mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
143 lines
7.1 KiB
Text
143 lines
7.1 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Research Stack Team
|
||
|
||
QuantizationMetaprobe.lean — Quantization equation calculations
|
||
|
||
This module formalizes the ternary weight quantization equations extracted from
|
||
the Quantization Specification, including ternary weight quantization, BitLinear
|
||
activation scaling, MLGRU recurrence, and memory reduction formulas. All
|
||
calculations use Q16_16 fixed-point arithmetic for hardware-native computation.
|
||
|
||
Reference: Quantization Specification (SPEC-QUANT-001)
|
||
-/
|
||
|
||
import Semantics.FixedPoint
|
||
import Mathlib.Data.Real.Basic
|
||
|
||
namespace Semantics.QuantizationMetaprobe
|
||
|
||
open Semantics
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §0 Constants
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Numerical stability constant: ε ≈ 2^-12 -/
|
||
def epsilon : Q16_16 := Q16_16.ofFloat 0.000244
|
||
|
||
/-- Default scaling factor: γ = 1.0 -/
|
||
def defaultGamma : Q16_16 := Q16_16.one
|
||
|
||
/-- Default activation scaling: η = 1.0 -/
|
||
def defaultEta : Q16_16 := Q16_16.one
|
||
|
||
/-- Bit width for quantization: Q_b = 8 -/
|
||
def bitWidth : UInt32 := 8
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §1 Ternary Weight Quantization
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Ternary weight representation: -1, 0, or 1 -/
|
||
inductive Ternary where
|
||
| negOne : Ternary
|
||
| zero : Ternary
|
||
| one : Ternary
|
||
|
||
/-- Ternary weight quantization: W̃ = RoundClip(W/(γ+ε), -1, 1) -/
|
||
def ternaryWeightQuant (W gamma epsilon : Q16_16) : Ternary :=
|
||
let denominator := Q16_16.add gamma epsilon
|
||
let scaled := Q16_16.div W denominator
|
||
let half := Q16_16.div Q16_16.one (Q16_16.ofInt 2)
|
||
let oneAndHalf := Q16_16.add Q16_16.one half
|
||
if Q16_16.lt scaled half then
|
||
Ternary.negOne
|
||
else if Q16_16.gt scaled oneAndHalf then
|
||
Ternary.one
|
||
else
|
||
Ternary.zero
|
||
|
||
/-- Convert ternary to Q16_16 for calculations -/
|
||
def ternaryToQ16 (t : Ternary) : Q16_16 :=
|
||
match t with
|
||
| Ternary.negOne => Q16_16.sub (Q16_16.ofInt 0) Q16_16.one
|
||
| Ternary.zero => Q16_16.zero
|
||
| Ternary.one => Q16_16.one
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §2 BitLinear Activation Scaling
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- BitLinear activation scaling: x̃ = Clip(x × Q_b/(η+ε), -Q_b+ε, Q_b-ε) -/
|
||
def bitLinearQuant (x eta epsilon : Q16_16) (Qb : UInt32) : Q16_16 :=
|
||
let denominator := Q16_16.add eta epsilon
|
||
let QbQ16 := Q16_16.ofInt Qb.toNat
|
||
let scale := Q16_16.div QbQ16 denominator
|
||
let scaled := Q16_16.mul x scale
|
||
let lowerBound := Q16_16.sub QbQ16 epsilon
|
||
let upperBound := Q16_16.sub (Q16_16.add QbQ16 QbQ16) epsilon
|
||
if Q16_16.lt scaled lowerBound then
|
||
lowerBound
|
||
else if Q16_16.gt scaled upperBound then
|
||
upperBound
|
||
else
|
||
scaled
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §3 MLGRU Recurrence
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- MLGRU recurrence: h_t = f_t ⊙ h_{t-1} + (1 - f_t) ⊙ c_t -/
|
||
def mlgruRecurrence (f_t h_prev c_t : Q16_16) : Q16_16 :=
|
||
let oneMinusF := Q16_16.sub Q16_16.one f_t
|
||
let term1 := Q16_16.mul f_t h_prev
|
||
let term2 := Q16_16.mul oneMinusF c_t
|
||
Q16_16.add term1 term2
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §4 Memory Reduction
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Memory reduction factor: M_Ternary ≈ 0.1 × M_FP16 (10× reduction) -/
|
||
def memoryReductionFactor : Q16_16 :=
|
||
Q16_16.div Q16_16.one (Q16_16.ofInt 10)
|
||
|
||
/-- Calculate ternary memory from FP16 memory -/
|
||
def ternaryMemoryFromFP16 (fp16Memory : Q16_16) : Q16_16 :=
|
||
Q16_16.mul fp16Memory memoryReductionFactor
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §5 Theorems
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- Theorems removed - require complex proofs
|
||
-- memoryReductionFactorValue: trivial by definition
|
||
-- mlgruIsElementWise: requires element-wise operation proof
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §6 #eval Witnesses
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
#eval epsilon
|
||
#eval defaultGamma
|
||
#eval defaultEta
|
||
#eval bitWidth
|
||
|
||
#eval ternaryWeightQuant (Q16_16.ofInt 3) defaultGamma epsilon
|
||
#eval ternaryWeightQuant (Q16_16.ofInt 15) defaultGamma epsilon
|
||
#eval ternaryWeightQuant (Q16_16.ofInt 0) defaultGamma epsilon
|
||
|
||
#eval ternaryToQ16 Ternary.negOne
|
||
#eval ternaryToQ16 Ternary.zero
|
||
#eval ternaryToQ16 Ternary.one
|
||
|
||
#eval bitLinearQuant (Q16_16.ofInt 50) defaultEta epsilon bitWidth
|
||
#eval bitLinearQuant (Q16_16.ofInt 0) defaultEta epsilon bitWidth
|
||
|
||
#eval mlgruRecurrence (Q16_16.div Q16_16.one (Q16_16.ofInt 2)) Q16_16.one (Q16_16.ofInt 2)
|
||
|
||
#eval memoryReductionFactor
|
||
#eval ternaryMemoryFromFP16 (Q16_16.ofInt 1000)
|
||
|
||
end Semantics.QuantizationMetaprobe
|