Experiments probing natural language processing by both humans and LLMs suggest that the meaning of a semantic expression is indeterminate prior to the act of interpretation rather than being specifiable simply as the sum of its parts (i.e. compositionality). This observer-dependent act dynamically actualizes meaning under genuine contextuality more consistent with quantum logical mechanisms than with classical Boolean approaches that assume separability, motivating an approach to language modeling that utilizes a Hilbert space formalism. In this work, we introduce Phase-Associative Memory (PAM) -- a complex-valued sequence model whose state S_t \in \mathbb{C}^{d \times d} accumulates outer products of complex token embeddings retrieved through the conjugate inner product $\mathrm{Re}\langle K \mid Q\rangle / \sqrt{d}$ -- and evaluate it against a structurally matched real-valued ablation. Both architectures train stably across a 5M--100M parameter sweep on WikiText-103 under identical conditions; PAM sits at higher absolute loss at every measured scale but improves more rapidly with parameter count, with power-law exponents of $-0.15$ vs.\ $-0.12$ in loss and $-0.65$ vs.\ $-0.49$ in perplexity that narrow the gap between the two architectures monotonically. Further investigation of complex-valued sequence modeling at larger scales could reveal that the loss plateau characteristic of real-valued state-of-the-art language models (e.g. transformers) is reachable with PAM-style architectures with an order of magnitude fewer parameters than the current frontier ($\sim$1T), implying that similar capabilities are achievable at sizes runnable on consumer-grade hardware.

翻译：人类与大型语言模型（LLMs）在自然语言处理中的实验表明，语义表达的含义在解释行为之前是不确定的，而非简单归结为其组成部分的叠加（即组合性）。这种依赖观察者的行为在真实语境性下动态实现意义，其机制更符合量子逻辑，而非假设可分离性的经典布尔方法，从而激发了利用希尔伯特空间形式进行语言建模的动机。本文提出相位关联记忆（Phase-Associative Memory, PAM）——一种复值序列模型，其状态S_t ∈ \mathbb{C}^{d×d}通过共轭内积$\mathrm{Re}\langle K \mid Q\rangle / \sqrt{d}$检索复令牌嵌入的外积累积而成——并对其与结构匹配的实值消融模型进行对比评估。两种架构在WikiText-103数据集上、参数规模5M至100M范围内、相同条件下均稳定训练；PAM在每个测量尺度上具有更高绝对损失，但其损失随参数数量增长而更快改善，损失函数的幂律指数为-0.15（对比-0.12），困惑度的幂律指数为-0.65（对比-0.49），表明两种架构间的差距单调缩小。进一步在更大规模下探索复值序列建模可能揭示：采用PAM风格的架构，可在参数数量比当前前沿（约1T）少一个数量级的情况下，达到实值最先进语言模型（如transformer）特征性的损失平台，这意味着在消费级硬件可运行的规模下即可实现相似能力。