Learning When to Optimize: Verified Optimization Skills from Expert GPU-Kernel Lineages

LLM-based agents are increasingly used to generate GPU kernels, but they often struggle to determine when an optimization is sound because its required code state and dependencies are implicit in expert implementations. We introduce KLineage, which learns this missing "when" knowledge from expert kernels: instead of relying on forward rollouts, KLineage walks expert implementations backward through validation-gated simplifications and reverses each accepted step into a reusable optimization skill. Each skill records not only the optimization intent, but also when to apply the optimization technique, including where it applies in code, what conditions made it valid, what effect it has, and what failures its assumptions avoid. A downstream LLM materializes these skills on new code surfaces under the same compile/correctness/profile gate. This guidance on when to apply each optimization can help downstream models to generate higher-performance kernels. On five expert workloads across two NVIDIA architectures, these lineage-derived skills serve as an effective optimization curriculum, exceeding recent memory-based LLM-kernel baselines in both final kernel quality and optimization efficiency under the same fixed budget. We also demonstrate that the KLineage framework extends beyond NVIDIA GPUs to Ascend NPUs. Our code is publicly available at https://github.com/ict-agent/klineage.