Read the equation
The expectation is taken under a variational distribution q(z); the integrand compares its log density with the joint generative density p(x,z). Under proper normalization, this equals a divergence from the posterior minus the log evidence. The project’s absolute-input penalty does not calculate these distributions.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
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
## 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
Exact original notation
Free energy: F = E[ln q(z) - ln p(x,z)]