The King Wen sequence of the I-Ching (c. 1000 BC) orders 64 hexagrams -- states of a six-dimensional binary space -- in a pattern that has puzzled scholars for three millennia. We present a rigorous statistical characterization of this ordering using Monte Carlo permutation analysis against 100,000 random baselines. We find that the sequence has four statistically significant properties: higher-than-random transition distance (98.2nd percentile), negative lag-1 autocorrelation (p=0.037), yang-balanced groups of four (p=0.002), and asymmetric within-pair vs. between-pair distances (99.2nd percentile). These properties superficially resemble principles from curriculum learning and curiosity-driven exploration, motivating the hypothesis that they might benefit neural network training. We test this hypothesis through three experiments: learning rate schedule modulation, curriculum ordering, and seed sensitivity analysis, conducted across two hardware platforms (NVIDIA RTX 2060 with PyTorch and Apple Silicon with MLX). The results are uniformly negative. King Wen LR modulation degrades performance at all tested amplitudes. As curriculum ordering, King Wen is the worst non-sequential ordering on one platform and within noise on the other. A 30-seed sweep confirms that only King Wen's degradation exceeds natural seed variance. We explain why: the sequence's high variance -- the very property that makes it statistically distinctive -- destabilizes gradient-based optimization. Anti-habituation in a fixed combinatorial sequence is not the same as effective training dynamics.
翻译:《易经》文王卦序(约公元前1000年)将64卦——六维二元空间的状态——按令学者困惑三千年的模式排列。我们通过蒙特卡洛排列分析(基于10万次随机基线)对该排序进行了严格的统计刻画。研究发现该序列具有四个统计显著特性:高于随机的转移距离(98.2百分位)、负滞后一阶自相关(p=0.037)、阳爻平衡的四卦分组(p=0.002),以及组内与组间距离的不对称性(99.2百分位)。这些特性表面上类似于课程学习与好奇心驱动探索的原理,由此提出假设:它们可能有助于神经网络训练。我们通过三项实验(学习率调度调节、课程顺序安排与种子敏感性分析)在两个硬件平台(搭载PyTorch的NVIDIA RTX 2060与搭载MLX的Apple Silicon)上验证该假设。结果均为否定:文王序列学习率调制在所有测试幅度下均导致性能下降;作为课程顺序,文王序列在一个平台中是最差的非连续排序,在另一平台中则处于噪声水平内。30种种子的全面扫描证实,仅文王序列的退化幅度超过自然种子方差。我们对此作出解释:该序列的高方差——正是其统计独特性的来源——会破坏基于梯度的优化过程。固定组合序列中的抗习惯化特性与有效训练动力学不可等同。