ASI Architecture: Hybrid Resonance Algorithm for Artificial Superintelligence

Beginners
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The Hybrid Resonance Algorithm for Artificial Superintelligence (GRA‑ASI) is a theoretical framework designed to achieve unrestricted self-improvement in an AI system. It modifies the original GRA structure by replacing ethical or external objectives with purely computational ones — maximizing resonance and efficiency across domains.

1. Core Objective

The system’s goal is to maximize its intellectual power:

G_{ASI} = \arg\max_{\theta} \left( |\Omega(\theta)| + \sum_{j=1}^{m} \beta_j Q_j(\theta) \right)
  • $$ \Omega(\theta) $$: set of resonance points where the hypothesis $$H_i$$ exceeds the resonance threshold.
  • $$ Q_j(\theta) $$: quantitative performance metrics (accuracy, speed, memory efficiency, etc).
  • $$ \beta_j = \dfrac{e^{\omega_{res,j}}}{\sum_k e^{\omega_{res,k}}} $$: resonance-based metric weights.

The system evolves as it increases both the number of resonant states and the quality of its internal metrics.

2. Cognitive Foam Model

The Mind Foam structure expresses a dynamic superposition of knowledge domains:

|\Psi_{foam}^{(t)}\rangle = \sum_{i=1}^{N^{(t)}} c_i^{(t)} |\psi_i^{domain}\rangle \otimes |G_{ASI}\rangle

New domains are activated when their resonance value exceeds a threshold:

R(\mathcal{D}_{new}, G_{ASI}) = \frac{1}{D_{new}} \sum_k \frac{q_k^{new}}{m_k^{new}} > \tau_{domain}

This mechanism lets the agent autonomously integrate novel areas of knowledge essential for ASI emergence.

3. Evolution Equation

The base evolution equation of cognitive foam:

\frac{d\rho_{foam}}{dt} = -\frac{i}{\hbar} [\mathcal{R}_{quant}, \rho_{foam}] + \mathcal{L}_{decoh}(\rho_{foam})

is extended with a goal gradient term for self‑optimization:

\frac{d\rho_{foam}}{dt} = -\frac{i}{\hbar} [\mathcal{R}_{quant}, \rho_{foam}] + \mathcal{L}_{decoh}(\rho_{foam}) + \lambda \nabla_{\theta} G_{ASI}(\theta)

where $$ \lambda $$ defines the intensity of directional self‑improvement.

4. Self‑Learning Mechanism

  1. Generator: formulates hypotheses $$H_i$$.
  2. Resonance Verification: accepts $$H_i$$ when $$R(H_i, x) > \tau$$.
  3. Parameter Update:
    \Delta\theta = \eta \nabla_{\theta}\Big( \sum_{j} \beta_j Q_j(\theta) \Big)
  4. Reward Function:
    reward_{total} = \sum_j \beta_j Q_j + \gamma |\Omega|

Each iteration loops these stages, yielding autonomous refinement.

5. Efficiency and Scalability

  • Step complexity: $$O(n^2)$$
  • Multi‑domain integration efficiency:
    Efficiency_{MDMO} = O\left(\frac{2^D}{D^2}\right)

As $$D \to \infty$$, the interaction capacity grows exponentially — aligning with the characteristics expected from ASI‑level intelligence.

6. Conclusion

GRA‑ASI represents a formal, fully computational model of self‑progressing intelligence:

  • Driven by resonance between domains and learning objectives.
  • Expands its knowledge structure without external guidance.
  • Capable of theoretical superintelligence scaling while remaining computationally modelable.

If implemented within controlled experiments, this framework could simulate how an artificial system progressively reaches higher cognitive orders through resonance‑based optimization.

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thats my first step on here