# CUDA-L2: Surpassing cuBLAS Performance for Matrix Multiplication through Reinforcement Learning

arXiv: https://arxiv.org/abs/2512.02551 · HTML: https://mlsanity.com/paper/2512.02551/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [KernelBench: Can LLMs Write Efficient GPU Kernels?](https://mlsanity.com/paper/2502.10517/) (2025)
- [MLPerf Inference Benchmark](https://mlsanity.com/paper/1911.02549/) (2019)
- [Kevin: Multi-Turn RL for Generating CUDA Kernels](https://mlsanity.com/paper/2507.11948/) (2025)
- [CUDA-L1: Improving CUDA Optimization via Contrastive Reinforcement Learning](https://mlsanity.com/paper/2507.14111/) (2025)
- [SwizzlePerf: Hardware-Aware LLMs for GPU Kernel Performance Optimization](https://mlsanity.com/paper/2508.20258/) (2025)

## Built on by (most cited first, 13 of 13)

- [KernelFoundry: Hardware-aware evolutionary GPU kernel optimization](https://mlsanity.com/paper/2603.12440/) (2026)
- [Towards Automated Kernel Generation in the Era of LLMs](https://mlsanity.com/paper/2601.15727/) (2026)
- [StitchCUDA: An Automated Multi-Agents End-to-End GPU Programing Framework with Rubric-based Agentic Reinforcement Learning](https://mlsanity.com/paper/2603.02637/) (2026)
- [CODA: Rewriting Transformer Blocks as GEMM-Epilogue Programs](https://mlsanity.com/paper/2605.19269/) (2026)
- [Making LLMs Optimize Multi-Scenario CUDA Kernels Like Experts](https://mlsanity.com/paper/2603.07169/) (2026)
- [OptiML: An End-to-End Framework for Program Synthesis and CUDA Kernel Optimization](https://mlsanity.com/paper/2602.12305/) (2026)
- [AscendOptimizer: Episodic Agent for Ascend NPU Operator Optimization](https://mlsanity.com/paper/2603.23566/) (2026)
- [Surprisal-Guided Selection: Compute-Optimal Test-Time Strategies for Execution-Grounded Code Generation](https://mlsanity.com/paper/2602.07670/) (2026)
- [Improving HPC Code Generation Capability of LLMs via Online Reinforcement Learning with Real-Machine Benchmark Rewards](https://mlsanity.com/paper/2602.12049/) (2026)
- [MobileKernelBench: Can LLMs Write Efficient Kernels for Mobile Devices?](https://mlsanity.com/paper/2603.11935/) (2026)
- [Step-TP: A Grounded, Step-Level Dataset with Chain-of-Thought Reasoning for LLM-Guided Tensor Program Optimization](https://mlsanity.com/paper/2605.25954/) (2026)
- [EGG: An Expert-Guided Agent Framework for Kernel Generation](https://mlsanity.com/paper/2606.26758/) (2026)
- [PTXBench: Benchmarking and Adapting LLMs for GPU Kernel Optimization with Architecture-specific PTX](https://mlsanity.com/paper/2608.17379/) (2026)

## Abstract (arXiv)

In this paper, we propose CUDA-L2, a system that combines large language models (LLMs) and reinforcement learning (RL) to automatically optimize Half-precision General Matrix Multiply (HGEMM) CUDA kernels. Using CUDA execution speed as the RL reward, CUDA-L2 automatically optimizes HGEMM kernels across 1,000 configurations. CUDA-L2 systematically outperforms major matmul baselines to date, from the widely-used torch.matmul to state-of-the-art Nvidia's closed-source libraries, i.e., cuBLAS, cuBLASLt. In offline mode, where kernels are executed consecutively without time intervals, CUDA-L2 yields +22.0% over torch.matmul on average; +19.2% over cuBLAS using the optimal layout configuration (normal-normal NN and transposed-normal TN); +16.8% over cuBLASLt-heuristic, which queries cuBLASLt library and selects the algorithm based on the heuristic's suggestion; and +11.4% over the most competitive cuBLASLt-AutoTuning model, which selects the fastest algorithm from up to 100 candidates from cuBLASLt's suggestions. In server mode, where kernels are executed at random intervals simulating real-time inference, the speedups further increase to +28.7%, +26.0%, +22.4%, and +15.9% for torch.matmul, cuBLAS, cuBLASLt-heuristic, and cuBLASLt-AutoTuning respectively. CUDA-L2 shows that even the most performance-critical, heavily-optimized kernels like HGEMM can be improved through LLM-guided RL automation by systematically exploring configuration spaces at scales impractical for humans. Project and code can be found at github.com/ornith-ai/CUDA-L2