Expected free energy as an information constraint on the Bethe Lagrangian

What the math gives to ML

The paper turns epistemic exploration into an explicit information-demand constraint on a Bethe variational objective, rather than treating information gain as an inseparable expected-free-energy term. The transferable asset is the KKT-controlled dual variable: a learned multiplier automatically moves between inactive, interior, and saturated information regimes, so exploration pressure is activated only when the predictive model fails to provide enough information. A practical neural analogue is to add a dual-controlled conditional-mutual-information constraint to latent world-model training or model-based RL, while using a Bethe-style chain objective for structured latent inference. This gives a falsifiable alternative to fixed curiosity coefficients and can be tested by measuring exploration, calibration, and task reward at equal model and environment-interaction budgets.