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💣 Machine learning which might blow up in your face 💣
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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288{-# LANGUAGE CPP #-}{-# LANGUAGE DataKinds #-}{-# LANGUAGE ScopedTypeVariables #-}{-# LANGUAGE GADTs #-}{-# LANGUAGE TypeOperators #-}{-# LANGUAGE TypeFamilies #-}{-# LANGUAGE MultiParamTypeClasses #-}{-# LANGUAGE FlexibleInstances #-}{-# LANGUAGE FlexibleContexts #-}{-# LANGUAGE UndecidableInstances #-}{-|Module : Grenade.Layers.ConvolutionDescription : Convolution layerCopyright : (c) Huw Campbell, 2016-2017License : BSD2Stability : experimental
This module provides the Convolution layer, which is critical in many computer vision tasks.
-}module Grenade.Layers.Convolution ( Convolution (..) , Convolution' (..) , randomConvolution ) where
import Control.Monad.Random hiding ( fromList )import Data.Maybeimport Data.Proxyimport Data.Serialize
import GHC.TypeLitsimport Data.Kind (Type)
import Numeric.LinearAlgebra hiding ( uniformSample, konst )import qualified Numeric.LinearAlgebra as LAimport Numeric.LinearAlgebra.Static hiding ((|||), build, toRows)
import Grenade.Coreimport Grenade.Layers.Internal.Convolutionimport Grenade.Layers.Internal.Update
-- | A convolution layer for a neural network.-- This uses the im2col convolution trick popularised by Caffe, which essentially turns the-- many, many, many, many loop convolution into a single matrix multiplication.---- The convolution layer takes all of the kernels for the convolution, which are flattened-- and then put into columns in the matrix.---- The kernel size dictates which input and output sizes will "fit". Fitting the equation:-- `out = (in - kernel) / stride + 1` for both dimensions.---- One probably shouldn't build their own layer, but rather use the randomConvolution function.data Convolution :: Nat -- Number of channels, for the first layer this could be RGB for instance. -> Nat -- Number of filters, this is the number of channels output by the layer. -> Nat -- The number of rows in the kernel filter -> Nat -- The number of column in the kernel filter -> Nat -- The row stride of the convolution filter -> Nat -- The columns stride of the convolution filter -> Type where Convolution :: ( KnownNat channels , KnownNat filters , KnownNat kernelRows , KnownNat kernelColumns , KnownNat strideRows , KnownNat strideColumns , KnownNat kernelFlattened , kernelFlattened ~ (kernelRows * kernelColumns * channels)) => !(L kernelFlattened filters) -- The kernel filter weights -> !(L kernelFlattened filters) -- The last kernel update (or momentum) -> Convolution channels filters kernelRows kernelColumns strideRows strideColumns
data Convolution' :: Nat -- Number of channels, for the first layer this could be RGB for instance. -> Nat -- Number of filters, this is the number of channels output by the layer. -> Nat -- The number of rows in the kernel filter -> Nat -- The number of column in the kernel filter -> Nat -- The row stride of the convolution filter -> Nat -- The columns stride of the convolution filter -> Type where Convolution' :: ( KnownNat channels , KnownNat filters , KnownNat kernelRows , KnownNat kernelColumns , KnownNat strideRows , KnownNat strideColumns , KnownNat kernelFlattened , kernelFlattened ~ (kernelRows * kernelColumns * channels)) => !(L kernelFlattened filters) -- The kernel filter gradient -> Convolution' channels filters kernelRows kernelColumns strideRows strideColumns
instance Show (Convolution c f k k' s s') where show (Convolution a _) = renderConv a where renderConv mm = let m = extract mm ky = fromIntegral $ natVal (Proxy :: Proxy k) rs = LA.toColumns m ms = map (take ky) $ toLists . reshape ky <$> rs
render n' | n' <= 0.2 = ' ' | n' <= 0.4 = '.' | n' <= 0.6 = '-' | n' <= 0.8 = '=' | otherwise = '#'
px = (fmap . fmap . fmap) render ms in unlines $ foldl1 (zipWith (\a' b' -> a' ++ " | " ++ b')) $ px
randomConvolution :: ( MonadRandom m , KnownNat channels , KnownNat filters , KnownNat kernelRows , KnownNat kernelColumns , KnownNat strideRows , KnownNat strideColumns , KnownNat kernelFlattened , kernelFlattened ~ (kernelRows * kernelColumns * channels)) => m (Convolution channels filters kernelRows kernelColumns strideRows strideColumns)randomConvolution = do s <- getRandom let wN = uniformSample s (-1) 1 mm = konst 0 return $ Convolution wN mm
