Read the equation
This relation defines ∂KL/∂μ in the source section “FREE ENERGY PRINCIPLE · ∂KL/∂μ”. 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
Read ∂KL/∂μ as the quantity being defined or updated by this relation.
Uses a derivative or gradient to describe a rate of change or a direction of variation.
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
Read the surrounding source passage
return kl - log_likelihood;
}
// Gradient of free energy w.r.t. mu
void gradient_mu(const float* observation, float* grad_out) const {
for (size_t i = 0; i < DIM; ++i) {
float var_p = sigma_prior[i] * sigma_prior[i];
// ∂KL/∂μ = (μ - μ_prior) / σ_prior²
grad_out[i] = (mu[i] - mu_prior[i]) / var_p;
}
}
// Update variational parameters to minimize free energy
void update(const float* observation, float log_likelihood, float lr) {
float grad[DIM];
gradient_mu(observation, grad);
for (size_t i = 0; i < DIM; ++i) {Exact original notation
∂KL/∂μ = (μ - μ_prior) / σ_prior²