State or environment definition

Read the equation

Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update operators.

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

1. Read X_\ell as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

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

1.1 Macro-neuron state and operator

For layer-neuron N_\ell:
•	State:
X_\ell = (S_\ell, D_\ell, E_\ell)
•	Internal “firing” operator (the thing it does when activated):
T_\ell(X_\ell) = (S_\ell^\*, D_\ell^\*)
defined by the argmin above.

So:

N_\ell: X_\ell \;\mapsto\; T_\ell(X_\ell)

X_\ell = (S_\ell, D_\ell, E_\ell)

Related builds