Write a custom CUDA kernel to optimize `torch.nn.MultiLabelMarginLoss`.

The original operation is defined by the formula:
`loss(x, y) = sum_{j,i} max(0, 1 - (x[y[j]] - x[i])) / (x.size(0) * x.size(1))`
where `y[j]` are the positive class indices for a sample and `i` are the negative class indices. This is computed per sample and then reduced.

**Problem Analysis:**
`MultiLabelMarginLoss` is notoriously difficult to vectorize efficiently in PyTorch. The performance bottlenecks are severe:
1.  **Irregular Data Access**: Each sample has a variable number of positive labels defined in `y`, which are padded with -1. Identifying the set of positive and negative classes for each sample requires complex, non-vectorized logic (e.g., masks, loops, or boolean indexing), which is slow.
2.  **Massive Intermediate Tensors**: A naive vectorized approach would require gathering scores for positive classes and broadcasting them for subtraction against scores of negative classes. This would create huge intermediate tensors and is highly memory-inefficient.
3.  **Complex Nested Loop Logic**: The core formula is a nested loop (`for each positive class`, `for each negative class`) for every sample, which is antithetical to efficient GPU execution without a custom kernel.

**Optimization Strategy: Fused Block-Level Parallelism with Shared Memory Caching**

The strategy is to implement the entire complex logic within a single CUDA kernel, using a block-per-sample parallelization model.

1.  **Parallelization Model**: A grid of `N` blocks is launched, where `N` is the batch size. Each thread block is assigned to compute the total loss for one sample.

2.  **Shared Memory Caching**: For each sample (block), the kernel first collaboratively reads the list of positive class indices from the `target` tensor. These indices (and their count) are cached in **shared memory**. This makes the critical metadata for the sample instantly accessible to all threads in the block.

3.  **Fused Computation Loop**: The threads within a block then work together to iterate through all `C` possible classes. For each class `i`, a thread checks if it's a positive or negative class using the cached shared memory data.
    *   If `i` is a negative class, the thread then iterates through the *positive class indices cached in shared memory*.
    *   For each positive-negative pair, it calculates the hinge loss term `max(0, 1 - (x_pos - x_neg))` and accumulates it into a thread-local register. This fuses the nested loops, indexing, subtraction, and `max` operations.

4.  **Efficient Intra-Block Reduction**: Once all classes are processed, a fast parallel reduction is performed using shared memory to sum the partial results from all threads within the block into a single total loss for that sample.

5.  **Finalization**: The first thread of each block performs the final division and writes the result to the output tensor. The kernel directly produces the per-sample losses (`reduction='none'`). The final batch reduction (`'mean'` or `'sum'`) is efficiently handled by a single PyTorch call on the small 1D output tensor.

This approach transforms the complex, memory-bound, and hard-to-vectorize PyTorch operation into a single, efficient, compute-focused CUDA kernel.
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
```python
import torch
import torch.nn as nn
import numpy as np

BATCH_SIZE = 512
NUM_CLASSES = 1024
REDUCTION = 'mean'
# 每个样本的正类标签数量范围
MIN_LABELS = 1
MAX_LABELS = 10

class Model(nn.Module):
    def __init__(self, reduction='mean'):
        super(Model, self).__init__()
        self.loss_fn = nn.MultiLabelMarginLoss(reduction=reduction)
    
    def forward(self, input_tensor: torch.Tensor, target_tensor: torch.Tensor) -> torch.Tensor:
        return self.loss_fn(input_tensor, target_tensor)

def get_inputs():
    input_tensor = torch.randn(BATCH_SIZE, NUM_CLASSES, dtype=torch.float32)
    
    # target每行包含正类索引，并用 -1 填充
    target_np = np.full((BATCH_SIZE, NUM_CLASSES), -1, dtype=np.int64)
    for i in range(BATCH_SIZE):
        num_labels = np.random.randint(MIN_LABELS, MAX_LABELS + 1)
        labels = np.random.choice(NUM_CLASSES, num_labels, replace=False)
        target_np[i, :num_labels] = labels
    target_tensor = torch.from_numpy(target_np)

    return [input_tensor.contiguous(), target_tensor.contiguous()]

def get_init_inputs():
    return [REDUCTION]