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 frontier models score 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 state-of-the-art 28.14% with GPT-5.1 (+5.59 pp absolute and +24.8% relative) on CL-Bench, 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.