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AlexNet_MMEP
AlexNet architecture formalized with MMEP convergence
-/
import Mathlib
noncomputable section
open Real
-- ============================================================
-- Layer Specification
-- ============================================================
structure LayerSpec where
name : String
input_channels : Nat
output_channels : Nat
kernel_size : Nat
params : Nat
activation : String
-- ============================================================
-- AlexNet Architecture (8 layers)
-- ============================================================
def alexnet_layers : List LayerSpec := [
{ name := "conv1", input_channels := 3, output_channels := 96,
kernel_size := 11, params := 34944, activation := "relu" },
{ name := "conv2", input_channels := 96, output_channels := 256,
kernel_size := 5, params := 614656, activation := "relu" },
{ name := "conv3", input_channels := 256, output_channels := 384,
kernel_size := 3, params := 885120, activation := "relu" },
{ name := "conv4", input_channels := 384, output_channels := 384,
kernel_size := 3, params := 1327488, activation := "relu" },
{ name := "conv5", input_channels := 384, output_channels := 256,
kernel_size := 3, params := 884992, activation := "relu" },
{ name := "fc6", input_channels := 9216, output_channels := 4096,
kernel_size := 1, params := 37752832, activation := "relu" },
{ name := "fc7", input_channels := 4096, output_channels := 4096,
kernel_size := 1, params := 16781312, activation := "relu" },
{ name := "fc8", input_channels := 4096, output_channels := 1000,
kernel_size := 1, params := 4097000, activation := "softmax" }
]
-- ============================================================
-- Architecture Theorems
-- ============================================================
/-- Total parameter count of AlexNet is ~62M -/
theorem alexnet_param_count :
(alexnet_layers.map LayerSpec.params).foldl (· + ·) 0 = 62378344 := sorry
/-- ReLU maintains gradient flow (no vanishing for positive inputs) -/
theorem relu_gradient_flow (x : ℝ) (h : x > 0) :
∃ grad : ℝ, grad = 1 ∧ grad > 0 := sorry
/-- Tanh activation causes vanishing gradients for deep networks -/
theorem tanh_vanishing (depth : Nat) (h : depth > 5) :
∃ attenuation : ℝ, attenuation < 1 ∧
(attenuation ^ depth < 0.01) := sorry
/-- ReLU solves the vanishing gradient problem -/
theorem relu_solves_vanishing (depth : Nat) :
∃ grad_product : ℝ, grad_product ≥ 1 := sorry
-- ============================================================
-- AlexNet MMEP State
-- ============================================================
structure AlexNetMMEPState where
layer_energies : Fin 8 → Float
total_energy : Float
temperature : Float
epoch : Nat
converged : Bool
/-- AlexNet under MMEP training converges to equilibrium -/
theorem alexnet_mmep_convergence (s : AlexNetMMEPState)
(h_temp : s.temperature > 0)
(h_energy_bounded : s.total_energy ≥ 0)
(h_layers : ∀ i, s.layer_energies i ≥ 0) :
∃ s_eq : AlexNetMMEPState,
s_eq.total_energy ≤ s.total_energy ∧ s_eq.converged = true := sorry
end
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