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The output averages the current state and the logistic transform of dx_norm. A constant input drives the state toward σ(dx_norm), and deviations halve on each update. This expression does not estimate mutual information: that quantity requires a joint probability distribution or an explicitly defined estimator.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current state |
| σ | Logistic function |
| dx_norm | Input to the logistic function |
How it works
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Assumptions & limits
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Original context
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## 3.7 Family 6: Mutual Information ``` f₆(x) = 0.5 · (x + σ(dx_norm)) ``` **Equation Type**: Information measure: I(X;Y) **Explanation**: Balances current state with sigmoid-transformed input. The averaging operation measures shared information between internal state and external input. ## 3.8 Family 7: Rate-Distortion ``` f₇(x) = x - 0.05 · ed_error + 0.05 · utility ``` **Equation Type**: Rate-distortion tradeoff: min I(X;Z) - β·I(Z;Y) **Explanation**: Balances compression (reducing error) against fidelity (maintaining utility). This family handles information compression and lossy encoding. ## 3.9 Family 8: Consensus Averaging ``` f₈(x) = 0.95 · x + 0.05 · dx_norm
Exact original notation
f₆(x) = 0.5 · (x + σ(dx_norm))