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Adaptive Entangled Game Modules in Artificial General Intelligence
Haochen Li, Xinshuai Guo, Jingdong Ouyang, Wei Zhang, Leilei Shi
TL;DR
The paper addresses the lack of a comprehensive, interpretable account of human-like intelligence by introducing a generalized behavioral-intelligence probability-wave framework for adaptive interacting agents. Applied to Chinese intraday trading data, the framework finds that adaptive entangled game patterns dominate observed decisions and uses these behaviors to examine the LCA hypothesis and motivate brain-inspired AGI modules.
Problem
AGI lacks a comprehensive, interpretable theory of human-like intelligence amid complex cognition, neural interactions, and opaque ANN-based systems.
Method
The paper derives GBI probability-wave models and testable eigenmodes for independent and mutually influential adaptive entangled games, using trading behavior as an indirect probe of brain mechanisms.
Results
82-94% (89% overall) of trading decisions follow adaptive entangled game patterns, while truly independent modes comprise less than 5%.
Takeaways & Limitations
The findings provide empirical support for the LCA hypothesis and highlight adaptive entangled game modules as a direction for AGI architectures and human-like processing units.
Takeaways & Limitations
The study is limited to Chinese stock-market data, does not cover the full breadth of behavioral intelligence, and leaves comparative real-world evaluation for future work.
Abstract
from arXiv · showhide
We introduce a probability-wave framework for modeling the collective behavior of interacting adaptive agents, deriving testable eigenmodes through a generalized behavioral intelligence (GBI) nonlocal probability-wave equation. This framework captures a broad range of human intelligence behaviors with analytical mechanisms and offers an indirect method to examine the Liu-Chen-Ao (LCA) hypothesis of nonlocal entangled nerve fibers in the brain through collective trader behaviors. Our empirical analysis of Chinese intraday stock market data demonstrates that adaptive entangled game modes explain 82-94% (89% overall) of observed decision patterns, a sharp contrast to the predictions of neoclassical finance based on independent rational agents. Moreover, 2-12% of behaviors show adaption to intraday news, events, and environments, characterized by dual equilibrium states and abrupt reference point shifts, while purely independent modes occur in less than 5% of cases. These findings empirically support the LCA hypothesis, as observable trading behaviors reflect underlying brain mechanisms and internal intelligence decision-making in behavioral psychology. Our results highlight the necessity of incorporating adaptive entangled game modules into artificial general intelligence (AGI) architectures, addressing the limitations of conventional artificial neural network (ANN)-based AI, which relies on trillions of opaque parameters. By integrating ANN-based AI with probability-wave-based entangled-brain simulations, machine learning can enrich AGI foundation models (FMs) and facilitate the development of human-like processing units (HPUs) that leverage brain-inspired mechanisms. Such HPUs may ultimately create more compact, efficient, and robust AGI systems, particularly for embodied intelligence and robotics.
1. Introduction
The paper frames AGI as an unresolved problem of modeling complex, human-like intelligence and proposes a probability-wave GBI framework linking behavioral econophysics, AI, and nonlocal brain mechanisms. Its empirical analysis reports that adaptive entangled game modes dominate observed trading behavior and motivates their incorporation into AGI architectures.
- AGI lacks a comprehensive, interpretable theory despite the complexity of human cognition and neural interactions.
- The GBI probability-wave equation extends trading volume-price probability-wave modeling to analytical descriptions of human intelligence behaviors.
- Observable trading behavior is used as a proxy for internal decision-making and brain mechanisms to examine the LCA hypothesis indirectly.
- 82-94% (89% overall) of observed trading behaviors follow adaptive entangled game modes, while purely independent behaviors occur in less than 5% of cases.Adaptive responses to news, events, and environments appear in 2-12% of cases and feature dual equilibria and abrupt shifts.
- The paper proposes adaptive entangled game modules and brain-inspired HPUs as complements to ANN-based AI and foundation models.It presents these systems as potentially more compact, efficient, and robust, especially for embodied intelligence and robotics.
2. Methods and Data
The methods formulate collective adaptive behavior through operant constructs, reference-point interactions, and a generalized behavioral-intelligence probability-wave equation. Tick-by-tick Chinese stock-market data provide the behavioral setting for indirectly examining the LCA hypothesis.
- The model defines collective operant action, momentum, force, and energy to quantify interaction intensity, reference-point effects, and distributional structure.
- Tick-by-tick Chinese stock-market data from 2003, 2007-2009, 2019, and 2026 are used to observe collective trading behavior in dynamic environments.
- The framework models intelligent agents as mutually influential participants in adaptive games shaped by heuristics, learning, optimization, and feedback.
- The formalism defines operant momentum as cumulative operant quantity over time, operant force as momentum’s time rate of change, and operant energy as force multiplied by the reinforcement variable.
- Interdependent causation is represented through feedback-linked relationships among operant energy, mutually influential energy, and reference-point potential.
- The GBI probability-wave equation is derived using methods analogous to Schrödinger’s approach and serves as the framework’s core wave-function model.
3. Results and Empirical Tests
The empirical tests compare probability-wave models with independent and traditional statistical alternatives across Chinese intraday trading data. Adaptive entangled models capture most observed decision patterns, while additional analyses test robustness, model complexity, and independent-agent alternatives.
- Pattern analysis: 82–94% (89% overall) of decision-making patterns matched adaptive entangled game modes across four datasets.Pass/fail used the fixed R^2 ≥ R^2_crit threshold, with sequential screening across three fitting rounds.
- Robustness and comparison: The prevalence estimates are descriptive and should not be conflated with the proportion of sessions containing dual reference points.Prevalence was analyzed by period for Huaxia SSE50 ETF using bootstrap 95% confidence intervals and shuffle-control comparisons.
