Agentic Context Learning with Self-Discovered Specification

Context learning is an emerging inference-time task where LLMs must learn and apply novel, task-specific knowledge from intricate contexts absent from pre-training; even the best model in the original CL-Bench evaluation scores under 24% task success. In this work, we conduct a comprehensive empirical study to understand why this setting remains difficult. A natural hypothesis is that failures stem from content access; yet across twelve retrieval, reflection, and verification baselines on CL-Bench, an extensive context learning benchmark, we find limited gains over direct full-context prompting. Further failure analysis reveals a key finding: unlike typical long-context tasks such as long-document understanding, context learning requires not only recovering local content but also acquiring local specifications that are often unspecified in the query but distributed across the context: domain-specific formats, local rules, and completeness conditions. Across all 31,592 rubric items, we find that 55.4% clearly evaluate specification acquisition, while only 22.6% evaluate content acquisition. Moreover, despite 76.7% of specifications being unspecified in the user query, 95.5% are traceable to the context, indicating these are learnable obligations rather than hidden requirements. To validate this diagnosis, we design a deliberately simple intervention, PSCI (private specification-contract induction), which extracts local specifications and enforces them through adversarial checking and repair; PSCI achieves 28.14% strict pass with GPT-5.1 (+5.59 pp absolute and +24.8% relative) on CL-Bench, outperforming all twelve evaluated alternatives, with improvements replicated on Qwen3.5-27B (+5.28 pp) and Gemini 3 Pro (+6.17 pp). Seventeen ablations further isolate the role of task-specific specifications. Overall, our results suggest context learning hinges on not only content acquisition but also specification acquisition.