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 Quantile Loss function with the same core optimizations as previous kernels, plus memory access enhancements for dual inputs:

Vectorized Memory Operations: Uses float4 loads/stores to process 4 elements per instruction from both y_pred and y_true tensors, improving memory bandwidth utilization.

Coalesced Memory Access: Threads access contiguous memory locations via vectorized operations, enabling efficient memory coalescing for both input tensors.

Fast Math & Loop Unrolling: Compiler flags enable fast approximate math and implicit loop unrolling improves instruction-level parallelism.

Performance Characteristics:

The conditional branch (if (diff > 0.0f)) may cause thread divergence within warps, potentially reducing parallelism efficiency when threads in the same warp process both positive and negative differences.

Efficient handling of two input tensors with aligned memory access patterns.

Final Operation: The forward method returns the mean of the elementwise losses, completing the quantile loss computation.



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, tau=0.5):
        super().__init__()
        self.tau = tau

    def forward(self, y_pred: torch.Tensor, y_true: torch.Tensor) -> torch.Tensor:
        diff = y_true - y_pred

        loss = torch.where(diff > 0, self.tau * diff, (self.tau - 1.0) * diff)

        return loss.mean()


batch_size = 128
feature_dim = 512


def get_inputs():
    y_pred = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    y_true = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    return [y_pred, y_true]


def get_init_inputs():
    return [0.