Statistical Properties of the King Wen Sequence: An Anti-Habituation Structure That Does Not Improve Neural Network Training

arXiv cs.LG / 4/13/2026

💬 OpinionIdeas & Deep AnalysisModels & Research

共有:

Key Points

The study provides a rigorous statistical characterization of the King Wen sequence using Monte Carlo permutation tests versus 100,000 random baselines, identifying four significant structural properties.
The authors test whether these properties—superficially reminiscent of curriculum learning and curiosity-driven exploration—could improve neural network training.
Across three experiments (learning-rate schedule modulation, curriculum ordering, and seed sensitivity analysis) on NVIDIA RTX 2060 (PyTorch) and Apple Silicon (MLX), the results are uniformly negative for using King Wen ordering as a training dynamic.
Learning-rate modulation based on the King Wen structure degrades performance at all tested amplitudes, and curriculum ordering performs worst on one platform and within noise on the other.
The paper argues that the sequence’s distinctive high variance destabilizes gradient-based optimization, showing that anti-habituation in a fixed combinatorial order does not translate to effective training dynamics.

Abstract

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.