Skills, as a useful abstraction for the procedural capabilities of large language models (LLMs), capture how models perform structured, multi-step reasoning and program execution. Existing approaches typically treat skills as explicit, surface-level constructs specified through prompts or programs, leaving open the question of how such procedural capabilities are represented inside the model and whether they can be manipulated as structured objects in latent space. In this empirical study, we investigate whether procedural LLM skills can be represented as directions in activation space and whether vector-space operations over these directions can express skill-level behaviors. We find that procedural skills admit a vector-space representation: individual skill directions can be activated to shift model behavior; independently extracted directions can compose to form higher-level skills. Contrastive directions yield context-conditioned algorithmic personalization and optimization trajectories over skill directions evolve non-monotonically, with intermediate states often surpassing fully optimized solutions. These results support a representation-level view of procedural LLM skills: they admit a latent vector-space organization that allows direct manipulation through internal interventions.

The rapid evolution of large language models (LLMs) and the real world has outpaced the static nature of widely used evaluation benchmarks, raising concerns about their reliability for evaluating LLM factuality. While substantial works continue to rely on the popular but old benchmarks, their temporal misalignment with real-world facts and modern LLMs, and their effects on LLM factuality evaluation remain underexplored. Therefore, in this work, we present a systematic investigation of this issue by examining five popular factuality benchmarks and eight LLMs released across different years. An up-to-date fact retrieval pipeline and three metrics are tailored to quantify benchmark aging and its impact on LLM factuality evaluation. Experimental results and analysis illustrate that a considerable portion of samples in the widely used factuality benchmarks are outdated, leading to unreliable assessments of LLM factuality. We hope our work can provide a testbed to assess the reliability of a benchmark for LLM factuality evaluation and inspire more research on the benchmark aging issue.