表征转变揭示复杂系统中的预测结构：临界系统中的轨迹级重构
Representation Transitions Reveal Predictive Structure in Complex Systems: A Trajectory-Level Reconstruction in a Critical System
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中文总结 AI 辅助
该研究针对临界复杂系统，通过系统性搜索不同表征形式，发现表征选择决定预测结构是否可及，连续低维压缩表征在8次交叉验证中表现稳健，能有效揭示复杂系统的预测结构。
中文摘要 AI 辅助
复杂系统中的轨迹常包含传统用于描述它们的总体平均标量统计量无法捕捉的结构。本文通过独立数值重模拟而非文献综述，对同一临界复杂系统的潜在轨迹集合应用了一系列系统性表征形式的搜索：从单个标量统计量，到两次独立的离散多特征分类尝试，再到轨迹级结构表征与诊断替代测试，最后到连续低维压缩。预测失败并非由相关性不足解释：某一离散表征自身最强的单个特征与目标的相关性（r=0.588）强于最终成功表征的核心统计量（r=0.540），却无法区分集合中两个最关键的案例；而连续表征在8次独立的尺度去除交叉验证中均表现稳健（r=0.677-0.717，所有p<0.001）。决定因素并非相关性强度，而是表征是否保留了与预测相关的结构。这些结果表明，表征的选择决定了复杂系统中的预测结构是否可被获取——这本身是一个科学变量，而非下游分析的选择。
英文摘要
Trajectories in complex systems often contain structure that is not captured by the population-averaged, scalar statistics traditionally used to describe them. Here we reconstruct, through independent numerical re-simulation rather than literature review, a systematic search across representational forms - from single scalar statistics, through two independent discrete multi-feature classification attempts, to a trajectory-level structural representation and a diagnostic surrogate test, to a continuous low-dimensional compression - applied to the same underlying trajectory ensemble in a critical complex system. Predictive failure is not explained by insufficient correlation: one discrete representation's own strongest individual feature correlates with the target more strongly ($r=0.588$) than the eventual successful representation's own headline statistic ($r=0.540$), yet fails to separate the ensemble's two most consequential cases - while the continuous representation succeeds, robustly, across eight independent scale-removal folds ($r=0.677$-$0.717$, all $p<0.001$). The determining factor was not correlation strength but whether the representation preserved the structure relevant to prediction. These results indicate that the choice of representation determines whether predictive structure in complex systems becomes accessible - a scientific variable in its own right, not a downstream analysis choice.
