Two different noise interfaces

Let $E_t,{G_t}^{\mathrm{in}}\in {\mathbb{R}}^d$ and ${G_t}^{\mathrm{hid}}\in {\mathbb{R}}^H$ be independent standard Gaussian vectors, independent of the latent example. The index $t$ denotes a step within one forward invocation.

The ordinary computation is

Here $\xi$ is the evaluator's additional input noise and $\tau$ is the source's ordinary stress_level.

The biased computation is

The readout in both cases is

The smallest maximizing index resolves ties.

The paths coincide when all their noise and bias intensities vanish. They otherwise perturb different spaces at different positions: ordinary stress enters the two-dimensional cell input, whereas biased stress enters the hidden update before the external activation.

The post-activation feed-forward bounds in Psy01-A and Psy03-A are therefore interface precedents, not formulas for (eq:ordinary) or (eq:biased) CheungPsy01A,CheungPsy03A.