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.
Technologies Used in This Code
Core Libraries & Frameworks
PyTorch: Deep learning framework

CUDA: NVIDIA's parallel computing platform for GPU acceleration

C++: For high-performance kernel implementation

PyTorch Specific Components
torch.nn.Module: Base class for neural network modules

torch.nn.functional.F.softmax: Softmax activation function

torch.utils.cpp_extension.load_inline: For inline compilation of CUDA/C++ extensions

PyTorch Tensors: Multi-dimensional arrays with automatic differentiation

CUDA/C++ Implementation Details
CUDA Kernels: Custom GPU kernel (bregman_divergence_kernel)

CUDA Math Functions: logf() for logarithmic computations

Parallel Reduction: Tree-based reduction using shared memory

Shared Memory: Using __shared__ for inter-thread communication

Atomic Operations: atomicAdd for thread-safe global updates

Grid-Stride Loops: Efficient memory access pattern

Mathematical Components
Bregman Divergence: General class of divergence measures

Convex Function: Using F(x) = x * log(x) (negative entropy)

Gradient Term: dF(q) = 1 + log(q) derivative

Three-Term Formula: F(p) - F(q) - dF(q) * (p - q)

Numerical Stability: Epsilon (eps) to prevent log(0)

Statistical/Information Theory Components
KL Divergence Special Case: This implementation reduces to KL divergence when F(x)=x*log(x)

Convexity Properties: Based on convex function properties

Information Geometry: Measures distance in statistical manifolds

Entropy-Based: Built on negative entropy convex function

Optimization Techniques
Shared Memory Reduction: Parallel tree reduction within thread blocks

Grid-Stride Loops: Efficient handling of arbitrary tensor sizes

Numerical Stability: Epsilon addition to log arguments

Fused Computation: Complete Bregman divergence calculation in single kernel

Batch Processing: Mean computation across batch dimension

Performance Features
Massive Parallelization: GPU acceleration for divergence computation

Memory Efficiency: Shared memory for intermediate reduction results

Numerical Safety: Protected against log(0) with epsilon

Atomic Operations: Safe parallel accumulation across thread blocks

Host-Device Coordination: Final batch averaging on CPU

Unique Implementation Aspects
Three-Term Bregman Formula: Explicit implementation of general form

Convex Function Specification: Uses negative entropy F(x) = x*log(x)

Derivative Computation: Analytic gradient calculation

Epsilon Protection: Numerical stability for probability distributions

General Framework: Can be extended to other convex functions

Comparison with Other Divergences
Generalization: Bregman divergences generalize many other divergences

Convexity Requirement: Requires specification of convex function F

Geometric Interpretation: Measures distance via convex function difference

Information-Theoretic: This specific instance is KL divergence equivalent




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, eps=1e-8):
        super(Model, self).__init__()
        self.eps = eps

    def forward(self, p, target):
        p_prob = F.softmax(p, dim=1)
        q_prob = F.softmax(target, dim=1)

        f_p = p_prob * torch.log(p_prob + self.eps)

        f_q = q_prob * torch.log(q_prob + self.eps)

        df_q = 1.0 + torch.log(q_prob + self.eps)

        term3 = df_q * (p_prob - q_prob)

        divergence = f_p - f_q - term3

        loss = torch.sum(divergence, dim=1)
        return loss.mean()


batch_size = 32
num_classes = 1000


def get_inputs():
    p = torch.randn(batch_size, num_classes, requires_grad=True)
    target = torch.randn(batch_size, num_classes)
    return [p, target]


def get_init_inputs():
    return []