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 optimized mutual information calculation with:

Memory Optimization:

Fixed 32×32 histogram in shared memory (4KB)

Vectorized memory access using float4 for 4x bandwidth

Shared memory for marginals and reduction buffers

Parallelization Strategy:

One block per batch sample

256 threads per block optimal configuration

Warp-level reduction for min/max/sum operations

Parallel histogram binning with atomic operations

Computational Optimization:

Efficient min/max reduction using warp shuffles

Vectorized range calculation for normalization

Double precision for MI summation to maintain accuracy

Epsilon stabilization to prevent log(0)

Work Distribution:

Threads process 4-element vectors via float4

Residual elements handled by thread 0

Parallel marginal probability computation

Final MI reduction across warps

The implementation efficiently handles histogram construction and MI calculation entirely in shared memory with optimized parallel reductions.







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, bins=32, sigma=0.1):
        super().__init__()
        self.bins = bins

    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        b, n = x.shape

        # Min-Max Normalization per sample
        min_x = x.min(dim=1, keepdim=True)[0]
        max_x = x.max(dim=1, keepdim=True)[0]
        min_y = y.min(dim=1, keepdim=True)[0]
        max_y = y.max(dim=1, keepdim=True)[0]

        x_norm = (x - min_x) / (max_x - min_x + 1e-6)
        y_norm = (y - min_y) / (max_y - min_y + 1e-6)

        # Quantize
        x_bin = torch.clamp((x_norm * self.bins).long(), 0, self.bins - 1)
        y_bin = torch.clamp((y_norm * self.bins).long(), 0, self.bins - 1)

        # Joint Histogram
        joint_idx = x_bin * self.bins + y_bin
        # (B, bins^2)
        hist = torch.zeros(b, self.bins * self.bins, device=x.device, dtype=torch.float32)
        ones = torch.ones_like(joint_idx, dtype=torch.float32)
        hist.scatter_add_(1, joint_idx, ones)

        # Normalize to probability
        p_xy = hist / n
        p_xy = p_xy.view(b, self.bins, self.bins)

        # Marginals
        p_x = p_xy.sum(dim=2)  # (B, bins)
        p_y = p_xy.sum(dim=1)  # (B, bins)

        # Mutual Information: sum p_xy * log(p_xy / (p_x * p_y))
        # Add eps to avoid log(0)
        eps = 1e-12
        p_x_p_y = torch.bmm(p_x.unsqueeze(2), p_y.unsqueeze(1))  # (B, bins, bins)

        mi = p_xy * torch.log((p_xy + eps) / (p_x_p_y + eps))
        return mi.sum(dim=(1, 2))


batch_size = 128
feature_dim = 512


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


def get_init_inputs():
    return [32]