Read the equation
The Laplacian ∇²x describes spatial diffusion and f(x) describes a local reaction. A numerical implementation must represent neighboring spatial positions and specify boundary conditions. The project scalar softsign update does not include this Laplacian, so the PDE is contextual rather than an executed equivalent.
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
## 3.3 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)
Exact original notation
Simplified reaction-diffusion: ∂x/∂t = D∇²x + f(x)