Manuscript Psy03-B@1 · Psy03-B-v1.tex · section · 8ca3caf9

Architecture, masks, and data

The exact classical forward map and longitudinal state › Architecture, masks, and data · lines 248–291

Psy03-B@1#eq:invariant

The source architecture has

n_{0} = 2, n_{1} = n_{2} = 512, n_{3} = 256, n_{4} = 4.

Its weight matrices contain

N_{1} = 1024, N_{2} = 262144, N_{3} = 131072, N_{4} = 1024, N_{W} = 395264

coordinates. There are $1284$ unpruned biases.

Write

W_{ℓ} \in R^{n_{ℓ} \times n_{ℓ - 1}}, M_{ℓ}, S_{ℓ} \in {0, 1}^{n_{ℓ} \times n_{ℓ - 1}}, B_{ℓ} = W_{ℓ} \circ M_{ℓ} .

Here $M$ is the active mask and $S$ is the permanent-scar mask. The structural invariant is

M \circ S = 0.

An active coordinate can contain a numerically zero weight. Structural counts therefore use masks, not a numerical zero threshold.

The source's ordinary input law is

Y \sim Unif {0, 1, 2, 3}, X = μ_{Y} + 0.8 Z, Z \sim N (0, I_{2}),

with

μ_{0} = (- 3, - 3), μ_{1} = (3, 3), μ_{2} = (- 3, 3), μ_{3} = (3, - 3) .

The clean-center evaluation uses the different law $X = μ_{Y}$ .

Displayed formulas in this passage

Psy03-B@1#eq:invariant · line 272
$M \circ S = 0.$
unlabeled · line 251
$n_{0} = 2, n_{1} = n_{2} = 512, n_{3} = 256, n_{4} = 4.$
unlabeled · line 255
$N_{1} = 1024, N_{2} = 262144, N_{3} = 131072, N_{4} = 1024, N_{W} = 395264$
unlabeled · line 264
$W_{ℓ} \in R^{n_{ℓ} \times n_{ℓ - 1}}, M_{ℓ}, S_{ℓ} \in {0, 1}^{n_{ℓ} \times n_{ℓ - 1}}, B_{ℓ} = W_{ℓ} \circ M_{ℓ} .$
unlabeled · line 281
$Y \sim Unif {0, 1, 2, 3}, X = μ_{Y} + 0.8 Z, Z \sim N (0, I_{2}),$
unlabeled · line 286
$μ_{0} = (- 3, - 3), μ_{1} = (3, 3), μ_{2} = (- 3, 3), μ_{3} = (3, - 3) .$