Read the equation
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and measurements supplied to it.
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^\* 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
This is allowed and mathematically safe because:
• the form of the loss is identical
• only the environment term changes per layer
• each derived loss is a restriction of the global one:
L_\ell^\* = L^\*|_{\text{layer } \ell}
This means each neuron/layer measures:
• its OWN environment,
• using the SAME mathematical shape,
• ensuring global consistency.
⸻Exact original notation
L_\ell^\* = L^\*|_{\text{layer } \ell}Related builds
Sources & provenance
L_\ell^\* = L^\*|_{\text{layer } \ell}