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 (tsallis_divergence_kernel)

CUDA Math Functions: powf() for floating-point exponentiation

Parallel Reduction: Tree-based reduction using shared memory

Shared Memory: Using __shared__ for inter-thread communication

Block-Level Parallelism: One CUDA block per batch element

Grid-Stride Loops: Efficient memory access within each row

Mathematical Components
Tsallis Divergence: Non-extensive entropy-based divergence measure

Power Operations: powf(p, q) * powf(q_dist, 1-q) formulation

Linear Normalization: (sum - 1) / (q - 1) scaling

Statistical Distance: Measures difference between probability distributions

q-Parameter: Controls divergence properties (q ≠ 1)

Memory & Parallelism Patterns
Per-Batch Block Assignment: One CUDA block processes one batch element

Shared Memory Reduction: Tree reduction within thread blocks

Row-Wise Processing: Threads parallelize across class dimensions within rows

Batch Independence: Parallel processing across batch dimension

Optimization Techniques
Grid-Stride Loops: Threads process multiple elements within their assigned row

Shared Memory Efficiency: Single buffer for intermediate sums

Fused Computation: Complete Tsallis divergence calculation per batch element

Numerical Stability: Linear scaling after summation

Coalesced Memory Access: Sequential memory access patterns

Performance Features
Massive Parallelization: GPU acceleration for divergence computation

Memory Efficiency: Shared memory reuse for reduction operations

Scalable Design: Efficient for varying batch sizes and class counts

Minimal Synchronization: Single __syncthreads() call per reduction

Batch Mean Computation: Final averaging performed on CPU

Unique Implementation Aspects
q-Parameter Naming: Note: Uses q_param (not to confuse with input q tensor)

Linear Scaling: Tsallis divergence uses linear rather than logarithmic scaling

Power Product: Similar to Rényi but with different normalization

Per-Sample Output: Each batch element gets its own divergence value

Non-Extensive Statistics: Based on Tsallis entropy formulation

Comparison with Similar Divergences
vs Rényi: Uses linear (sum-1)/(q-1) instead of logarithmic log(sum)/(q-1)

vs Alpha Divergence: Similar power structure but different normalization

Parameter Range: Typically q > 0, q ≠ 1 for proper divergence definition






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, q=0.5):
        super(Model, self).__init__()
        self.q = q

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

        sum_term = torch.sum((p_prob ** self.q) * (q_prob ** (1.0 - self.q)), dim=1)
        loss = (sum_term - 1.0) / (self.q - 1.0)

        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 [0.5]