Neuron-specific restriction of a layer loss

Read the equation

The loss for neuron i in layer ℓ is the layer loss evaluated with that neuron’s structural/input parameter Uᵢ and the environment slice Eℓ. This specialization is intended to retain one objective structure while changing the local inputs. It does not supply the missing form of the global loss or its solver.

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,i}^\*(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

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

Neuron i has its own structural parameters (Uᵢ, Vᵢ, dKᵢ) and maybe its own operator Dᵢ′, Bᵢ:

L_{\ell,i}^\*(S',D') =
L_\ell^\*(S',D'; U_i, E_\ell)

So:

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

L_{\ell,i}^\*(S',D') =
L_\ell^\*(S',D'; U_i, E_\ell)

Related builds