What Context Must Survive Summarization? Interface Sufficiency for Multi-Turn Context Management

Large language models can solve complex tasks using natural-language instructions in zero-shot prompt settings. However, they eventually fail as the problem size grows, often observed in algorithmic domains. Multi-turn decomposition is a natural approach to address this scaling limitation. However, it underperforms monolithic prompting in the absence of proper context management. We show that the key factor for successful decomposition is contextual independence of the factorized distribution in the multi-turn generation. Decomposition is effective only if the factorized distribution of the decomposed task remains valid given the context propagated from preceding tasks. In controlled algorithmic domains, where the required context is known and can be systematically ablated, we show that sufficient interface context recovers the accuracy of the monolithic prompts and multi-turn decomposition prompting scales beyond the capacity cutoff of the monolithic prompting. In addition, we demonstrate that the interface context for multi-turn decomposition can be designed from the structure of the problem domains on two challenging travel scheduling tasks.