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88 lines
2.7 KiB
Text
88 lines
2.7 KiB
Text
/-
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DSPTranslation.lean - DSP to Neuromorphic Formal Bridge
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Migrates legacy f64 state matrices to fixed point bounds.
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-/
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import Semantics.Bind
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namespace Semantics.DSPTranslation
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abbrev Q16_16 := UInt32
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namespace Q16_16
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def scale : Nat := 65536
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def maxNat : Nat := 4294967295
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def satFromNat (n : Nat) : Q16_16 :=
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if n > maxNat then UInt32.ofNat maxNat else UInt32.ofNat n
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def mul (x y : Q16_16) : Q16_16 :=
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satFromNat ((x.toNat * y.toNat) / scale)
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end Q16_16
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-- Agreed constants
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def neuronCount : Nat := 20
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def featureDim : Nat := 50
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structure FeatureRecord where
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chunkId : UInt64
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paramHash : UInt32
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dspFeature : Array Q16_16
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waveprobeFeature : Array Q16_16
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miFeature : Array Q16_16
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deriving Repr, Inhabited
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structure PriorRecord where
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batchId : UInt64
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epochId : UInt64
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neuromorphicPrior : Array Q16_16
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candidateMask : Array Q16_16
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proposalWeight : Array Q16_16
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lagBias : Array Q16_16
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deriving Repr, Inhabited
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structure NeuromorphicState where
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membranePotential : Array Q16_16
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neuronWeights : Array Q16_16
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neuronThresholds : Array Q16_16
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firingRate : Array Q16_16
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deriving Repr, Inhabited
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structure TranslationMatrix where
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weights : Array (Array Q16_16)
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deriving Repr, Inhabited
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-- Q16.16 representation of 0.995
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def decayFactor : Q16_16 := 65208
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-- Q16.16 representation of 0.005
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def growthFactor : Q16_16 := 327
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/-- STDP Learning update evaluated strictly over integers -/
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def advanceMatrixBatch (mat : TranslationMatrix) : TranslationMatrix :=
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let newWeights := mat.weights.mapIdx fun i row =>
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row.mapIdx fun _j w =>
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let decayed := Q16_16.mul w decayFactor
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-- Growth proportional to neuron index
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let iRatio := (i * Q16_16.scale) / neuronCount
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let growthDelta := Q16_16.mul growthFactor (Q16_16.satFromNat iRatio)
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decayed + growthDelta
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{ weights := newWeights }
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/-- Geodesic cost is the drift sum in the feature space array after applying priors -/
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def geometricCost (prior : PriorRecord) (state : NeuromorphicState) (_metric : Metric) : UInt32 :=
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-- Minimal deterministic placeholder mapping
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if prior.batchId > 0 then prior.neuromorphicPrior.size.toUInt32 else 0
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def priorInvariant (p : PriorRecord) : String := s!"prior:{p.batchId}"
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def stateInvariant (s : NeuromorphicState) : String := s!"state:{s.membranePotential.size}"
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def geometricBindEval (prior : PriorRecord) (state : NeuromorphicState) (metric : Metric) : Bind PriorRecord NeuromorphicState :=
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geometricBind prior state metric geometricCost priorInvariant stateInvariant
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/-- Verify bound mapping for evaluation constraints -/
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def verifyStdpDecay : Q16_16 :=
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let x : Q16_16 := 65536 -- 1.0
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Q16_16.mul x decayFactor
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#eval verifyStdpDecay
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end Semantics.DSPTranslation
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