Gain, protection, biased noise, and offsets

Let $a\in [0,1]$ denote the source's multiplicative inhibition_strength, $g\ge 0$ its gain_multiplier, and $p\in [0,1]$ its protection coordinate. The number $p$ is not a clinical protection probability.

With $c=1.05$, the source's gain function is exactly

Set

Although $a\le 1$, the effective multiplier $q$ can exceed one.

For independent standard Gaussian vectors $G_x,G_1,G_2,G_3$, activation $\phi \in \{\mathrm{ReLU},\tanh \}$, input-noise intensity $\xi \ge 0$, challenge bias $\beta \in \mathbb{R}$, and hidden-noise intensity $\sigma \ge 0$, define

This is the source's biased forward computation. Its ordinary forward computation is the case $\beta =0$ with the configured stress intensity.

The smallest maximizing class index resolves ties. Define

All probabilities below are fractions, not percentages. The source reports $100Q$.