Compute weight gradient: ∂L/∂w_ij = δ_j · x_i · @brief Compute weight gradient: ∂L/∂w_ij

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This relation defines @brief Compute weight gradient: ∂L/∂w_ij in the source section “Compute weight gradient: ∂L/∂w_ij = δ_j · x_i · @brief Compute weight gradient: ∂L/∂w_ij”. Uses a derivative or gradient to describe a rate of change or a direction of variation. 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 Compute weight gradient: ∂L/∂w_ij as the quantity being defined or updated by this relation.

2. Uses a derivative or gradient to describe a rate of change or a direction of variation.

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 Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j)
 */
inline double backprop_delta(double sum_weighted_deltas, double derivative) {
    return sum_weighted_deltas * derivative;
}

/**
 * @brief Compute weight gradient: ∂L/∂w_ij = δ_j · x_i
 */
inline double weight_gradient(double delta, double input) {
    return delta * input;
}

/**
 * @brief Apply weight update with L2 regularization
 */
inline double weight_update(double w, double gradient, double lr = ETA, double decay = WEIGHT_DECAY) {
    return w - lr * (gradient + decay * w);

@brief Compute weight gradient: ∂L/∂w_ij = δ_j · x_i

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