Layer sensitivity to an environment aspect

Read the equation

Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not itself specify a physical action.

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 C^{(a)}(t+1) 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

3.2 Shared “aspect context”

For each aspect a, define a shared context variable C^{(a)}:

C^{(a)}(t+1) = F_a\Big(C^{(a)}(t), \{ m_{\ell \to a}(t) \}_{\ell=1}^7 \Big)
•	All 7 layers send messages about E^{(a)}.
•	The function F_a (deterministic) aggregates these into a new aspect context C^{(a)}.
•	Then C^{(a)} is fed back into the environment description for the next step.

Update the actual aspect:

E^{(a)}_{\text{next}} = G_a\big(E^{(a)}_{\text{current}}, C^{(a)}\big)

C^{(a)}(t+1) = F_a\Big(C^{(a)}(t), \{ m_{\ell \to a}(t) \}_{\ell=1}^7 \Big)

Related builds