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
Read E_\ell as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
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
Read the surrounding source passage
2. Now apply this full equation to each environment slice
Each environment layer sees its own environment field:
E_\ell = \Pi_\ell(E)
Applying the entire equation to a layer gives:
(S_\ell^\*, D_\ell^\*) = \arg\min_{S_\ell', D_\ell'}
\Big[
\|D_\ell'(U,E_\ell)-B_\ell(S_\ell',E_\ell)\|
+ W_\ell(U,E_\ell)\cdot \text{Cost}_\ell(S_\ell',S_\ell)Exact original notation
E_\ell = \Pi_\ell(E)