SynKer: Synthesize, Kernelize, Reinforce - Teaching GPU Kernel Generation to Small Language Models

Combining test-time scaling with verifier execution feedback has demonstrated glimpses of frontier language models (LMs) being able to generate GPU kernels. However, small LMs still lack the capability to robustly produce compilable backend-specific code. We argue that this is largely due to a lack of diverse training environments and validated kernel datasets, representative of the target domain. To this end, we introduce SynKer, a general recipe for improving LM kernel generation capabilities via synthetic task and solution generation: By evolving and translating natural-language task descriptions, we generate a large-scale set of diverse target operations. We then leverage evolutionary test-time search to generate an end-to-end validated kernel dataset across target backends. Finally, we use the resulting dataset to post-train open-source LMs of different families and scales using supervised fine-tuning and reinforcement learning. The resulting set of task environments contains 2365 validated and configurable synthetic tasks and a kernel archive consisting of approximately 100k kernels across three backends. We demonstrate that the synthetic data enables effective post-training across a range of LMs. We further find that, under supervised fine-tuning (SFT), increased task diversity improves both validation performance and generalization to the held-out task, while the resulting SFT checkpoints provide better initializations for the subsequent reinforcement learning process. Together, these results indicate that SynKer offers a practical and effective pipeline to improve the LMs kernel generation capabilities.