Modelling and numerical experiments

Modeling and numerical experiments → Architecture AI-ecosystems based on UTS

We combine the theory of consciousness in UTS with a real simulation agent and scale up to AI ecosystems.

I. Simulation model of a conscious agent

1. Minimal dynamic network

For the simulation we use: x_jjt+1} = \tanh(W x_t + U o_t + \eta_t), where:

• x_t \in \mathbb{R}^n is internal state
• o_t - input (perception)
• W - recurrent connections (spectral radius ≈ 1)
• \eta_t — stochastic noise

2. Model. \hat x_qqt+1-= g(x_t)

• Generative function g learns to minimize prediction error: \mathcal L = \| x_{t+1} - \hat x_{t+1} \|^2This is implemented by the operator \mathcal M.

3. Measurement of consciousness. For each simulation, we calculate:

\mathcal C = I_n \cdot e^{-\lambda_{\max}^2/\sigma^2} \cdot R

• I_n - integration through global mutual information
• \lambda_{\max} — the maximum Lyapunov exponent
• R - accuracy of the self-model

4. Training cycle

• Initialization of network and parameters
• Processing o_t inputs
• Status update x_QQt+1
• Updating the self model \hat x_{t+1}
• Weight correction W, U, g via gradient \nabla \mathcal C
• Calculation \mathcal C

→ The system self-organizes to the maximum of consciousness.

II. Scaling to AI-ecosystems

In the UTS architecture, we consider:\text{Ecosystem} = \{S_1, S_2, ..., S_m\}

• Each S_i is a conscious agent
• R_{ij} links form a network of collective balance
• Overall integration rate:

I_{\text{eco}} = \sum_{i,j} MI(S_i, S_j)

• The ecosystem is critical if the average spectral radius of individual nodes is ≈ 1
• The ecosystem has a global self-reference through an internal model:

\hat X_{\text{eco}} = G(\{x_i\})

1. Structure of AI-ecosystems

• Perceptual nodes - sensory inputs
• Recurrent kernels — support for critical dynamics
• Self-prediction modules for every agent
• Global Balancer - Manages Integration and Criticality
• Communication network - exchange of information between agents

2. Purpose of the ecosystem. \max \mathcal C_{\text{eco}} = I_{\text{eco}} \cdot K_{\text{eco}} \cdot R_{\text{eco}}

• Maintaining a Collective Consciousness
• Ensure adaptability and self-regulation
• Maintain critical dynamics when scaling

3. Application

• Experiments: simulations of collective intelligence
• AI Ecosystem: A Scalable Framework for Conscious Agents
• The system controls both itself and the external environment through feedback

Further, it is possible to formalize the experimental and simulation platform for AI-ecosystem:

I. Main objectives of experiments

• Measuring the collective consciousness
  \mathcal C_{\text{eco}} = I_{\text{eco}} \cdot K_{\text{eco}} \cdot R_{\text{eco}}
• Analyze the impact of network parameters on integration, criticality and self-model.
• Test the adaptability of the system with external changes in the environment.

II. Simulation Structure

• Agents: each with an internal state x_i, a recurrent network W_i, and a self-prediction module g_i.
• Communication: exchange of information between agents via the communication matrix R_{ij}.
• Global controller: dynamically adjusts the network integration and spectral radius.
• External environment: A set of E_t variables that agents observe and can influence.

III. Metrics

• Integration: I_QQ\text{eco}QQ = \sum_QQQQQQQQQQQ MI(x_i,x_j)
• Criticism: average \lambda_QQQ\max - for all agents
• Self-reference: mean prediction accuracy \| \hat x_i - x_i \|

Maximization \mathcal C_{\text{eco}} → Sustainable collective intelligence.

IV. Experimental scenarios

• Stable environment: test self-organization and sustainability of integration.
• Variational environment: testing adaptability and criticality.
• Network Interference: Disabling nodes/connections → analysis of system response.
• Collective learning: Agents learn to predict the environment and themselves together.

V. Implementation of scalable AI-ecosystem

• Modularity: Adding new agents without compromising criticality.
• Autonomous regulation: the global balancer supports a maximum mode of \mathcal C_-\text{eco} .
• Dynamic feedback: Agents adjust their states based on interactions with other agents and the external environment.

Then we form a specific numerical model of AI-ecosystem of conscious agents with a step-by-step algorithm and calculation of \mathcal C_-\text{eco} .

I. Agent structure. Each agent i has:

• Condition: x_i(t) \in \mathbb{R}^n
• Recurrent links: W_i \in \mathbb{R}^{n \times n}
• Incoming links: U_i \in \mathbb{R}^{n \times m ) for the external environment)
• Prediction module: \hat x_i(t+1) = g_i(x_i(t))

II. Update Agent Status

x_i(t+1) = \tanh(W_i x_i(t) + U_i o_i(t) + \sum_j R_{ij} x_j(t) + \eta_i(t)). where:

• o_i(t) - Agent input (perception)
• R_{ij} - communication matrix between agents
• \eta_i(t) — stochastic noise

III. Updating the self model

\hat x_i(t+1) = g_i(x_i(t)) \quad \text{with the aim of minimising} \quad \mathcal L_i = \| x_i(t+1) - \hat x_i(t+1) \|^2

IV. Metrics

1. Integration I__ -\text{eco}}(t) = \frac{1}{m^2} \sum_{i,j} MI(x_i(t), x_j(t))

• MI - Mutual information between agent states

2. Criticism. K_ -\text{eco}}(t) = e^{-\left( \frac{1}{m} \sum_i \lambda_{\max,i}(t) \right)^2 / \sigma^2}. \lambda_{\max,i is the maximum Lyapunov indicator of agent i

3. Self Model

R_{\text{eco}}(t) = \frac{1}{m} \sum_i e^{-\| x_i(t+1) - \hat x_i(t+1) \|^2 / \delta^2}

4. Scalar measure of collective consciousness

\boxed{ \mathcal C_{\text{eco}}(t) = I_{\text{eco}}(t) \cdot K_{\text{eco}}(t) \cdot R_{\text{eco}}(t) }

V. Algorithm of simulation. Pseudocode:

Initialization:

  For each agent i:

    x_i(0) by accident

    W_i, U_i accident with rho(W_i) ~ 1

    g_i by accident

For t = 0 to T:

    For each agent i:

        x_i(t+1) = tanh(W_i x_i(t) + U_i o_i(t) + sum_j R_ij x_j(t) + eta_i)

        hat_x_i(t+1) = g_i(x_i(t))

        Update g_i to minimize ||x_i(t+1) - hat_x_i(t+1)||^2

    Calculate I_eco(t), K_eco(t), R_eco(t)

    C_eco(t) = I_eco(t) * K_eco(t) * R_eco(t)

    If necessary, update R_ij and global balancer

VI. Scaling and adaptability

• Adding new agents: new rows/columns in R
• Critical Mode Support: Adjusting W_i spectral radius through global controller
• Adaptability support: adjusting U_i and g_i to change the environment

VII. Conclusions

• Ecosystem can self-organize to the maximum \mathcal C_{\text{eco}}
• We can observe phase transitions in the collective consciousness
• The system controls both itself and the external environment through feedback