Sienna Meridian Satterwhite
982cf5755d
Lean 4 formalization of the decision tree + MLP ensemble architecture. Axiomatizes Float properties (sigmoid bounds, ReLU nonnegativity) since Lean's Float ops are extern-backed. Proves MLP output is bounded in (0,1) and ensemble output is always a valid decision. No mathlib dependency. Signed-off-by: Sienna Meridian Satterwhite <sienna@sunbeam.pt>
26 lines
718 B
Lean4
26 lines
718 B
Lean4
namespace Sunbeam
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/-- Decisions that a model component can output. -/
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inductive Decision where
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| block : Decision
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| allow : Decision
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| defer : Decision
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deriving Repr, DecidableEq
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/-- A fixed-size vector of floats. -/
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def FloatVec (n : Nat) := Fin n → Float
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/-- Dot product of two float vectors. -/
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def dot {n : Nat} (a b : FloatVec n) : Float :=
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(List.finRange n).foldl (fun acc i => acc + a i * b i) 0.0
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/-- Matrix-vector product. Matrix is row-major: m rows × n cols. -/
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def matVecMul {m n : Nat} (mat : Fin m → FloatVec n) (v : FloatVec n) : FloatVec m :=
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fun i => dot (mat i) v
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/-- Vector addition. -/
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def vecAdd {n : Nat} (a b : FloatVec n) : FloatVec n :=
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fun i => a i + b i
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end Sunbeam
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