text: We can now rewrite the first term of the right-hand side as the KL divergence of the 
  approximate posterior from the joint likelihood, which is equal to the expression used in 
  Equation (2): 
  
  DKL[q(s)∥p(s|o)] = DKL[q(s)∥p(o, s)] + ln p(o) 
  (4) 
  
  We now define the VFE (F [q(s), o]) as the KL divergence of the approximate posterior from 
  the joint likelihood. The VFE is only a function of q(s) and o (and the generative model m), 
  and we can therefore calculate it without knowing the model evidence p(o): 
  
  q(s) 
  p(o, s) 
  F ≜ DKL[q(s)∥p(o, s)] = ∑ 
  q(s) ln  (5) 
  s 
  
  The probability-weighted sum can be rewritten as an expectation, and the joint likelihood 
  can be decomposed into a prior and a likelihood: 
  
  (cid:20)  (cid:21) 
  
  q(s) 
  p(o, s) 
  F ≜ E  = E 
  q(s)[ln q(s) − ln p(o|s) − ln p(s)] 
  ln  (6) 
  q(s) 