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.

Image Difference Captioning (IDC) aims to generate natural language descriptions that highlight subtle differences between two visually similar images. While recent advances leverage pre-trained vision-language models to align fine-grained visual differences with textual semantics, existing supervised approaches often overfit to dataset-specific language patterns and fail to capture accurate preferences on IDC, which often indicates fine-grained and context-aware distinctions. To address these limitations, we propose an adversarial direct preference optimization (ADPO) framework for IDC, which formulates IDC as a preference optimization problem under the Bradley-Terry-Luce model, directly aligning the captioning policy with pairwise difference preferences via Direct Preference Optimization (DPO). To model more accurate and diverse IDC preferences, we introduce an adversarially trained hard negative retriever that selects counterfactual captions, This results in a minimax optimization problem, which we solve via policy-gradient reinforcement learning, enabling the policy and retriever to improve jointly. Experiments on benchmark IDC datasets show that our approach outperforms existing baselines, especially in generating fine-grained and accurate difference descriptions.

While large language models (LLMs) are increasingly capable of handling longer contexts, recent work has demonstrated that they exhibit the ”lost in the middle” phenomenon (Liu et al., 2024) of unevenly attending to different parts of the provided context. This hinders their ability to cover diverse source material in multi-document summarization, as noted in the DiverseSumm benchmark (Huang et al., 2024). In this work, we contend that principled content selection is a simple way to increase source coverage on this task. As opposed to prompting an LLM to perform the summarization in a single step, we explicitly divide the task into three steps—(1) reducing document collections to atomic key points, (2) using determinantal point processes (DPP) to perform select key points that prioritize diverse content, and (3) rewriting to the final summary. By combining prompting steps, for extraction and rewriting, with principled techniques, for content selection, we consistently improve source coverage on the DiverseSumm benchmark across various LLMs. Finally, we also show that by incorporating relevance to a provided user intent into the DPP kernel, we can generate personalized summaries that cover relevant source information while retaining coverage.