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Recursive Feedback Systems: A Universal Equation for Balance Across Domains

1 points by txtatech 2y ago

txtatech 2y ago
Stabilization and symmetry are at the core of everything—from physics and biology to AI and economics. I have been working on a system that models this universal principle using *Recursive Feedback Systems (RFS)*. The concept is deceptively simple yet incredibly powerful: 1. *The Equation:* At the heart of the system is this balancing formula: $$ R_t(i) = \frac{w_{f,t} \cdot X(i) + w_{b,t} \cdot X'(i)}{w_{f,t} + w_{b,t}} $$ - *Forward Input ($X(i)$):* Pushes the system forward (growth, supply, signal). - *Backward Input ($X'(i)$):* Pulls it back (constraints, demand, noise). - *Weights ($w_{f,t}, w_{b,t}$):* Adjust dynamically based on feedback to find balance. 2. *Why It Matters:* The same principle applies to: - *Physics:* Modeling time-reversible systems and wave dynamics. - *AI:* Enhancing neural network training by balancing forward propagation and error correction. - *Economics:* Stabilizing markets by dynamically balancing supply and demand. - *Signal Processing:* Reducing noise while preserving information. 3. *What Makes It Unique:* - Simple, universal formula with dynamic, recursive adjustments. - Properties like *boundedness*, *convergence*, and *diversity preservation* ensure stability without rigidity. - Scales seamlessly across domains, from 1D sequences to multi-dimensional systems. 4. *Dive Deeper:* - *Code Examples:* [GitHub Repository](https://github.com/thatoldfarm/universal-stabilization https://github.com/thatoldfarm/universal-stabilization) - *Applications and Theory:* [Project Overview on Hive](https://peakd.com/stemsocial/@jacobpeacock/bidirectional-recursive-feedback-systems-a https://peakd.com/stemsocial/@jacobpeacock/bidirectional-rec...) I would love your thoughts and feedback. How do you see this approach impacting your domain or interest?