AGI: recursive, compositional, and hierarchical intelligence

• Identify the current state and possible next states.

• Use the transition matrix P(Xn∣Xn−1)P(Xn∣Xn−1) to organize all steps; every state carries features that will be analyzed for patterns (e.g., symptoms, signs, historical status).

Recursive Propagation

• Multiply the state matrix by the transformation matrix as logic or external stimuli propagate recursively:

P(i)n,m(new)=Tk⋅P(i)n,m(old)P(i)n,m(new)=Tk⋅P(i)n,m(old)

• After each recursion, collect new feature sets for pattern analysis.

Timing/Transition Evaluation

• For each transition between states or logic flows, calculate waiting time:

ai=1νiai=νi1

• These timings can influence when pattern recognition subroutines are activated.

Generator Matrix Application

• Use the generator matrix to set the rates at which pattern recognition or feature analysis is called for each node or module:

Qn,m={−ann=man⋅p(i)n,mn≠mQn,m={−anan⋅p(i)n,mn=mn=m

• At each transition, update features and call the pattern-finder.

Recursive Logic Reflection

• Track the evolution of logic states, reflective computation:

T(n)=(n×R)+(n−1)×1+(n−2)×0T(n)=(n×R)+(n−1)×1+(n−2)×0

• Pass these states into the pattern routine to compare for cyclical or mirrored features.

Superposition—Pattern Mixing

• For any set of states (e.g., symptoms, biomarkers, conditions), represent the total state as a superposition:

∣Ψ⟩=13(∣A⟩+∣B⟩+∣Reflection⟩)∣Ψ⟩=31(∣A⟩+∣B⟩+∣Reflection⟩)

• Run the normalized pattern-finding equation on each component.

Hebbian Learning—Recursive Memory Update

• As learning occurs, update weights (features, pattern probabilities) and run the pattern routine after each update:

wij(t+1)=wij(t)+η xi xj+ξ(t)wij(t+1)=wij(t)+ηxixj+ξ(t)

• xi,xjxi,xj are the measured feature values.

 Integration—Pattern Across Modules

• At higher levels, compute overall system patterns from the sum (or other functions) of all pattern recognition routines run on subsystems:

Φ=Output of integrated pattern routinesΦ=Output of integrated pattern routines

Pattern-Finding Subroutine

For any set of features or states, repeatedly apply:

P(xi)=xi∑jxjP(xi)=∑jxjxi

• Normalize your feature vectors at every state/step (output from the other equations).

• Compare the resulting probability vector against reference patterns or templates.

• Use difference/scoring metrics to recognize, classify, or detect anomalies.

Summary Algorithm Flow

1. Progress through the recursive state/model steps (1-8).

2. At each step or recursion, extract features, normalize with the pattern equation.

3. Match normalized vectors to known patterns or use them for anomaly detection.

4. Integrate results to update global system or make decisions.

This synthesis yields a grand recursive brain algorithm with embedded pattern recognition, enhancing insight and adaptability at every step, as supported in recursive neural program literature and neuromorphic brain-inspired frameworks.tandfonline+3