标题:卦象层:一种基于《易经》二进制编码的离散瓶颈架构及其移动端验证 Title:Hexagram Layer: A Discrete Bottleneck Architecture Based on the Binary Encoding of the Book of Changes and Its Mobile Verification

大模型连续隐状态缺少显式结构约束,容易引发语义漂移与逻辑不一致;《易经》六十四卦作为完备的6位64状态符号系统,长期局限于哲学解读,缺少可训练、可复现的计算实证。本文提出卦象层,一种融合周易卦象二进制编码的离散瓶颈可微架构。首先将六十四卦映射为6位二进制状态,对错卦、综卦、互卦、变卦四类卦变操作给出严格形式化定义,借助邻接矩阵构建卦变状态转移约束;其次提出爻象结构化初始化策略,为原型向量注入卦象先验偏置,替代传统随机初始化;推导得到结构先验有效性、判别边界迁移充分条件、粗粒化信息单调性三条理论定理。在Android移动端基于纯C++标准库完成全部前向、反向逻辑实现,不依赖深度学习框架,开展三组对照实验。实验结果表明:爻象结构化初始化能够显著加速离散瓶颈层判别边界迁移;不满足学习率充分条件时模型无法收敛;粗粒化变换符合信息单调不增规律;迭代互卦映射时观测到由既济、未济二卦构成的周期‑2极限环,该现象与《易经》以两卦收束全篇的文本特征存在观察层面的呼应。本文为传统符号文化的计算化实证提供一套可复现的实现范式。 Abstract The continuous hidden states of large‑scale models lack explicit structural constraints, which may lead to semantic drift and logical inconsistency. As a complete symbolic system with 6 bits and 64 states, the sixty‑four hexagrams in the Book of Changes have long been limited to philosophical interpretation, lacking trainable and reproducible computational evidence. This paper proposes the Hexagram Layer, a differentiable discrete‑bottleneck architecture integrated with binary encoding of I‑Ching hexagrams. Firstly, the sixty‑four hexagrams are mapped to 6‑bit binary states. Four hexagram‑transformation operations, namely inverse hexagram, reversed hexagram, mutual hexagram and changed hexagram, are formally defined, and hexagram‑transition constraints are constructed via adjacency matrix. Secondly, a hexagram‑structured initialization strategy is proposed to inject hexagram‑based prior bias into prototype vectors instead of conventional random initialization. Three theoretical theorems are derived concerning the validity of structural prior, sufficient conditions for decision‑boundary migration, and information monotonicity of coarse‑graining. All forward and backward computations are implemented purely in C++ standard library on Android mobile devices without deep‑learning frameworks, and three groups of comparative experiments are carried out. Experimental results demonstrate that hexagram‑structured initialization greatly accelerates decision‑boundary migration of the discrete bottleneck layer; the model fails to converge when the sufficient condition of learning rate is violated; coarse‑graining transformation satisfies the monotonic non‑increase property of information. A period‑2 limit cycle formed by Ji‑Ji and Wei‑Ji is observed during mutual‑hexagram iteration, which is observationally consistent with the textual feature that the Book of Changes ends with these two hexagrams. This work provides a reproducible paradigm for computational verification of traditional cultural symbols.