GPU Parallelization Strategies for Forward and Backward Propagation in Shallow Neural Networks: A CUDA-Based Comparative Study

The exponential growth in demand for GPU computing resources has created an urgent need for automated CUDA optimization strategies. While recent advances in LLMs show promise for code generation, current SOTA models achieve low success rates in improving CUDA speed. In this paper, we introduce CUDA-L1, an automated reinforcement learning framework for CUDA optimization that employs a novel contrastive RL algorithm. CUDA-L1 achieves significant performance improvements on the CUDA optimization task: trained on A100, it delivers an average speedup of x3.12 with a median speedup of x1.42 against default baselines over across all 250 CUDA kernels of KernelBench, with peak speedups reaching x120. In addition to the default baseline provided by KernelBench, CUDA-L1 demonstrates x2.77 over Torch Compile, x2.88 over Torch Compile with reduce overhead, x2.81 over CUDA Graph implementations, and x7.72 over cuDNN libraries. Furthermore, the model also demonstrates portability across different GPU architectures. Beyond these benchmark results, CUDA-L1 demonstrates several properties: it 1) discovers a variety of CUDA optimization techniques and learns to combine them strategically to achieve optimal performance; 2) uncovers fundamental principles of CUDA optimization, such as the multiplicative nature of optimizations; 3) identifies non-obvious performance bottlenecks and rejects seemingly beneficial optimizations that actually harm performance. The capabilities demonstrate that, RL can transform an initially poor-performing LLM into an effective CUDA optimizer through speedup-based reward signals alone, without human expertise or domain knowledge. This paradigm opens possibilities for automated optimization of CUDA operations, and holds promise to substantially promote GPU efficiency and alleviate the rising pressure on GPU computing resources. Project: deepreinforce-ai.github.io/cudal1_blog

Formal neural network verification -- proving that a network satisfies safety properties for all inputs in a specified domain -- is bounded in practice by GPU memory: standard implementations of bound-propagation algorithms (IBP, CROWN, $α$-CROWN) require weight and relaxation-coefficient matrices to reside entirely on one accelerator. We adapt two parallelism techniques originally developed for large-scale model training to the auto_LiRPA / $α,β$-CROWN verification framework. Tensor Parallelism (TP) shards both weight and $A$-matrices across GPUs, achieving ${\approx}2\times$ peak-memory reduction at $P{=}2$; soundness is confirmed on VNN-COMP 2022 MNIST-FC benchmarks, though bound tightness degrades with the number of sharded zones due to forced IBP substitution for intermediate bounds inside sharded zones. Fully Sharded Data Parallelism (FSDP) shards only weight matrices with a per-layer AllGather, producing bounds that are bitwise identical to the single-GPU baseline: baseline memory drops by 80--90%, peak memory by 34--39% on wide MLPs. FSDP integrates cleanly with complete verification ($β$-CROWN + Branch-and-Bound) and with convolutional layers (BoundConv); a complete unsat result is obtained for CIFAR-100 ResNet-large (VNN-COMP 2024) under FSDP. Across all experiments the memory bottleneck in $α$-CROWN+BaB mode proves to be per-neuron alpha tensors, not weight matrices, pointing to the key direction for future work.

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/deepreinforce-ai/CUDA-L2