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.

Core Optimization Techniques:

Performance Optimizations

Vectorized Memory Access - Uses float4 to process 4 elements simultaneously

Two-Stage Reduction - Warp-level + block-level shared memory reduction

Grid Size Optimization - Replaces std::min with ternary operator

Loop Unrolling - #pragma unroll for instruction-level parallelism

Memory Optimizations

Memory Coalescing - Ensures contiguous memory access patterns

Partial Sums Reduction - Distributed inter-block reduction strategy

Vectorized I/O - Uses float4 for both forward and backward passes

Numerical Stability

Stable BCE Computation - Log-sum-exp trick to prevent numerical overflow

Double Precision - Uses double for intermediate calculations

Epsilon Protection - Prevents division by zero errors

Focal Loss Specific Optimizations

Modulating Factor - Efficient computation of (1 - p_t)^gamma

Alpha Balancing - Class-balanced weighting calculation

Complete Gradient - Full gradient including both BCE and modulating terms

Kernel Design

Separate Paths - Distinct handling of reduction vs non-reduction paths

Remainder Processing - Efficient handling of elements after vectorization

Multi-Reduction Support - Full support for 'none', 'mean', and 'sum' reductions

These optimizations enable maximum performance for focal loss computation while maintaining numerical stability.



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 FocalLoss(nn.Module):
    def __init__(self, reduction='mean', alpha=0.25, gamma=2.0):
        super().__init__()
        self.reduction = reduction
        self.alpha = float(alpha)
        self.gamma = float(gamma)
        self.epsilon = 1e-8

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

        bce_loss = F.binary_cross_entropy_with_logits(input, target, reduction='none')

        p = torch.sigmoid(input)

        p_t = p * target + (1 - p) * (1 - target)

        modulating_factor = (1.0 - p_t).pow(self.gamma)

        alpha_t = self.alpha * target + (1 - self.alpha) * (1 - target)

        loss = alpha_t * modulating_factor * bce_loss

        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', alpha=0.25, gamma=2.0):
        super().__init__()
        self.op = FocalLoss(reduction, alpha, gamma)

    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', 0.25, 2.0]