Assuming exponential-family distributions for variational posteriors and priors extends the free-energy principle–predictive coding correspondence to exhibit biological neural properties such as nonlinearity, heterogeneity, and positive firing rates, with training via local plasticity rules.
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For Gamma-family fits to NYSE volume-price data the shape parameter follows diffusive mean-reverting dynamics while the scale parameter shows dominant jump-diffusion with elevated higher moments, and jumps explain a large share of variance; the log-normal model reverses the pattern.