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{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE DeriveGeneric #-}
module Main where
import Control.DeepSeq
import Criterion
import Criterion.Main
import qualified Data.Vector as V
import GHC.Generics (Generic)
import qualified Numeric.ADDual as ADD
type Matrix s = V.Vector s
data FNeural a = FNeural [(Matrix a, V.Vector a)] (V.Vector a)
deriving (Show, Functor, Foldable, Traversable, Generic)
instance NFData a => NFData (FNeural a)
fneural :: (Floating a, Ord a) => FNeural a -> a
fneural (FNeural layers input) =
let dotp v1 v2 = V.sum (V.zipWith (*) v1 v2)
mat @. vec =
let n = V.length vec
m = V.length mat `div` n
in V.fromListN m $ map (\i -> dotp (V.slice (n*i) n mat) vec) [0 .. m-1]
(+.) = V.zipWith (+)
relu x = if x >= 0.0 then x else 0.0
safeSoftmax vec = let m = V.maximum vec
factor = V.sum (V.map (\z -> exp (z - m)) vec)
in V.map (\z -> exp (z - m) / factor) vec
forward [] x = safeSoftmax x
forward ((weights, bias) : lys) x =
let x' = V.map relu ((weights @. x) +. bias)
in forward lys x'
in V.sum $ forward layers input
makeNeuralInput :: FNeural Double
makeNeuralInput =
let genMatrix nin nout =
V.fromListN (nin*nout) [sin (fromIntegral @Int (i+j))
| i <- [0..nout-1], j <- [0..nin-1]]
genVector nout = V.fromListN nout [sin (0.41 * fromIntegral @Int i) | i <- [0..nout-1]]
-- 50 inputs; 2 hidden layers (100; 50); final softmax, then sum the outputs.
nIn = 50; n1 = 100; n2 = 50
in FNeural [(genMatrix nIn n1, genVector n1)
,(genMatrix n1 n2, genVector n2)]
(genVector nIn)
main :: IO ()
main = defaultMain
[env (pure makeNeuralInput) $ \input ->
bench "neural" $ nf (\inp -> ADD.gradient' @Double fneural inp 1.0) input]
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