gh-eq-47d8bc25403dcd20documented-equation
Read the equation
The state moves in the direction of utility−x, with step magnitude 0.2|utility−x|/(1+|utility−x|). For a fixed utility, the error is multiplied by 1−0.2/(1+|error|), which lies between 0.8 and 1; the update reduces that error without crossing the target. This is a target-tracking rule, not the gradient of an arbitrary utility function.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current scalar state |
| utility | Target value |
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
A genuine objective optimizer needs the objective and an argument whose value is being optimized.
Original context
Read the surrounding source passage
## 3.4 Family 3: Optimization ``` f₃(x) = x + 0.2 · softsign(utility - x) ``` **Equation Type**: Gradient ascent: x* = arg max U(x) **Explanation**: Actively seeks to maximize utility by moving toward higher-value states. The larger 0.2 coefficient makes this an aggressive optimizer. The softsign prevents overshooting. ## 3.5 Family 4: Bayesian Inference ``` f₄(x) = clamp₀₁((x + utility) / (1 + |utility|)) ``` **Equation Type**: Posterior update: P(θ|D) ∝ P(D|θ)P(θ) **Explanation**: Implements belief updating where the current state serves as prior and utility as likelihood. Division by (1 + |utility|) normalizes the posterior. Used for probabilistic reasoning. ## 3.6 Family 5: Learning / Weight Update ``` f₅(x) = x + 0.1 · dx_norm
Exact original notation
f₃(x) = x + 0.2 · softsign(utility - x)
Related builds
Sources & provenance
01
That AI Guy Core — Mathematical Reference v1.0.0
Lines 129–129
02
That AI Guy Core — Mathematical Reference v1.0.0
Lines 129–129