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Every intermediate component is multiplied by the shared normalization factor b(t+1). A shared positive multiplier preserves component signs and relative proportions but reduces their magnitudes when b<1. The norm bound derived for the normalization function applies only if this b is computed from the same intermediate vector.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| b | Norm-dependent shared scale |
| Ψ_triple_prime | Intermediate vector after stability gating |
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Original context
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## 4.5 Final Normalization ``` Ψ_i(t+1) = Ψ'''_i(t+1) · b(t+1) ``` **Where**: - `b(t+1)` = normalization factor from equation 2.2 **Explanation**: All family activations are scaled by the normalizer, ensuring bounded behavior. --- # 5. Objective Function (Omega) ## 5.1 Complete Objective ``` Ω = Surprise + Uncertainty - Value + Penalty ``` **Explanation**: The system seeks to minimize Ω. This is analogous to free energy in variational inference - the system wants low surprise, low uncertainty, high value, and low penalty. ## 5.2 Surprise Component
Exact original notation
Ψ_i(t+1) = Ψ'''_i(t+1) · b(t+1)