Layer or device behavior mapping

Read the equation

Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.

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 C_\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

2.1 Layer-level cost (macro Cℓ)

Use the minimized loss itself as the “activation cost”:

C_\ell = L_\ell^\*(S_\ell^\*, D_\ell^\*; U, E_\ell)

where

L_\ell^\* =
\|D_\ell'(U,E_\ell)-B_\ell(S_\ell',E_\ell)\|
+ W_\ell\cdot \text{Cost}_\ell
+ R_\ell

C_\ell = L_\ell^\*(S_\ell^\*, D_\ell^\*; U, E_\ell)

Related builds