Read the equation
The state receives the increment 0.05(utility−|dx_norm|). The absolute-value term penalizes input magnitude regardless of its sign, while utility contributes with its sign intact. This operation does not compute variational free energy, because it contains neither the variational distribution q nor a generative density p.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current state |
| dx_norm | Magnitude-penalized input |
| utility | Utility contribution |
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
## 3.12 Family 11: Variational Free Energy ``` f₁₁(x) = x - 0.05 · |dx_norm| + 0.05 · utility ``` **Equation Type**: Free energy: F = E[ln q(z) - ln p(x,z)] **Explanation**: Minimizes surprise (absolute change) while maximizing utility. This implements the free energy principle from theoretical neuroscience. ## 3.13 Family 12: Compression / Rate Control ``` f₁₂(x) = x - 0.05 · |dx_norm| ``` **Equation Type**: Compression: minimize description length **Explanation**: Actively reduces complexity by damping large changes. Used for finding minimal representations. ## 3.14 Family 13: Memory Trace (Zecher) ``` f₁₃(x) = x + 0.02 · (dx_norm + utility)
Exact original notation
f₁₁(x) = x - 0.05 · |dx_norm| + 0.05 · utility