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>
24 lines
697 B
Lean4
24 lines
697 B
Lean4
import Sunbeam.Model.Basic
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namespace Sunbeam
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/-- A decision tree node (inductive = automatic termination for structural recursion). -/
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inductive TreeNode where
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| leaf (decision : Decision) : TreeNode
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| split (featureIdx : Nat) (threshold : Float) (left right : TreeNode) : TreeNode
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deriving Repr
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/-- Tree prediction by structural recursion (termination is automatic). -/
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def treePredictAux {n : Nat} (input : Fin n → Float) : TreeNode → Decision
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| .leaf d => d
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| .split idx thr left right =>
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if h : idx < n then
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if input ⟨idx, h⟩ ≤ thr then
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treePredictAux input left
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else
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treePredictAux input right
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else
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Decision.defer
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end Sunbeam
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