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A weighted sum of prior binary states is compared with a threshold through a step function H. The result is a binary next state. The exact convention at equality and the direction of each stored weight index must be supplied by the implementation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| s_i | Binary state |
| w_ji | Input weight |
| theta_i | Threshold |
| H | Step function |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
*
* 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>Exact original notation
- G4: sᵢ(t+1) = H(Σw_{ji}·sⱼ - θᵢ)