AI 中文总结
该研究提出SCROLL方法，通过共享主干的自由路由最后一层信念组合多可观测量似然，在随机动力学基准及真实空气质量数据上实现了更优的预测性能与校准。
AI 中文摘要
预测随机动力学系统很少只需要单个数值，人们需要多个可观测量——未来状态、阈值事件、状态标签——每个都有自身的似然性。标准多任务方法平衡各任务损失，经调优或学习得到。我们则在共享主干网络上，通过每个任务自由路由的最后一层信念来组合可观测量的似然性；这将依赖单位的损失缩放吸收到同一梯度传递中学习的似然参数里。随机动力学提供了静态基准无法提供的内容：可计算的预测方差真值。结果符合理论预期：在指定良好的同方差Ornstein–Uhlenbeck过程上，学习到的预测律恢复了解析核，且与正确指定的基准表现相当；在异方差系统（随机Lorenz-63、真实空气质量数据）上，信念的输入依赖方差得以分离：在状态和状态任务上取得了最佳单运行负对数似然（NLL），校准仅被那些NLL优于它的方法匹配，且成本仅为调优网格的一小部分；在真实序列上，状态边际在五个滚动原点上保持稳定。
英文摘要
Forecasting a stochastic dynamical system rarely means a single number: one wants several observables---future state, threshold event, regime label---each with its own likelihood. Standard multi-task recipes balance per-task losses, tuned or learned. We instead compose the observables' likelihoods in per-task free-routed last-layer beliefs on a shared backbone; this absorbs unit-dependent loss scaling into likelihood parameters learned in the same gradient pass. Stochastic dynamics supply what static benchmarks cannot: computable ground truth for the predictive variance. Results land where theory puts them: on the well-specified, homoscedastic Ornstein--Uhlenbeck process the learned predictive law recovers the analytic kernel and correctly specified baselines tie. On heteroscedastic systems (stochastic Lorenz-63, real air-quality data) the belief's input-dependent variance separates: best single-run NLL on the state and regime tasks, calibration matched only by arms whose NLL it beats, at a fraction of the tuned grids' cost. On the real series the state margin holds across five rolling origins.
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