- Model-agnostic analysis: Bessel-Shi models were compared with Normal, Lognormal, and GMM2 baselines using model-agnostic time-series analyses of 635 Huaxia SSE50 ETF sessions.The analyses used weighted maximum likelihood, information criteria, bootstrap uncertainty, and shuffle falsification controls.
- Model-agnostic analysis: Real trading sessions exhibited stronger probability-wave coherent structure than randomized controls, with multi-center structure revealed across models.Jensen-Shannon divergence quantified departure from unimodal shape and volume-price coupling.
- Robustness and comparison: Out-of-sample and complexity-penalized analyses found that Bessel-Shi models reproduced multi-center structure parsimoniously with 2 explicit parameters versus 5 for GMM2, or up to 11 when BIC selected components.The broader analyses also tested reference-point mechanisms, independent-agent null hypotheses, and regime dependence of mutual influence intensity.
4. Discussions
The discussion presents the probability-wave framework as an interpretable alternative for modeling adaptive, interaction-driven behavior and connecting collective trading patterns to proposed brain mechanisms. It reports empirical support for adaptive entangled dynamics while emphasizing model-selection trade-offs, AGI applications, and important limits on interpretation and generalization.
- Motivation: ANN-based AI uses trillions of opaque parameters, motivating interpretable brain-inspired alternatives for AGI.The discussion links this challenge to ongoing efforts to simulate human brain mechanisms.
- Framework: The paper extends prior nonlocal brain and many-body wave research into a probability-wave framework for adaptive entangled behaviors and AGI foundation models.It positions the framework as part of a sequence of work connecting brain mechanisms, nonlocal systems, and machine learning.
- Empirical findings: 82-94% (89% overall) of decision-making patterns align with mutually influential adaptive entangled modes, while 2-12% show dual reference points and abrupt shifts.Fewer than 5% correspond to independent modes, and adaptive behavior predominates across the cited market-cycle observations.
- Interpretation: The results challenge independent-rational-agent assumptions and are presented as empirical support for the LCA hypothesis and interaction-driven nonlocal dynamics.The paper distinguishes interaction-coherent brain states from energy-quantum entanglement and relates them to observable market behavior.
- AGI implications: The GBI probability-wave approach represents uncertainty through interpretable eigenvalues and mutually influential energy equations rather than opaque parameters.Its proposed AGI role includes adaptive entangled game modules and human-like processing units for embodied intelligence and robotics.
- Model comparison: Across 635 sessions, the single wave model has lower BIC than GMM2 in 83.6% and beats the best unimodal baseline in 87.1%, but flexible mixtures lead raw held-out likelihood in 86.5%.The paper therefore argues for mechanism-level interpretability and parsimony rather than universal goodness-of-fit superiority.
- Limitations: The study does not cover the full breadth of behavioral intelligence, has so far used Chinese stock-market data, and does not establish out-of-sample directional predictability.The authors also reserve broader real-world evaluation and direct LCA testing for future work.
5. Conclusions
The paper reports that adaptive entangled game patterns dominate Chinese intraday trading decisions and motivates integrating these mechanisms with ANN-based AI for AGI.
- Opaque parameters in ANN-based AI impede understanding of embodied intelligence and advanced robotics within AGI.
- 82-94% of trading decisions, 89% overall, follow adaptive entangled game patterns rather than independent rational-agent behavior.The analysis uses Chinese intraday stock market data.
- 2~12% of behaviors exhibit dual equilibria and abrupt reference-point changes.
- Less than 5% of behaviors comprise truly independent modes.
- The proposed AGI direction combines ANN-based AI with adaptive entangled behaviors and brain-inspired human-like processing units.The paper presents this integration as a pathway toward compact, efficient, and robust systems for embodied intelligence and robotics.
Appendix 1: Mutually Influential Energy Equation
Appendix 1 formulates mutually influential energy within a general uncertain-system framework and connects the resulting equations to interdependent causation in complex adaptive systems.
- The appendix begins with assumptions for a formulation applicable to any uncertain system.
- The formulation defines q, q0, m, M, P, E(q,t), PE(q,t), and U(q) as reinforcement, quantity, probability, energy, cross-energy, and potential constructs.
- The cross energy term (m/M)E(q,t) represents mutually influential energy and is traceable to the Ising model.
- Substituting earlier equations produces a derived expression that can be rearranged into Eq. (4).
- Both resulting forms apply to complex adaptive systems and capture interdependent causation between inputs and outputs.
Appendix 2: Generalized behavioral intelligence probability wave equation
Appendix 2 derives the generalized behavioral intelligence probability-wave equation through Hamiltonian, variational, and separation-of-variables steps, while explicitly treating one conservative-system equation as an empirical extension for open systems.
- The appendix introduces an unknown function ψ(q,t) and a special solution within the probability-wave derivation.
- The appendix identifies q, t, R, S(q,t), B, and i in the wave representation, including the dimensional role of B and the imaginary-unit relation i^2=-1.
- The Hamiltonian formulation is acknowledged as strictly valid for energy-conservative systems but adopted phenomenologically for open GBI systems with empirical validation.The assumption is stated as falsifiable through robustness and out-of-sample reproduction of observed crowd operant dynamics.
- Separating variables transforms the preceding equation into two equations for further analysis.
- The derivation defines operant momentum Q and operant force Fm from the special-solution equation.
- A Lagrange functional is constructed, varied, and used with the Euler-Lagrange equation to derive the time-independent GBI probability-wave equation.
- The normalized function represents cumulative operant frequency or probability at q and satisfies a normalization condition.