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.

Core Optimization Techniques:

Performance Optimizations

Double Precision Reduction - Uses double for accumulation to maintain numerical accuracy

Two-Stage Reduction - Warp-level shuffle reduction + block-level shared memory reduction

Parallel Sample Processing - Each CUDA block processes one sample (N-wise parallelization)

Grid Size Optimization - Limits grid size to MAX_GRID_SIZE for optimal resource usage

Memory Optimizations

Intermediate Storage - Stores dot products and norms for backward pass reuse

Memory Coalescing - Ensures contiguous memory access patterns

Shared Memory Reduction - Uses shared memory for efficient block-level reductions

Numerical Stability

Double Precision - All intermediate calculations use double to prevent precision loss

Epsilon Protection - Adds epsilon to denominators to prevent division by zero

Stable Cosine Similarity - Properly handles norm calculations with epsilon protection

Mathematical Optimizations

Efficient Cosine Distance - Computes 1 - cos_sim for angular distance

Analytical Gradients - Implements exact mathematical derivatives for cosine similarity:

grad_u_i = (cos_sim * u_i / norm_i_sq) - (v_i / norm_mult)

grad_v_i = (cos_sim * v_i / norm_t_sq) - (u_i / norm_mult)

Kernel Design

Separate Forward/Backward Kernels - Optimized kernels for each pass

Flexible Reduction Support - Handles 'none', 'mean', and 'sum' reduction types

Atomic Reduction - Uses atomicAdd for efficient multi-block reduction

Key Features

High Precision - Double precision ensures numerical accuracy for angular calculations

Efficient Gradient Computation - Reuses precomputed terms from forward pass

Proper Normalization - Correctly handles vector normalization in both forward and backward passes

Memory Efficient - Stores only necessary intermediate terms for gradients

This implementation provides highly accurate angular distance computation with proper gradient propagation, essential for metric learning and similarity-based tasks



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

N, D = 32, 64


class AngularDistance(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.reduction = reduction
        self.epsilon = 1e-6

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:

        dot_product = (input * target).sum(dim=1)

        norm_input = input.norm(p=2, dim=1)
        norm_target = target.norm(p=2, dim=1)

        norm_mult = norm_input * norm_target

        cosine_sim = dot_product / (norm_mult + self.epsilon)

        loss = 1.0 - cosine_sim

        if self.reduction == 'mean':
            return loss.mean()
        elif self.reduction == 'sum':
            return loss.sum()
        else:
            return loss


class Model(nn.Module):
    def __init__(self, reduction='mean', beta=1.0):
        super().__init__()
        self.op = AngularDistance(reduction, beta)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        if isinstance(input, (list, tuple)) and len(input) > 0:
            input = input[0]
            target = target[0] if len(target) > 0 else target

        return self.op(input, target)


def get_inputs():
    input = torch.randn(N, D, dtype=torch.float32)
    target = torch.randn(N, D, dtype=torch.float32)
    return [input, target]


def get_init_inputs():
    return ['mean', 1.0]