STaD: Scaffolded Task Design for Identifying Compositional Skill Gaps in LLMs

Humans cannot always intuit what scenarios are most challenging to LLMs. Hoping to capture challenging edge cases, developers either design problems to be difficult for humans or curate extensive benchmarks. What if we could instead anticipate which scenarios a model will fail on? In this paper, we use an LLM's representational geometry to predict which concept combinations it will fail on. We attribute this compositional failure to interference between salient features. In tasks that require systematic composition - toy programmatic settings, multihop reasoning, multilingual factual recall - we find that when a pair of concepts is encoded near-orthogonally, the model reliably composes them. When their linear encodings are close, producing interference, the model fails to compose them. Our method reliably anticipates failure modes across different compositional tasks, without evaluating specific inputs. These results lay the groundwork to use representational geometry to identify high-risk examples, construct targeted stress tests, and provide a scalable foundation for active learning in real-world deployment.

Skill documents, structured natural-language instructions that guide Large Language Model (LLM) agents, are critical to modern agent frameworks, yet LLMs struggle to write skills that actually work. On SkillsBench, human-authored skills improve pass rates by 16.2 percentage points, while LLM-authored skills provide no measurable gain. We introduce SkillAxe, a fully unsupervised framework that enables LLMs to iteratively diagnose and refine their own skills. SkillAxe decomposes skill quality into four interpretable dimensions (quality impact, trigger precision, instruction compliance with fault attribution, and solution-path coverage), producing structured improvement briefs that require no ground-truth labels, test suites, or environment rewards. On SkillsBench, SkillAxe improves pass rates by 28% relative over unimproved LLM skills and closes 47--67% of the gap to human-authored skills. We validate the approach as a continuous improvement engine in the wild on SpreadsheetBench, where a SkillAxe-built skill library learns from past agent trajectories and raises pass rate from 16.0% to 52.0% using only 22 skills.

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.