Selecting an appropriate LLM configuration for a given query is critical, yet existing routing frameworks operate within a single computational paradigm. To address this gap, we formalize the Cross-System Routing Problem, a hierarchical decision-making task that decomposes routing into intra-regime configuration selection and inter-regime system selection. Building on this, we propose BiCSRouter, a bi-level cross-system routing framework that integrates two orthogonal regimes: intensive reasoning via single-agent systems and extensive collaboration via multi-agent systems. BiCSRouter performs policy learning within each system and employs a lightweight inter-regime router that selects the optimal regime based on predicted performance and cost. Experiments on the MBPP and MATH benchmarks demonstrate that BiCSRouter outperforms 15 representative baselines across three types. On MBPP, compared to the performance ceiling of GPT-5, BiCSRouter achieves a 46% reduction in cost with only a 2% drop in accuracy. Finally, we show that BiCSRouter can extend to additional regimes, highlighting its generality as a cross-system routing framework.

To better handle commonsense knowledge, which is difficult to acquire in ordinary training of language models, commonsense knowledge graphs and commonsense knowledge models have been constructed. The former manually and symbolically represents commonsense, and the latter stores these graphs’ knowledge in the models’ parameters. However, the existing commonsense knowledge models that deal with events do not consider granularity or time axes. In this paper, we propose a time-aware commonsense knowledge model, TaCOMET. The construction of TaCOMET consists of two steps. First, we create TimeATOMIC using ChatGPT, which is a commonsense knowledge graph with time. Second, TaCOMET is built by continually finetuning an existing commonsense knowledge model on TimeATOMIC. TimeATOMIC and continual finetuning let the model make more time-aware generations with rich commonsense than the existing commonsense models. We also verify the applicability of TaCOMET on a robotic decision-making task. TaCOMET outperformed the existing commonsense knowledge model when proper times are input. Our dataset and models will be made publicly available.