We study sparse and continual reinforcement learning fine-tuning of language models through attention-head ranking and partitioning. For sparse learning, we rank attention heads by gradient norm to identify a small subset of heads that can be trained effectively. For continual learning, we partition heads across tasks to reduce cross-task interference and preserve previously learned capabilities. Theoretically, we relate gradient norm to training effectiveness, and further characterize why sparse, separated head updates can remain stable. Empirically, across math, instruction-following, and coding tasks, tuning higher-ranked heads consistently outperforms tuning lower-ranked ones while often matching denser baselines, and head partitioning improves retention while preserving adaptation to new tasks.

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