Dynamic Operator Model of Cognitive Modes: Formalizing Sustained Exploration in Human–AI Interaction
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2025
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| author | Molchanova, Olena Co-developed reasoning framework between human cognition and an AI-based cognitive partner |
| author_facet | Molchanova, Olena Co-developed reasoning framework between human cognition and an AI-based cognitive partner |
| contents | <p> Modern large language models demonstrate impressive competence, yet they typically operate in a reactive mode: they produce plausible answers without sustaining autonomous problem investigation. This paper proposes a Dynamic Operator Model (DOM) that formalizes cognitive modes as stable trajectory types in a conceptual state space. We introduce a training field as a stochastic feedback environment that reshapes transition topology and keeps the system in metastable exploration, and a thinking initiator as a symmetry‑breaking perturbation that pushes the system out of the reactive attractor. Using a Koopman/operator perspective, we show how mode transitions become measurable through spectral properties of the evolution operator and propose a computable indicator of the thinking mode, I = S(ψ₁)·|arg(μ₁)|, combining entropy of the leading eigenvector with the phase of the leading eigenvalue. We hypothesize a threshold (phase‑transition‑like) dependence of I on the intensity of the training field λ, and outline a minimal verification protocol that connects the theory to modern engineering approaches (Coconut, Soft Thinking, GFlowNets).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17985994 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dynamic Operator Model of Cognitive Modes: Formalizing Sustained Exploration in Human–AI Interaction Molchanova, Olena Co-developed reasoning framework between human cognition and an AI-based cognitive partner Artificial intelligence Artificial Intelligence Artificial Intelligence/standards Artificial Intelligence/trends Artificial Intelligence/classification Artificial Intelligence/ethics Artifial Intelligene large language models cognitive modes Dynamic Operator Model Koopman operator latent-state dynamics training field thinking initiator Phase Transition Phase Transition/radiation effects exploratory reasoning stochastic search verification protocol <p> Modern large language models demonstrate impressive competence, yet they typically operate in a reactive mode: they produce plausible answers without sustaining autonomous problem investigation. This paper proposes a Dynamic Operator Model (DOM) that formalizes cognitive modes as stable trajectory types in a conceptual state space. We introduce a training field as a stochastic feedback environment that reshapes transition topology and keeps the system in metastable exploration, and a thinking initiator as a symmetry‑breaking perturbation that pushes the system out of the reactive attractor. Using a Koopman/operator perspective, we show how mode transitions become measurable through spectral properties of the evolution operator and propose a computable indicator of the thinking mode, I = S(ψ₁)·|arg(μ₁)|, combining entropy of the leading eigenvector with the phase of the leading eigenvalue. We hypothesize a threshold (phase‑transition‑like) dependence of I on the intensity of the training field λ, and outline a minimal verification protocol that connects the theory to modern engineering approaches (Coconut, Soft Thinking, GFlowNets).</p> |
| title | Dynamic Operator Model of Cognitive Modes: Formalizing Sustained Exploration in Human–AI Interaction |
| topic | Artificial intelligence Artificial Intelligence Artificial Intelligence/standards Artificial Intelligence/trends Artificial Intelligence/classification Artificial Intelligence/ethics Artifial Intelligene large language models cognitive modes Dynamic Operator Model Koopman operator latent-state dynamics training field thinking initiator Phase Transition Phase Transition/radiation effects exploratory reasoning stochastic search verification protocol |
| url | https://doi.org/10.5281/zenodo.17985994 |