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dd14c26 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | import Mathlib
import OAI.Probability.LogConcave.OraclePrograms.Expression
namespace OAI
section
section
noncomputable section
namespace LogConcaveSampling.SeedCompiler
open OracleCompiler OracleCompiler.Expression
lemma terminalMean_equivariant {d : ℕ} (r σ : ℝ) (Δ : Point d) :
(terminalMean d r σ).Equivariant
(moveSeed (fun x => x+r • Δ) (terminalShift 1) Δ) id := by
apply Program.oneQuery_equivariant
· intro z
exact terminalQuery_invariant _ _ _ _
· intro z a
simp [moveSeed,shiftSlots,terminalShift]
lemma terminalSample_equivariant {d : ℕ} (r η : ℝ) (Δ : Point d) :
(terminalSample d r η).Equivariant
(moveSeed (fun x => x+r • Δ) (terminalShift 2) Δ) (fun y => y-Δ) := by
apply Program.oneQuery_equivariant
· intro z
exact terminalQuery_invariant _ _ _ _
· intro z a
simp [moveSeed,shiftSlots,terminalShift]
module
lemma terminalSample_reserved {d : ℕ} (r η : ℝ) (Δ : Point d) :
(terminalSample d r η).Equivariant
(moveSeed id (fun i => if i=2 then 1 else 0) Δ) (fun y => y+(η/2) • Δ) := by
apply Program.oneQuery_equivariant
· intro z
simp [moveSeed,shiftSlots]
· intro z a
simp [moveSeed,shiftSlots,smul_add]
abel
end LogConcaveSampling.SeedCompiler
end
end
end
end OAI
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