用量子模型解释决策中的情境依赖,揭示内在状态与外部记忆的权衡。
Minimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model
- 基于量子态的三能级模型,用单个状态捕捉情境依赖决策过程。
- 实验验证了非定域性边界被打破,证明经典概率无法完全描述该决策系统。
- 适合研究认知科学、人工智能中的状态表示与记忆机制的读者。
决策常表现出难以用单一非侵入式经典概率模型解释的情境依赖性。本文发展了一种量子类的拔河(QTOW)决策模型,探讨此类情境依赖是否可由单一受约束的内部状态表示。该模型采用三能级量子态(qutrit)、破坏状态的广义决策工具、决策与奖励条件下的保范反馈,以及在同一状态空间内的可选探测操作。三能级表示允许构建类似KCBS的探测族,其状态违反非情境性界限,提供了一个证据:指定的操作族无法嵌入单一非情境性经典概率空间。本文不主张从决策推导出量子理论;经典重构可通过引入显式情境标签、存储历史或扩展状态描述保持描述充分性;亦可通过限制可接受探测集避免非情境性证言。量子概率则为所考虑的情境操作族提供了紧凑的单状态实现。从自然与人工智能视角看,这一结果揭示了架构层面的表征权衡:情境信息可内置于共享内部状态的变换中,或外化为额外的状态与记忆资源。
原文摘要 · Abstract (English)
Decision making often exhibits context dependence that is difficult to accommodate within a single non-invasive classical probability model. This paper develops a quantum-like extension of the Tug-of-War (QTOW) decision-making model to ask when such context dependence can be represented by a single constrained internal state. The QTOW construction uses a qutrit state, a state- disturbing generalized decision instrument, decision- and reward-conditioned norm-preserving feedback, and optional probing operations within one state space. The qutrit representation admits KCBS-type probe families and states that violate a non-contextuality bound, providing a witness that the specified operation family cannot be embedded in a single non-contextual classical prob- ability space. The claim is not that quantum theory is uniquely derived from decision making. Classical reconstructions can retain descriptive adequacy by introducing explicit context labels, stored history, or enlarged state descriptions; alternatively, the non-contextuality witness can be avoided by restricting the admissible probe set. Quantum probability instead supplies a compact single-state realization of the contextual operation family considered here. From the perspective of natural and artificial intelligence, the result identifies an architecture-level representational trade-off: contextual information may be carried intrinsically by transformations of a shared internal state or externalized into additional state and memory resources.
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