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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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 | import OAI.Probability.MatroidProphet.LayerOnline
import OAI.Probability.MatroidProphet.Density.Birth
import Mathlib.Data.Finset.Sort
namespace OAI
namespace MatroidProphet
open Set Finset
structure MainMasks (n : ℕ) where
H : Finset (Fin n)
D : Finset (Fin n)
C : Finset (Fin n)
T : Finset (Fin n)
odd : Bool
def mainSeedBits (n : ℕ) : ℕ := 4*n+2
def seedMask {n : ℕ} (r : Seed (mainSeedBits n)) (j : Fin 4) : Finset (Fin n) :=
univ.filter fun e => r ⟨4*e.val+j.val, by dsimp [mainSeedBits]; omega⟩ = true
def mainMasks {n : ℕ} (r : Seed (mainSeedBits n)) : MainMasks n where
H := seedMask r 0
D := seedMask r 1
C := seedMask r 2
T := seedMask r 3
odd := r ⟨4*n+1, by dsimp [mainSeedBits]; omega⟩
def mainBranch {n : ℕ} (r : Seed (mainSeedBits n)) : Bool :=
r ⟨4*n, by dsimp [mainSeedBits]; omega⟩
namespace MainAlgorithm
variable {n : ℕ}
def higher (f : Fin n) (a : Option ℤ) (e : Fin n) (b : Option ℤ) : Prop :=
match a, b with
| some i, some j => j < i ∨ j = i ∧ f < e
| some _, none => True
| _, _ => False
def candidate (M : Matroid (Fin n)) (d : MainMasks n) (seen : Fin n → Option ℤ)
(e : Fin n) (w : Option ℤ) : Prop :=
w ≠ none ∧ e ∉ d.H ∧ e ∉ M.closure {f | f ∈ d.H ∧ higher f (seen f) e w}
noncomputable def listed (M : Matroid (Fin n)) (d : MainMasks n)
(seen : Fin n → Option ℤ) : Finset ℤ := by
classical
exact d.D.biUnion fun e => if candidate M d seen e (seen e) then (seen e).toFinset else ∅
noncomputable def groups (M : Matroid (Fin n)) (d : MainMasks n)
(seen : Fin n → Option ℤ) : List ℤ := (listed M d seen).sort (· ≤ ·)
def groupMask (M : Matroid (Fin n)) (d : MainMasks n) (seen : Fin n → Option ℤ)
(mask : Finset (Fin n)) (h : ℕ) : Set (Fin n) :=
{e | e ∈ mask ∧ candidate M d seen e (seen e) ∧ seen e = (groups M d seen)[h]?}
noncomputable def finalPath (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (seen : Fin n → Option ℤ) : ℤ → Set (Fin n) :=
guardedPath M hE (2^100) (groupMask M d seen d.D) (groupMask M d seen d.C)
(groups M d seen).length
noncomputable def birth (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (seen : Fin n → Option ℤ) (e : Fin n) (i : ℤ) : ℤ :=
nominalBirth M hE (2^100) (groupMask M d seen d.D) (groupMask M d seen d.C)
((groups M d seen).idxOf i) e
def eligible (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (seen : Fin n → Option ℤ) (e : Fin n) (i : ℤ) : Prop :=
e ∉ d.H ∪ d.D ∪ d.C ∧ candidate M d seen e (some i) ∧ i ∈ groups M d seen ∧
e ∈ d.T ∧ activation ((groups M d seen).idxOf i) + 2 ≤ birth M hE d seen e i ∧
(birth M hE d seen e i) % 2 = (if d.odd then 1 else 0) ∧
e ∉ finalPath M hE d seen (birth M hE d seen e i - 2)
noncomputable def assign (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (seen : Fin n → Option ℤ) (e : Fin n) : Option ℤ → Option ℤ := by
classical
exact fun w => match w with
| none => none
| some i => if eligible M hE d seen e i then some (birth M hE d seen e i) else none
noncomputable def core (M : Matroid (Fin n)) (hE : M.E = Set.univ) :
OnlineRule n (mainSeedBits n) :=
layerOnlineRule M (roundedLevel weightBase) (measurable_roundedLevel weightBase)
(fun r seen b => finalPath M hE (mainMasks r) seen (b-2))
(fun r seen => assign M hE (mainMasks r) seen)
noncomputable def hidden (M : Matroid (Fin n)) (hE : M.E = Set.univ) :
HiddenRule n (mainSeedBits n) where
mask r := (mainMasks r).H ∪ (mainMasks r).D ∪ (mainMasks r).C
core := core M hE
end MainAlgorithm
end MatroidProphet
end OAI
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