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 code implements CenterNet loss with CUDA optimizations:

Multi-kernel design - Separate kernels for heatmap loss and regression losses (width/height + offset).

Global buffer accumulation - Uses global memory buffer (5 floats) to accumulate partial sums from all threads.

Warp reduction + atomic addition - Combines warp-level reduction with atomic adds for thread-safe accumulation.

Custom focal loss variant - Implements modified focal loss with positive/negative term separation.

Masked regression loss - Only computes loss where mask=1 (valid positions).

Numerical stability - Clips predictions to [1e-6, 0.999999] to avoid log(0) issues.

Weighted negative samples - Applies (1-t)^4 weighting for negative samples in heatmap loss.

Grid-stride loops - Threads process multiple elements with stride for load balancing.

Final weighted combination - Combines heatmap loss + 0.1×WH loss + 1.0×reg loss in final kernel.

Memory efficiency - Reuses same kernel for both WH and regression losses with output index parameter.

Batch processing - Handles batched predictions with spatial dimensions.



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


class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()

    def forward(self, pred_hm, gt_hm, pred_wh, gt_wh, pred_reg, gt_reg, mask):
        pred_hm = torch.clamp(pred_hm, 1e-6, 1 - 1e-6)

        pos_inds = gt_hm.eq(1).float()
        neg_inds = gt_hm.lt(1).float()
        neg_weights = torch.pow(1 - gt_hm, 4)

        pos_loss = torch.log(pred_hm) * torch.pow(1 - pred_hm, 2) * pos_inds
        neg_loss = torch.log(1 - pred_hm) * torch.pow(pred_hm, 2) * neg_weights * neg_inds

        num_pos = pos_inds.sum()
        pos_loss_sum = pos_loss.sum()
        neg_loss_sum = neg_loss.sum()

        if num_pos > 0:
            hm_loss = -(pos_loss_sum + neg_loss_sum) / num_pos
        else:
            hm_loss = -neg_loss_sum

        mask_expanded = mask.expand_as(pred_wh)
        wh_loss = torch.sum(torch.abs(pred_wh - gt_wh) * mask_expanded)
        reg_loss = torch.sum(torch.abs(pred_reg - gt_reg) * mask_expanded)

        if num_pos > 0:
            wh_loss = wh_loss / num_pos
            reg_loss = reg_loss / num_pos

        return hm_loss + 0.1 * wh_loss + 1.0 * reg_loss


batch_size = 4
channels = 4
height = 128
width = 128


def get_inputs():
    pred_hm = torch.sigmoid(torch.randn(batch_size, channels, height, width))
    gt_hm = torch.bernoulli(torch.full((batch_size, channels, height, width), 0.1))
    pred_wh = torch.randn(batch_size, 2, height, width)
    gt_wh = torch.randn(batch_size, 2, height, width)
    pred_reg = torch.randn(batch_size, 2, height, width)
    gt_reg = torch.randn(batch_size, 2, height, width)
    mask = torch.bernoulli(torch.full((batch_size, 1, height, width), 0.1))
    return [pred_hm, gt_hm, pred_wh, gt_wh, pred_reg, gt_reg, mask]


def get_init_inputs():
    return []