Continual learning (CL) is commonly studied under the assumption that sequential tasks are semantically related or structurally similar. However, in highly heterogeneous settings, where tasks differ substantially in reasoning patterns and input-output formats, existing methods often suffer from catastrophic forgetting and inefficient capacity allocation. To address this challenge, we propose Task-differentiated Atomic Skill Expansion and Routing (\texttt{TASER}), a CL framework that jointly determines how many new atomic skills to introduce for each task and which skills to activate. The framework first uses atomic skill incremental learning to dynamically expand capacity based on task divergence and model uncertainty. It then applies orthogonality-enhanced skill detection to ensure these skills remain semantically distinct and independently reusable. Finally, a skill dynamic routing mechanism composes task-relevant skills through lightweight task-conditioned gating. We further introduce \texttt{HeteroCLBench}, a highly heterogeneous benchmark for CL, comprising 19 diverse tasks across 9 cognitive dimensions under a standardized sequential protocol. Experiments on \texttt{HeteroCLBench} show that \texttt{TASER} consistently outperforms strong baselines by improving plasticity and reducing catastrophic forgetting.

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