认知的路径积分模型

中文摘要 AI 辅助

我们发展了认知成本优化的数学和物理公式，其为意识的路径积分模型奠定基础。目标导向的认知过程被建模为在投影哈密顿量下的虚时演化（ITE），该哈密顿量奖励与目标概念一致的构型。我们建立了三个结果。首先，这种ITE与双括号流一致，因此是希尔伯特 - 施密特成本的黎曼梯度流，其唯一最小值是解。其次，维克旋转将这种非酉下降重新表示为同一希尔伯特空间上的等效酉演化，它允许精确的离散路径积分表示，其中预言机和初始态扩散投影器分别扮演势能和动能的角色。第三，我们通过认知系统与神经环境探测器之间酉相互作用的强度来识别从无意识处理到有意识处理的连续统，在马尔可夫弱耦合极限下恢复了浅野等人的戈里尼 - 科萨克夫斯基 - 苏达山 - 林德布拉德（GKSL）退相干模型，在强耦合极限下恢复了优化态的投影、可报告的固定，即类似顿悟的“Aha”端点。两种情况共享相同的ITE和路径积分结构，只是测量相互作用强度不同。因此，维克旋转是一种重新描述的技术，而非物理状态变化。

英文摘要

We develop the mathematical and physical formulation of cognitive cost optimization that underlies the path-integral model of consciousness. The goal-directed cognitive process is modeled as imaginary-time evolution (ITE) under a projector Hamiltonian that rewards configurations consistent with a target concept. We establish three results. First, this ITE coincides with a double-bracket flow and is therefore the Riemannian gradient flow of a Hilbert--Schmidt cost whose unique minimum is the solution. Second, a Wick rotation re-expresses this non-unitary descent as an equivalent unitary evolution on the same Hilbert space, which admits an exact discrete path-integral representation in which the oracle and the initial-state diffusion projector play the roles of potential and kinetic energy. Third, we identify the continuum from unconscious to conscious processing with the strength of the unitary interaction between the cognitive system and a neural-environment probe, recovering the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) decoherence model of Asano \textit{et al.} in the Markovian weak-coupling limit, and the projective, reportable fixation of an optimized state in the strong-coupling limit, an insight-like ``Aha'' endpoint. Both regimes share the same ITE and path-integral structure, and only the measurement-interaction strength varies. The Wick rotation is therefore a technique of re-description, not a physical regime change.

发表机构

• Hokkaido University（北海道大学）
• RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心（iTHEMS））
• Teikyo University Advanced Comprehensive Research Organization (ACRO)（帝京大学高级综合研究机构（ACRO））
• The University of Osaka（大阪大学）
• Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院（CIFAR））
• Linnaeus University（林奈大学）

机构由 AI 辅助整理，请以论文原文为准。

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备注

17 pages, 2 figures,1 table