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 Fast Average Precision (FastAP) loss with CUDA optimizations:

Shared memory caching - Stores query vector and histogram bins in shared memory for fast access.

Per-sample parallelism - One CUDA block processes all comparisons for a single query (batch_size blocks).

Distance binning with soft assignment - Uses triangular kernel for soft histogram assignment (weight = 1 - |dist-center|/width).

Vectorized distance computation - 4-wide unrolled loop for efficient Euclidean distance calculation.

Parallel histogram accumulation - Uses atomicAdd for thread-safe updates to positive/negative histograms.

Cumulative precision calculation - Sequential scan over bins to compute AP using CDFs of positive/negative distributions.

Batch normalization integration - Input vectors are L2-normalized before computation.

Numerical stability - Adds 1e-10 to denominators to prevent division by zero.

Shared memory layout - Efficiently allocates: query vector, positive histogram, negative histogram.

Simplified AP computation - Approximates Average Precision through histogram-based precision-recall calculation.




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, num_bins=10):
        super(Model, self).__init__()
        self.num_bins = num_bins
        self.max_dist = 4.0

    def forward(self, x: torch.Tensor, labels: torch.Tensor) -> torch.Tensor:
        x = F.normalize(x, p=2, dim=1)

        dist = torch.cdist(x, x, p=2).pow(2)

        width = self.max_dist / self.num_bins
        centers = torch.linspace(width / 2, self.max_dist - width / 2, self.num_bins, device=x.device)

        d = dist.unsqueeze(-1)
        c = centers.view(1, 1, -1)

        bin_weights = torch.relu(1.0 - torch.abs(d - c) / width)

        eq_labels = labels.unsqueeze(1) == labels.unsqueeze(0)
        diag_mask = torch.eye(x.size(0), device=x.device, dtype=torch.bool)

        pos_mask = eq_labels & (~diag_mask)
        neg_mask = (~eq_labels) & (~diag_mask)

        pos_hist = (bin_weights * pos_mask.unsqueeze(-1)).sum(dim=1)
        neg_hist = (bin_weights * neg_mask.unsqueeze(-1)).sum(dim=1)

        pos_cdf = torch.cumsum(pos_hist, dim=1)
        neg_cdf = torch.cumsum(neg_hist, dim=1)

        precision = pos_cdf / (pos_cdf + neg_cdf + 1e-10)

        total_pos = pos_cdf[:, -1].unsqueeze(1) + 1e-10
        delta_recall = pos_hist / total_pos

        ap = (precision * delta_recall).sum(dim=1)

        return 1.0 - ap.mean()


batch_size = 128
input_dim = 1024
num_classes = 32


def get_inputs():
    x = torch.randn(batch_size, input_dim)
    labels = torch.randint(0, num_classes, (batch_size,))
    return [x, labels]


def get_init_inputs():
    return []