FISHER INFORMATION METRIC · Natural gradient: ∇̃L

Read the equation

This relation defines Natural gradient: ∇̃L in the source section “FISHER INFORMATION METRIC · Natural gradient: ∇̃L”. 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 Natural gradient: ∇̃L 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

                float dtheta_j = theta2[j] - theta1[j];
                ds2 += g[i][j] * dtheta_i * dtheta_j;
            }
        }
        return std::sqrt(std::max(0.0f, ds2));
    }

    // Natural gradient: ∇̃L = G⁻¹∇L
    void natural_gradient(const float* grad, float* nat_grad) const {
        // Simplified: use diagonal approximation
        for (size_t i = 0; i < DIM; ++i) {
            float g_ii = g[i][i];
            if (g_ii > 1e-8f) {
                nat_grad[i] = grad[i] / g_ii;
            } else {
                nat_grad[i] = grad[i];
            }
        }

Natural gradient: ∇̃L = G⁻¹∇L

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