Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²) · @brief Normalized Hebbian: Δw

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This relation defines @brief Normalized Hebbian: Δw in the source section “Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²) · @brief Normalized Hebbian: Δw”. 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 @brief Normalized Hebbian: Δw 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

 * @brief Classic Hebbian: Δw = η·x_i·x_j
 */
inline double hebbian_classic(double x_pre, double x_post, double eta = ETA) {
    return eta * x_pre * x_post;
}

/**
 * @brief Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²)
 * Prevents unbounded weight growth
 */
inline double hebbian_normalized(double x_pre, double x_post, double w,
                                  double alpha = 0.1, double eta = ETA) {
    return eta * (x_pre * x_post - alpha * w * x_post * x_post);
}

/**
 * @brief BCM Learning: Δw = η·x_i·x_j·(x_j - θ)
 * Threshold θ adapts based on activity

@brief Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²)

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