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>
31 lines
1.0 KiB
Lean4
31 lines
1.0 KiB
Lean4
import Sunbeam.Model.Basic
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import Sunbeam.Model.Sigmoid
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import Sunbeam.Model.ReLU
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namespace Sunbeam
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/-- Weights for a 2-layer MLP (input → hidden → scalar output). -/
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structure MLPWeights (inputDim hiddenDim : Nat) where
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w1 : Fin hiddenDim → FloatVec inputDim
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b1 : FloatVec hiddenDim
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w2 : FloatVec hiddenDim
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b2 : Float
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/-- Forward pass: input → linear1 → ReLU → linear2 → sigmoid. -/
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def mlpForward {inputDim hiddenDim : Nat}
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(weights : MLPWeights inputDim hiddenDim) (input : FloatVec inputDim) : Float :=
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let hidden := vecAdd (matVecMul weights.w1 input) weights.b1
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let activated := reluVec hidden
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let output := dot weights.w2 activated + weights.b2
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sigmoid output
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/-- MLP output is bounded in (0, 1) — follows directly from sigmoid bounds. -/
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theorem mlp_output_bounded {inputDim hiddenDim : Nat}
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(weights : MLPWeights inputDim hiddenDim) (input : FloatVec inputDim) :
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0 < mlpForward weights input ∧ mlpForward weights input < 1 := by
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constructor
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· exact sigmoid_pos _
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· exact sigmoid_lt_one _
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end Sunbeam
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