gh-eq-1388750b6f58e64ddocumented-equation
Read the equation
The actual scalar update is 0.95x+0.05 softsign(dx_norm). It smooths a bounded transform of the input, approaching that transform when the input is constant. No spatial neighbors, Laplacian, or diffusion coefficient appear in this operation; reaction-diffusion is the family’s motivating label, not the spatial PDE computed here.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current state |
| dx_norm | Input transformed by softsign |
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 reaction-diffusion PDE requires a spatial derivative or a specified discrete neighbor operator.
Original context
Read the surrounding source passage
## 3.3 Family 2: Reaction-Diffusion ``` f₂(x) = x + 0.05 · (softsign(dx_norm) - x) ``` **Equation Type**: Simplified reaction-diffusion: ∂x/∂t = D∇²x + f(x) **Explanation**: Models pattern formation and spreading activation. The softsign function bounds the diffusion term, preventing runaway reactions. Used for spatial reasoning and pattern recognition. ## 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|))
Exact original notation
f₂(x) = x + 0.05 · (softsign(dx_norm) - x)
Related builds
Sources & provenance
01
That AI Guy Core — Mathematical Reference v1.0.0
Lines 119–119
02
That AI Guy Core — Mathematical Reference v1.0.0
Lines 119–119