用量子力学原理建模语言序列,实现更优的语义消歧。
Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function
- 将语言状态视为量子波函数,通过哈密顿量调控相位实现信息增强与抑制。
- 在特定消歧任务中,该模型仅需维度N,而传统模型需Ω(N²)才能达到同等效果。
- 适合对模型可解释性、信息流动追踪感兴趣的学者研究量子启发架构。
我们提出一种序列建模框架,其隐状态为有限维希尔伯特空间上的复值波函数,由学习得到的时间依赖哈密顿量驱动演化。与依赖门控机制抑制竞争假设的标准循环结构不同,本框架利用量子干涉:哈密顿量调节复振幅相位,使冲突解释相消,一致解释增强。动态过程严格保幅(单位酉),通过凯利(克兰克-尼科尔森)离散化实现。词元概率由玻恩规则提取,该二次测量算子耦合幅度与相对相位。主要理论贡献是分离定理:定义了一类消歧任务,维度为N的复数酉模型可精确求解,而任何具备标准仿射-软最大读出的实值正交模型需Ω(N²)维度。该二次差距源于玻恩规则隐式将N维状态映射至秩一厄米矩阵空间,从而访问线性投影无法获取的成对相位关联。最后,我们推导出潜变量概率质量的连续性方程,获得守恒的成对流,作为信息在维度间流动的内置诊断工具。
原文摘要 · Abstract (English)
We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that rely on gating mechanisms to suppress competing hypotheses, our framework utilizes quantum interference: the Hamiltonian steers the phases of complex amplitudes so that conflicting interpretations cancel while compatible ones reinforce. The dynamics are strictly unitary, ensuring that the state norm is preserved exactly at every time step via a Cayley (Crank--Nicolson) discretization. Token probabilities are extracted using the Born rule, a quadratic measurement operator that couples magnitudes and relative phases. Our primary theoretical contribution is a separation theorem characterizing the representational advantage of this readout: we define a family of disambiguation tasks that a complex unitary model of dimension $N$ solves exactly, but which requires a state dimension of $Ω(N^2)$ for any real-valued orthogonal model equipped with a standard affine-softmax readout. This quadratic gap arises because the Born rule implicitly lifts the $N$-dimensional state into the space of rank-one Hermitian matrices, accessing pairwise phase correlations that are inaccessible to linear projections. Finally, we derive a continuity equation for the latent probability mass, yielding conserved pairwise currents that serve as a built-in diagnostic for tracing information flow between dimensions.
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