发表机构
AlphaNova（AlphaNova）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出“城市”概念压缩横截面信号方向，证明城市夹角可保守估计历史夹角，并在大规模数据中验证其有效性，同时揭示方向摘要的局限与信息恢复途径。
AI 中文摘要
横截面信号是在每个日期对$d$个资产的预测向量；经去均值并归一化后，它成为球面上的一个点。其“城市”是其在共同目标对齐框架中时间平均向量的方向，是一种压缩摘要。两个城市之间的夹角何时能作为历史之间夹角的保守估计？对于独立的均匀历史，当城市夹角至多为90度时，历史夹角至少为城市夹角的概率趋近于1，且误差界为$O(T^{-1/2})$，该误差界对维度一致成立。选择正平均信息系数（IC）会将无条件极限改变为$\gamma_q>1/2$，对于20个资产约为56%。该界可扩展到具有时间依赖性的独立旋转对称历史；滞后相关性的可求和乘积保持条件极限。平稳遍历定理允许共享信号运动，并识别决定极限排序的总体边际。在AlphaNova 2026年5月竞赛的266,815个正IC配对中，历史夹角至少为城市夹角的占比总体为58.9%，在城市夹角不超过90度时为74.1%，超过90度时为1.5%。这些频率描述了观测库，并不验证均匀零假设：残差一致性大多为正，且经验二阶矩诊断无法仅通过调整时间依赖性在该零假设内匹配。在全部776个信号的样本中，城市夹角至少为60度选择出的配对在同一历史夹角阈值下的成功率为94.3%，而基础率为85.0%，并保留了72.5%的配对。显式构造展示了仅用方向摘要的局限性，保留长度给出尖锐界，共享时间块可恢复缺失信息，此处仅在精细分辨率下有效。持续的正IC将城市限制并约束其运动；收敛还需要稳定的平均方向。
英文摘要
A cross-sectional signal is a forecast vector over $d$ assets at each date; demeaned and normalized, it is a point on a sphere. Its city is the direction of its time-averaged vector in a common target-aligned frame, a compressed summary. When is the angle between two cities a conservative estimate of the angle between the histories? For independent uniform histories, the probability that the history angle is at least the city angle tends to one when the city angle is at most 90 degrees, with an $O(T^{-1/2})$ error bound uniform in dimension. Selecting for positive average information coefficient (IC) changes the unconditional limit to $γ_q>1/2$, about 56% for 20 assets. The bound extends to independent, rotationally symmetric histories with temporal dependence; summable products of lag correlations preserve the conditional limit. A stationary ergodic theorem allows shared signal movement and identifies the population margin determining the limiting ordering. Among 266,815 positive-IC pairs in AlphaNova's Competition May 2026, the history angle is at least the city angle for 58.9% overall, 74.1% at city angles up to 90 degrees, and 1.5% beyond. These frequencies describe the observed library and do not validate the uniform null: residual agreement is mostly positive, and an empirical second-moment diagnostic cannot be matched within that null by adjusting temporal dependence alone. On the full 776-signal sample, a city angle of at least 60 degrees selects pairs with a 94.3% success rate at the same history-angle threshold, against an 85.0% base rate, and retains 72.5% of pairs. Explicit constructions show the limits of direction-only summaries, retained lengths give sharp bounds, and shared time blocks recover missing information, here only at fine resolution. Persistent positive IC confines cities and bounds their motion; convergence also requires a stable mean direction.
Comments45 pages, 1 figure, 13 tables
