Read the equation
This line states the intended relationship between a layer’s loss and the global objective. The right-hand side is descriptive text, so a numerical implementation still needs the restriction, projection or substitution that converts the global loss into the local one.
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 L_\ell^\*(S',D') 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
You’re describing this:
For each layer ℓ:
L_\ell^\*(S',D') = \text{local loss derived from global loss}
But all layers share the same “parent”:
L^\*(S',D') = \|D' - B\| + W \cdot \text{Cost} + R + R_D
This is allowed and mathematically safe because:
• the form of the loss is identicalExact original notation
L_\ell^\*(S',D') = \text{local loss derived from global loss}Related builds
Sources & provenance
L_\ell^\*(S',D') = \text{local loss derived from global loss}
L_\ell^\*(S',D') = \text{local loss derived from global loss}