Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j) · @brief Propagate delta backward: δ_j

Read the equation

This relation defines @brief Propagate delta backward: δ_j in the source section “Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j) · @brief Propagate delta backward: δ_j”. 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 Propagate delta backward: δ_j 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 Compute output delta: δ = (y - target) · f'(net)
 */
inline double output_delta(double y, double target, double derivative) {
    return (y - target) * derivative;
}

/**
 * @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 Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j)

Related builds