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The source expression adds dx times a sigmoid of the current scalar’s weighted value. The body additionally caps the increment magnitude at 0.2 and clips the final value to the unit interval. These two bounds are part of the implemented transition and affect its response to large inputs.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current scalar |
| dx | Proposed change scale |
| w | Sigmoid input weight |
How it works
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Assumptions & limits
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Original context
Read the surrounding source passage
}
}
/**
* @brief Layer transition functions (tight coupling)
*/
namespace transitions {
// T₁₂: X' = X + dx·σ(W·X)
inline double L1_to_L2(double x, double dx, double w = 0.8) {
double activation = math::sigmoid(w * x);
double x_prime = x + dx * activation;
double delta = std::abs(x_prime - x);
if (delta > 0.2) {
x_prime = x + 0.2 * (x_prime > x ? 1.0 : -1.0);
}
return math::clamp(x_prime);
}
Exact original notation
T₁₂: X' = X + dx·σ(W·X)