CoCre-Sam (Kokkuri-san): Modeling Ouija Board as Collective Langevin Dynamics Sampling from Fused Language Models

Tadahiro Taniguchi; Masatoshi Nagano; Haruumi Omoto; Yoshiki Hayashi

cs.MAJul 16, 2025

CoCre-Sam (Kokkuri-san): Modeling Ouija Board as Collective Langevin Dynamics Sampling from Fused Language Models

Authors: Tadahiro Taniguchi, Masatoshi Nagano, Haruumi Omoto, Yoshiki Hayashi

Organizations: Graduate School of Informatics, Kyoto University, Japan · Ritsumeikan University, Japan · University of Reading, UK

Abstract

Collective human activities like using an Ouija board (or Kokkuri-san) often produce emergent, coherent linguistic outputs unintended by any single participant. While psychological explanations such as the ideomotor effect exist, a computational understanding of how decentralized, implicit linguistic knowledge fuses through shared physical interaction remains elusive. We introduce CoCre-Sam (Collective-Creature Sampling), a framework modeling this phenomenon as collective Langevin dynamics sampling from implicitly fused language models. Each participant is represented as an agent associated with an energy landscape derived from an internal language model reflecting linguistic priors, and agents exert stochastic forces based on local energy gradients. We theoretically prove that the collective motion of the shared pointer (planchette) corresponds to Langevin MCMC sampling from the sum of individual energy landscapes, representing fused collective knowledge. Simulations validate that CoCre-Sam dynamics effectively fuse different models and generate meaningful character sequences, while ablation studies confirm the essential roles of collective interaction and stochasticity. Altogether, CoCre-Sam provides a novel computational mechanism linking individual implicit knowledge, embodied collective action, and emergent linguistic phenomena, grounding these complex interactions in the principles of probabilistic sampling.

Figures & tables

Figure 1: Conceptual illustration of the CoCre-Sam framework. Multiple agents interact with a shared planchette on a letter board. Each agent $i$ possesses an internal language model $P_{i}(c_{\tau+1}|c_{1:\tau})$ defining an energy landscape $E_{i}$ . They exert micro-forces $a_{i}(t)$ based on their local energy gradient $-\nabla E_{i}$ and stochastic noise (Langevin dynamics). The collective force $a(t)=\sum_{i}a_{i}(t)$ guides the planchette $x(t)$ , effectively performing sampling from the fused energy landscape $E_{\rm fused}=\sum_{i}E_{i}$ . As a result, a character sequence is generated not from either agent’s distribution alone, but from a fused probabilistic model that approximates a product-of-experts form. This leads to the attribution of agency to an imaginary creature named “Kokkuri-san,” distinct from either agent, as the perceived author of the outcome.

Figure 2: (Left) The CoCre-Sam simulation environment, representing the Ouija board as a 2D embedding space. Each letter, plus ’BOS’ (Begin) and ’EOS’ (End) tokens, is assigned a specific target location

g_{c}

. (Right) An example trajectory of the planchette

x(t)

from a simulation with

N=2

agents. The collective Langevin dynamics, driven by the agents’ fused energy landscapes (Eq. (4)), stochastically sample the coherent sequence ’P-E-O-N-Y-EOS’. Each color represents the trajectory segment as the dynamics converge on the goal location for each successive character, demonstrating the model’s generative process.

	Agent 1 ( $P_{1}$ )		Agent 2 ( $P_{2}$ )		CoCre-Sam ( $\propto\sqrt{P_{1}P_{2}}$ )
#	String	Freq (mean $\pm$ SD)	String	Freq (mean $\pm$ SD)	String	Freq (mean $\pm$ SD)
1	petunia	$21.6\pm 3.9$	quassia	$27.6\pm 5.2$	quaker	$23.6\pm 1.6$
2	jacobinia	$16.0\pm 2.6$	quaker	$17.6\pm 3.4$	jacobinia	$17.6\pm 2.9$
3	quince	$12.0\pm 2.4$	primrose	$\phantom{0}9.8\pm 4.3$	petunia	$15.8\pm 3.5$
4	iris	$11.2\pm 2.3$	rue	$\phantom{0}9.6\pm 2.4$	rockrose	$12.4\pm 3.0$
5	kalmia	$\phantom{0}8.8\pm 1.6$	jacobinia	$\phantom{0}8.2\pm 1.6$	quassia	$\phantom{0}8.4\pm 4.5$

Table 1: Top 5 generated flower names and their frequencies under various conditions. CoCre-Sam (

\propto\sqrt{P_{1}P_{2}}

) is the proposed model. ’No Noise’ (

\mathcal{T}_{i}=0.0

) is a deterministic gradient descent, ’Middle Noise’ (

\mathcal{T}_{i}=0.5

) an intermediate setting, and ’High Noise’ (

\mathcal{T}_{i}=1.0

) approaches a random walk. Frequencies are reported as mean

\pm

SD across 5 random seeds , with 100 trials per (seed, condition).

	Evaluated by LM:
Gen. by	$P_{1}$	$P_{2}$	Fused ( $\sqrt{P_{1}P_{2}}$ )
Agent 1	$\mathbf{1.840\pm 0.027}$	$2.128\pm 0.076$	$1.920\pm 0.038$
Agent 2	$2.509\pm 0.133$	$\mathbf{1.935\pm 0.046}$	$2.139\pm 0.074$
CoCre-Sam	$1.951\pm 0.037$	$\mathbf{1.855\pm 0.020}$	$\mathbf{1.862\pm 0.017}$

Table 2: Perplexity of generated valid words (mean

\pm

SD across 5 random seeds, 100 trials each; word-level, then averaged with denominator 100 to match the generative process). Each row indicates the generating model; each column indicates the evaluation LM. Lower perplexity means higher predictability. The lowest entry in each row is bold ; for CoCre-Sam,

P_{2}

and Fused are both bolded because they are statistically tied (paired

t

-test,

|t|=0.64

p>0.40

n=5

seeds).

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : Flowchart of the hierarchical control in CoCre-Sam. The outer loop for character sequence generation (see Algorithm A.1 ) determines the energy function by weighting elemental energy functions based on the context $c_{1:\tau}$ , while the inner loop simulates the probabilistic convergence of the planchette dynamics driven by the resulting energy landscape.

Figure D.2 : Step-by-step visualization of the word generation process for the word PEONY , followed by the [EOS] token. The six panels, arranged left-to-right, then top-to-bottom in a 3

\times

2 layout, show the evolution of the fused energy landscape

E_{\rm fused}

and the planchette’s trajectory as each new character is selected.

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