Behavior–design loss for L_\ell^\*(S',D')

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

1. Read L_\ell^\*(S',D') 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

L^\*(S',D'; U,E)\big|\_{E \mapsto E_\ell}

Explicitly:

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

Same form, layer-specific ingredients.

⸻

2. Neuron loss (within a layer ℓ, neuron i)

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

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