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.
Custom CUDA kernel extension via torch.utils.cpp_extension.load_inline

Variational information distillation (VID) loss computation (Gaussian negative log-likelihood)

Element-wise parallelization using fixed block size (256 threads)

NLL formula: log(variance) + (target - mean)² / variance

Numerical stability with small epsilon added to variance

Contiguous tensor handling for memory coalescing

Dynamic grid sizing based on element count

Mean reduction across all elements

Logarithmic computation via logf for variance term




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):
        super(Model, self).__init__()

    def forward(self, pred_mean, pred_var, target):
        loss = torch.log(pred_var) + (target - pred_mean).pow(2) / (pred_var + 1e-6)
        return loss.mean()

batch_size = 32
feature_dim = 128

def get_inputs():
    m = torch.randn(batch_size, feature_dim, requires_grad=True)
    v = torch.abs(torch.randn(batch_size, feature_dim, requires_grad=True)) + 0.1
    t = torch.randn(batch_size, feature_dim)
    return [m, v, t]

def get_init_inputs():
    return []