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 Diversity Loss function with a hybrid CPU-GPU approach:

CUDA Kernel Optimizations:
Vectorized Elementwise Square: Uses float4 loads/stores to square 4 elements per instruction, improving memory bandwidth utilization for the similarity matrix S.

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

Simple Computation: Just performs v * v per element - very lightweight operation.

Overall Pipeline (Hybrid):
CPU: Compute similarity matrix S = embeddings @ embeddings.T (matrix multiplication)

GPU: Square each element of S (S_sq[i] = S[i] * S[i]) using vectorized CUDA kernel

CPU: Extract off-diagonal elements using mask (~torch.eye(N, dtype=bool))

CPU: Compute mean of off-diagonal squared similarities

Performance Considerations:
Bottleneck: Matrix multiplication embeddings @ embeddings.T is likely more expensive than the elementwise squaring

Memory Usage: Creates full N × N similarity matrix (O(N²) memory)

CPU-GPU Transfers: Similarity matrix stays on GPU for squaring, then off-diagonal extraction happens on CPU

Loss Computation:
L = mean(S[i,j]²) for all i ≠ j (encourages orthogonality/uncorrelation between different embeddings)

Potential Improvement:
Could compute squared off-diagonal sum directly in CUDA to avoid creating full S_sq matrix and CPU masking operations.


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):
        super().__init__()

    def forward(self, embeddings: torch.Tensor) -> torch.Tensor:
        S = torch.matmul(embeddings, embeddings.transpose(0, 1))
        N = embeddings.size(0)

        S_sq = S.pow(2)

        M_diag = torch.eye(N, dtype=torch.bool, device=embeddings.device)

        S_off_diag_sq = S_sq.masked_select(~M_diag)

        return S_off_diag_sq.mean()


batch_size = 128
feature_dim = 512


def get_inputs():
    embeddings = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    embeddings = F.normalize(embeddings, p=2, dim=1)
    return [embeddings]


def get_init_inputs():
    return []