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 Poly Loss function with a different optimization strategy compared to previous elementwise kernels:

Key Optimizations:
Per-Thread Row Processing: Each thread processes an entire row (sample) independently, handling all classes sequentially. This avoids inter-thread communication overhead.

Numerical Stability: Implements log-sum-exp trick to avoid overflow:

First computes row_max = max(logits)

Then computes sum_exp = sum(exp(logits - row_max))

Finally computes log_sum_exp = row_max + log(sum_exp)

Memory Access Pattern: Each thread accesses contiguous memory for its assigned row, enabling good cache utilization.

Computational Flow:
Max Reduction: Thread finds maximum logit value in its row

Softmax Computation: Computes stable softmax via log-sum-exp

Target Probability: Extracts probability of true class p_t = exp(logit_t - log_sum_exp)

Poly Loss: Combines cross-entropy with polynomial adjustment: L = CE + ε * (1 - p_t)

Differences from Previous Kernels:
No vectorization (float4) - each row has variable length (num_classes)

Two-pass reduction (max then sum) for numerical stability

Single output per thread (not per element)

Classifies by row index rather than elementwise processing

Performance Considerations:
Good for moderate batch sizes where threads have enough work

Memory access pattern is strided by num_classes for logits

Labels accessed as 1D array (efficient)

Final forward method returns mean of per-sample losses



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, epsilon=1.0):
        super().__init__()
        self.epsilon = epsilon
        self.ce_loss = nn.CrossEntropyLoss(reduction='none')

    def forward(self, logits: torch.Tensor, labels: torch.Tensor) -> torch.Tensor:
        l_ce = self.ce_loss(logits, labels)

        p = F.softmax(logits, dim=-1)

        p_t = p.gather(1, labels.unsqueeze(-1)).squeeze(-1)

        poly_loss = l_ce + self.epsilon * (1.0 - p_t)

        return poly_loss.mean()


batch_size = 128
feature_dim = 10


def get_inputs():
    logits = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    labels = torch.randint(0, feature_dim, (batch_size,), dtype=torch.long)
    return [logits, labels]


def get_init_inputs():
    return [1.0]