Toward to understanding socio-cognitive dynamical systems : Stewardship for human collective behavior through artificial agents Kazuya Horibe

Society in the real world is dynamic Suppose the game can be formulated as a game and the landscape can be written, ● Defining an optimal solution is difficult or impossible ● There is no fixed attractor to which the population should converge ● Attractors change over time as new problems emerge, both endogenous and exogenous Background Understanding the process by which groups adapt to different games and contexts (social adaptation) is more important than optimization of a specific game. [Galesic+ 2023] 231215_MA_JC

Can social adaptation be numerically/theoretically modeled? Challenges1：High dementional dynamamical system ● Need to low dimensionalization ● The game's landscape is dynamic. ○ A metagame description that allows for rule changes is necessary. ○ Potential for alternative formulations or approximations. Challenges2：Local optimization for each player (does not align grolverly with theory) ● Players do not have complete knowledge of the entire payoff landscape. ● Humans do not always act optimally. ○ It is necessary to evaluate deviations from the optimal theoretical values. Question

Challenges and Strategies for Modeling Social Adaptation Strategy Challenges1：High dementional dynamamical system ● Need to low dimensionalization ● The game's landscape is dynamic. ○ A metagame description that allows for rule changes is necessary. ○ Potential for alternative formulations or approximations. Challenges2：Local optimization for each player (does not align grolverly with theory) ● Players do not have complete knowledge of the entire payoff landscape. ● Humans do not always act optimally. ○ It is necessary to evaluate deviations from the optimal theoretical values. ● Dimensionality reduction ● Estimating the entire system from partial information(From partial to whole) ● Emulating local optimization with a group of LLMs New methods for dynamical adaptation LLMs as models of non-rational and imperfect humans

Dimensionality reduction 1: Energy landscape analysis Advantages ● Any type of binarized time-series data ● Allows understanding of collective dynamics as trajectories in a landscape ● A landscape corresponds to the probability of state occurrences Disadvantages ● The dimension of the time series is not scalable (empirically, up to about N~15 can be analyzed) [Ezaki+ 2017] Strategy

Dimensionality reduction 2: conventional methods: UMAP/PCA 231111_MA_JC he Iterated Evolutionary Prisoner's Dilemma Game for a Group Using LLM (N=30) [Suzuki & Arita 2024] Advantages ● Commonly used Disadvantages ● Difficult to interpret the axes after dimension reduction Strategy

From partial to whole 1: Estimating bifurcation with reservoir computing Capabilities ● Predict bifurcations in phase space from time series data before bifurcation. [Kim+ 2021] Strategy

From partial to whole 2: Connecting local geometries through linear approximation Capabilities ● Approximating geometry from local time-series data ● Stochastically describing transitions between approximated geometries ● Can apply to neural dynamics of C. elegans [Costa+ 2019] Strategy

Challenge 1:What can we ultimately achieve? Challenges1：High dementional dynamamical system ● Low dimensionalization ○ Energy landscape analysis ○ Dimensionality reduction ● From partial to whole (keep high dimension) ○ Estimating bifurcation ○ Connecting of linear approximations attractor ■ Partitioning of chaos attractors Could formulate the dynamics of a group as trajectories on an adaptive geometry Strategy

Challenges and Strategies for Modeling Social Adaptation Challenges1：High dementional dynamamical system ● Need to low dimensionalization ● The game's landscape is dynamic. ○ A metagame description that allows for rule changes is necessary. ○ Potential for alternative formulations or approximations. Challenges2：Local optimization for each player (does not align grolverly with theory) ● Players do not have complete knowledge of the entire payoff landscape. ● Humans do not always act optimally. ○ It is necessary to evaluate deviations from the optimal theoretical values. ● Dimensionality reduction ● Estimating the entire system from partial information(From partial to whole) ● Emulating local optimization with a group of LLMs New methods for dynamical adaptation LLMs as models of non-rational and imperfect humans Strategy

LLMs as models of non-rational and imperfect humans Strategy [Akata+ 2023] LLMs can adjust non-rational and imperfect aspects through prompts Playing repeated games in an example game of Battle of the Sexes

Challenge 2: What can we ultimately achieve? Strategy Challenges2：Local optimization for each player (does not align grolverly with theory) ● LLMs can adjust non-rational and imperfect aspects through prompts Could evaluate deviations from the optimal theoretical values using LLM Trajectory with noise Branching induced by noise

Challenges and Strategies for Modeling Social Adaptation Strategy Challenges1：High dementional dynamamical system ● Need to low dimensionalization ● The game's landscape is dynamic. ○ A metagame description that allows for rule changes is necessary. ○ Potential for alternative formulations or approximations. Challenges2：Local optimization for each player (does not align grolverly with theory) ● Players do not have complete knowledge of the entire payoff landscape. ● Humans do not always act optimally. ○ It is necessary to evaluate deviations from the optimal theoretical values ● Dimensionality reduction ● Estimating the entire system from partial information(From partial to whole) ● Emulating local optimization with a group of LLMs New methods for dynamical adaptation LLMs as models of non-rational and imperfect humans Challenges3：Improveing performance of human collective behavior through artificial agent

LLMs debate improves hallucination and enhances reasoning abilities [Du+ 2023] Strategy Debating elementary school math problems The number of agents and the debate rounds improve the accuracy of reasoning

Artificial agents and robots enhance cooperation among human groups Method [Sebo+ 2018]

Challenge 3: What can we ultimately achieve? Strategy Challenges3：Improveing of human collective behavior through artificial agent ● Debate improves hallucination and enhances reasoning abilities ○ When the problem is made more complex, can increasing the number of agents solve it? ■ Dose phase transition exist or not? ● Artificial agents and robots enhance cooperation among human groups Verbal interventions by agents might facilitate trajectory design Verbal interventions by agents may be used to examine properties of trajectories, such as robustness

Toy model 1: Simple coordination game Research plan

Toy model 2: Social Learning in Reinforcement learning N-armed bandit problem ● Agents have three actions: innovate (non-social learning), observe (social learning), and exploit (rewards are obtained only through exploitation). ● Evolution ● Temporal changes in the rewards of the bandit Research plan [Rendall+ 2010]

Challenges and Strategies for Modeling Social Adaptation Summary Challenges1：High dementional dynamamical system ● Need to low dimensionalization ● The game's landscape is dynamic. ○ A metagame description that allows for rule changes is necessary. ○ Potential for alternative formulations or approximations. Challenges2：Local optimization for each player (does not align grolverly with theory) ● Players do not have complete knowledge of the entire payoff landscape. ● Humans do not always act optimally. ○ It is necessary to evaluate deviations from the optimal theoretical values. ● Dimensionality reduction ● Estimating the entire system from partial information(From partial to whole) ● Emulating local optimization with a group of LLMs New methods for dynamical adaptation LLMs as models of non-rational and imperfect humans Challenges3：Improveing performance of human collective behavior through artificial agent

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