118 119/-! ## §2. J-descent operators on probability distributions -/ 120 121/-- A **J-descent operator** on probability distributions over `Ω` with 122 equilibrium `peq` is a step `step : Distrib Ω → Distrib Ω` such that 123 124 1. `step peq = peq` (the equilibrium is a fixed point), and 125 2. for every distribution `q`, 126 `D_KL(step q ‖ peq) ≤ D_KL(q ‖ peq)` (KL non-expansiveness). 127 128 Inside RS, the recognition operator R̂ projected onto the distribution 129 layer is a J-descent operator with `peq = gibbsPD sys X`. More generally, 130 any deterministic Markov kernel that has `peq` as its stationary distribution 131 satisfies these properties via the data-processing inequality. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.