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Table 1:
Glossary of Variables.
NotationVariable
P(·) Probability distribution 
Q(·) Variational posterior or empirical prior distribution 
F Variational free energy 
G Expected free energy 
uτ Action at time τ 
o=(o1,o2,,oτ,) Observation 
s=(s1,s2,,sτ,) Hidden (latent) states 
π Policy (sequence of actions) 
sτπ Expectation of state at time τ under Q(sτ|π) 
sτu Expectation of state at time τ under Q(sτ|uτ) 
vτπ Log expectation of state at time τ under Q(sτ|π) 
oτu Expectation of observation at time τ under Q(oτ|u<τ) 
uτo Expectation of action at time τ under Q(uτ|oτ) 
A Parameters of categorical likelihood distribution 
B Parameters of categorical transition probabilities 
C Parameters of categorical prior preferences 
D Parameters of categorical initial state probabilities 
H Conditional entropy of likelihood distribution 
a,a Prior and posterior Dirichlet parameters for A 
b,b Prior and posterior Dirichlet parameters for B 
d,d Prior and posterior Dirichlet parameters for D 
Cat(·) Categorical probability distribution 
Dir(·) Dirichlet probability distribution 
EP[·] Expectation under the subscripted probability distribution 
H[·] Shannon entropy of a probability distribution 
DKL[··] Kullback-Leibler divergence between probability distributions 
ψ(·) Digamma function 
σ(·) Softmax (normalized exponential) function 
NotationVariable
P(·) Probability distribution 
Q(·) Variational posterior or empirical prior distribution 
F Variational free energy 
G Expected free energy 
uτ Action at time τ 
o=(o1,o2,,oτ,) Observation 
s=(s1,s2,,sτ,) Hidden (latent) states 
π Policy (sequence of actions) 
sτπ Expectation of state at time τ under Q(sτ|π) 
sτu Expectation of state at time τ under Q(sτ|uτ) 
vτπ Log expectation of state at time τ under Q(sτ|π) 
oτu Expectation of observation at time τ under Q(oτ|u<τ) 
uτo Expectation of action at time τ under Q(uτ|oτ) 
A Parameters of categorical likelihood distribution 
B Parameters of categorical transition probabilities 
C Parameters of categorical prior preferences 
D Parameters of categorical initial state probabilities 
H Conditional entropy of likelihood distribution 
a,a Prior and posterior Dirichlet parameters for A 
b,b Prior and posterior Dirichlet parameters for B 
d,d Prior and posterior Dirichlet parameters for D 
Cat(·) Categorical probability distribution 
Dir(·) Dirichlet probability distribution 
EP[·] Expectation under the subscripted probability distribution 
H[·] Shannon entropy of a probability distribution 
DKL[··] Kullback-Leibler divergence between probability distributions 
ψ(·) Digamma function 
σ(·) Softmax (normalized exponential) function 
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