Growth-Based AGI Whitepaper
Vortex formation, sparsity resilience, and information density as a measurable path to robust AGI.
Key Measures (from paper)
- Vortex count and persistence over time.
- Information density and entropy profiles.
- Sparsity resilience across removal strategies.
- Recovery time to target information flow.
Formalism
We track information concentration and circulation using entropy, flow fields, and topological summaries.
Local Shannon entropy: $$ H(\mathbf{x}, t) = - \sum_i p_i(\mathbf{x}, t)\, \log p_i(\mathbf{x}, t) $$
Fisher information (parameterized): $$ I(\theta) = \int \left( \partial_{\theta} \log p(\mathbf{x}; \theta) \right)^2 p(\mathbf{x}; \theta)\, d\mathbf{x} $$
Rényi entropy: $$ H_{\alpha} = \frac{1}{1-\alpha} \log \sum_i p_i^{\alpha} $$
Information flow field and vorticity analog: $$ \mathbf{J} = - D\, \nabla \rho + \rho\, \mathbf{v}, \qquad \boldsymbol{\omega} = \nabla \times \mathbf{J} $$
Vortex persistence (thresholded) over horizon T: $$ P_{\text{vtx}} = \frac{1}{T} \sum_{t=1}^{T} \mathbb{1}\{ \|\boldsymbol{\omega}(t)\| \ge \tau \} $$
Recovery time to 95% information flow: $$ T_{95\%} = \inf\{ t : \Phi(t) \ge 0.95\, \Phi_\text{baseline}\} $$
Method at a Glance
- Estimate p(x, t) over space or agent graph; compute local entropy and density ρ.
- Derive information flow \(\mathbf{J}\), then vorticity \(\boldsymbol{\omega}\); identify centers and boundaries.
- Run sparsity sweeps; compute persistence curve and AUC.
- Perturb and measure recovery time \(T_{95\%}\).
- Summarize topology via persistence diagrams and Betti curves.
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