A Path Integral Model of Cognition
Haruki Emori, Kazunori Kondo, Atsushi Iriki, Andrei Khrennikov
arXiv (Cornell University) July 10, 2026 preprint DOI: 10.48550/arxiv.2607.24807 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper |
|---|---|
| Key points | The authors propose that goal-directed cognition can be modeled as imaginary-time evolution under a projector Hamiltonian, which coincides with a double-bracket flow and the Riemannian gradient flow of a Hilbert-Schmidt cost with a unique minimum. They argue that a Wick rotation re-expresses this non-unitary descent as unitary evolution with an exact discrete path-integral representation, and that varying the strength of interaction between the cognitive system and a neural-environment probe spans unconscious to conscious processing, recovering the GKSL decoherence model in the weak-coupling limit and an insight-like 'Aha' fixation in the strong-coupling limit. |
Abstract
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.