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>
22 lines
486 B
Lean4
22 lines
486 B
Lean4
import Sunbeam.Model.Basic
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namespace Sunbeam
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/-- ReLU activation: max(0, x). -/
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def relu (x : Float) : Float :=
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if x > 0.0 then x else 0.0
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/-- Pointwise ReLU on a vector. -/
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def reluVec {n : Nat} (v : FloatVec n) : FloatVec n :=
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fun i => relu (v i)
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/-! ## Trust boundary: ReLU axioms -/
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/-- ReLU output is non-negative. -/
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axiom relu_nonneg (x : Float) : relu x ≥ 0.0
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/-- ReLU is monotone. -/
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axiom relu_monotone {x y : Float} (h : x ≤ y) : relu x ≤ relu y
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end Sunbeam
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