
        self.smooth = smooth

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

        probs = logits.sigmoid()
        probs = probs.flatten(1)
        targets_f = targets_f.flatten(1)

        intersection = (probs * targets_f).sum(dim=1)
        union = probs.sum(dim=1) + targets_f.sum(dim=1)

        angle = 1.0 - (2.0 * intersection + self.smooth) / (union + self.smooth)
        angular_loss = (angle * (1.0 - angle)).mean()

        bce_loss = F.binary_cross_entropy_with_logits(logits, targets_f, reduction='mean')

        return self.alpha * angular_loss + (1.0 - self.alpha) * bce_loss


batch_size = 128
feature_dim = 64

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, 1e-6]