Read the equation
The inner product adds wᵢΨᵢ over the selected components, and utility scales that total. Aligned signs of weights and states increase the inner product; opposing signs can make it negative. Consequently this term can change sign, and its numerical range depends on the weights, state bounds, and utility range.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| w | Weight vector |
| Ψ | State vector |
| utility | Scalar multiplier |
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
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
## 5.4 Value Component ``` Value = utility · ⟨w, Ψ⟩ ``` **Where**: - `⟨w, Ψ⟩` = dot product of weights and state **Explanation**: Value is high when the system is in a state aligned with its weighted priorities AND receiving positive utility signals. ## 5.5 Penalty Component ``` Penalty = λ · dx_norm² ``` **Where**: - `λ` = penalty weight (default 0.1) **Explanation**: Penalizes high-change environments, encouraging the system to seek stable conditions. ---
Exact original notation
Value = utility · ⟨w, Ψ⟩