cuda-l2-kernel-optimization

name	cuda-l2-kernel-optimization
title	CUDA-L2: Surpassing cuBLAS via Reinforcement Learning for Matrix Multiplication
version	0.0.2
engine	skillxiv-v0.0.2-claude-opus-4.6
license	MIT
url	https://arxiv.org/abs/2512.02551
keywords	["cuda-optimization","reinforcement-learning","kernel-tuning","matrix-multiplication","systems-ml"]
description	Uses LLMs with RL to automatically optimize HGEMM CUDA kernels across 1,000 configurations, systematically outperforming NVIDIA's cuBLAS and cuBLASLt through continued pretraining, general RL, and specialized HGEMM RL stages.

Summary

CUDA-L2 combines large language models with reinforcement learning to automatically optimize Half-precision General Matrix Multiply (HGEMM) CUDA kernels. The system employs a three-stage training approach: continued pretraining on diverse CUDA code, general kernel RL training, and specialized HGEMM RL training using execution speed as the reward signal.

Core Technique

Multi-Stage LLM Training:

1. Continued Pretraining: Fine-tune LLM on high-quality CUDA kernel code to understand optimization patterns
2. General RL: Teach the model to generate working kernels and improve via speed rewards
3. Specialized HGEMM RL: Focus RL on matrix multiplication variants and configurations

Kernel Generation: The LLM generates complete CUDA kernel source code as text. Each generation is compiled, executed, and evaluated on speed.

Reward Signal: Execution time on representative workloads:

reward = baseline_speed / optimized_speed

Higher reward indicates better optimization.

Implementation

Continued pretraining data: Collect CUDA kernel implementations:

# Dataset: [kernel_code, optimization_notes, performance_hints]
pretrain_data = [(kernel1, notes1), (kernel2, notes2), ...]

General RL training:

for iteration in range(num_iterations):
    # Generate kernel code
    kernel_code = llm.generate(prompt=problem_spec)
    # Compile and execute
    compiled = compile_cuda(kernel_code)
    speed = measure_execution_time(compiled, workload)
    # Compute reward
    reward = baseline_speed / speed if compiled_successfully else -1.0
    # Update LLM
    llm.update_with_rl(trajectory, reward)

HGEMM specialization: Create specialized prompts:

task_prompt = """
Optimize HGEMM for:
- Matrix size: 4096x4096
- Batch size: 16
- Hardware: A100 GPU
Requirements: maximize throughput
"""

When to Use

• Kernel optimization when manual tuning is insufficient