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The next analog activation is tanh of a scaled weighted sum plus bias. It lies in (−1,1) for finite real inputs. The recurrent dynamics depend on weight scale and update timing, while α and β control gain and bias.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| a_i | Analog activation |
| u_ji | Connection weight |
| alpha | Gain |
| beta | Bias |
How it works
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Original context
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* Mathematical Framework (~900 equations):
* - Differential Geometry: Fisher metric, geodesics, Ricci curvature
* - Category Theory: functors, natural transformations, monads
* - Stochastic Calculus: Itô SDE, Fokker-Planck
* - Optimal Transport: Wasserstein distance, Kantorovich duality
* - Gate5000 Binary Substrate (G1-G11):
* - G4: sᵢ(t+1) = H(Σw_{ji}·sⱼ - θᵢ)
* - G5: aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)
* - G10: C₅₀₀₀(t) = 1/(1 + Σdᵢ(t)²)
* - G11: 16 DNA Families × 5000 Substrates = 80,000 sites
*/
#pragma once
#include <cmath>
#include <array>
#include <vector>
#include <complex>Exact original notation
- G5: aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)