G5: Analog activation update (unchanged, already efficient) · aᵢ(t+1)

Read the equation

This relation defines aᵢ(t+1) in the source section “G5: Analog activation update (unchanged, already efficient) · aᵢ(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

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 aᵢ(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

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

            state[i] = (mix & threshold_mask) | (old_state[i] & ~threshold_mask);
        }
    }

    /**
     * @brief G5: Analog activation update (unchanged, already efficient)
     *
     * aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)
     */
    void update_analog() {
        prev_activation = activation;

        // Compute new activation from density
        const double d = density();
        const double input = ALPHA * d * dna_modulation + BETA;

        // Apply tanh with golden scaling (branchless)
        const double x = input * PHI;

aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)

Related builds