Read the equation
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron or task instance. Each version needs the source-specific behavior/design functions, environment and weights before it can be numerically evaluated.
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
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
+ R_{D,\ell}
So:
• Small C_i before was per neuron.
• Now C_\ell is per layer-neuron, equal to “how much loss is left” after optimizing that layer.
2.2 Layer loop ΦℓExact original notation
L_\ell^\* =
\|D_\ell'(U,E_\ell)-B_\ell(S_\ell',E_\ell)\|
+ W_\ell\cdot \text{Cost}_\ell
+ R_\ell
+ R_{D,\ell}Related builds
Sources & provenance
L_\ell^\* = \|D_\ell'(U,E_\ell)-B_\ell(S_\ell',E_\ell)\| + W_\ell\cdot \text{Cost}_\ell + R_\ell + R_{D,\ell}
L_\ell^\* = \|D_\ell'(U,E_\ell)-B_\ell(S_\ell',E_\ell)\| + W_\ell\cdot \text{Cost}_\ell + R_\ell + R_{D,\ell}