instance ( KnownNat channels , KnownNat filters , KnownNat kernelRows , KnownNat kernelColumns , KnownNat strideRows , KnownNat strideColumns , KnownNat (kernelRows * kernelColumns * channels) ) => UpdateLayer (Convolution channels filters kernelRows kernelColumns strideRows strideColumns) where type Gradient (Convolution channels filters kernelRows kernelColumns strideRows strideColumns) = (Convolution' channels filters kernelRows kernelColumns strideRows strideColumns) runUpdate lp (Convolution oldKernel oldMomentum) (Convolution' kernelGradient) = let (newKernel, newMomentum) = descendMatrix (learningRate lp) (learningMomentum lp) (learningRegulariser lp) oldKernel kernelGradient oldMomentum in Convolution newKernel newMomentum
createRandom = randomConvolution
instance ( KnownNat channels , KnownNat filters , KnownNat kernelRows , KnownNat kernelColumns , KnownNat strideRows , KnownNat strideColumns , KnownNat (kernelRows * kernelColumns * channels) ) => Serialize (Convolution channels filters kernelRows kernelColumns strideRows strideColumns) where put (Convolution w _) = putListOf put . toList . flatten . extract $ w get = do let f = fromIntegral $ natVal (Proxy :: Proxy filters) wN <- maybe (fail "Vector of incorrect size") return . create . reshape f . LA.fromList =<< getListOf get let mm = konst 0 return $ Convolution wN mm
-- | A three dimensional image (or 2d with many channels) can have-- an appropriately sized convolution filter run across it.instance ( KnownNat kernelRows , KnownNat kernelCols , KnownNat filters , KnownNat strideRows , KnownNat strideCols , KnownNat inputRows , KnownNat inputCols , KnownNat outputRows , KnownNat outputCols , KnownNat channels , ((outputRows - 1) * strideRows) ~ (inputRows - kernelRows) , ((outputCols - 1) * strideCols) ~ (inputCols - kernelCols) , KnownNat (kernelRows * kernelCols * channels) , KnownNat (outputRows * filters) ) => Layer (Convolution channels filters kernelRows kernelCols strideRows strideCols) ('D3 inputRows inputCols channels) ('D3 outputRows outputCols filters) where
type Tape (Convolution channels filters kernelRows kernelCols strideRows strideCols) ('D3 inputRows inputCols channels) ('D3 outputRows outputCols filters) = S ('D3 inputRows inputCols channels)
runForwards (Convolution kernel _) (S3D input) = let ex = extract input ek = extract kernel ix = fromIntegral $ natVal (Proxy :: Proxy inputRows) iy = fromIntegral $ natVal (Proxy :: Proxy inputCols) kx = fromIntegral $ natVal (Proxy :: Proxy kernelRows) ky = fromIntegral $ natVal (Proxy :: Proxy kernelCols) sx = fromIntegral $ natVal (Proxy :: Proxy strideRows) sy = fromIntegral $ natVal (Proxy :: Proxy strideCols) ox = fromIntegral $ natVal (Proxy :: Proxy outputRows) oy = fromIntegral $ natVal (Proxy :: Proxy outputCols)
c = vid2col kx ky sx sy ix iy ex mt = c LA.<> ek r = col2vid 1 1 1 1 ox oy mt rs = fromJust . create $ r in (S3D input, S3D rs) runBackwards (Convolution kernel _) (S3D input) (S3D dEdy) = let ex = extract input ix = fromIntegral $ natVal (Proxy :: Proxy inputRows) iy = fromIntegral $ natVal (Proxy :: Proxy inputCols) kx = fromIntegral $ natVal (Proxy :: Proxy kernelRows) ky = fromIntegral $ natVal (Proxy :: Proxy kernelCols) sx = fromIntegral $ natVal (Proxy :: Proxy strideRows) sy = fromIntegral $ natVal (Proxy :: Proxy strideCols) ox = fromIntegral $ natVal (Proxy :: Proxy outputRows) oy = fromIntegral $ natVal (Proxy :: Proxy outputCols)
c = vid2col kx ky sx sy ix iy ex
eo = extract dEdy ek = extract kernel
vs = vid2col 1 1 1 1 ox oy eo
kN = fromJust . create $ tr c LA.<> vs
dW = vs LA.<> tr ek
xW = col2vid kx ky sx sy ix iy dW in (Convolution' kN, S3D . fromJust . create $ xW)
-- | A two dimentional image may have a convolution filter applied to itinstance ( KnownNat kernelRows , KnownNat kernelCols , KnownNat filters , KnownNat strideRows , KnownNat strideCols , KnownNat inputRows , KnownNat inputCols , KnownNat outputRows , KnownNat outputCols , ((outputRows - 1) * strideRows) ~ (inputRows - kernelRows) , ((outputCols - 1) * strideCols) ~ (inputCols - kernelCols) , KnownNat (kernelRows * kernelCols * 1) , KnownNat (outputRows * filters) ) => Layer (Convolution 1 filters kernelRows kernelCols strideRows strideCols) ('D2 inputRows inputCols) ('D3 outputRows outputCols filters) where type Tape (Convolution 1 filters kernelRows kernelCols strideRows strideCols) ('D2 inputRows inputCols) ('D3 outputRows outputCols filters) = S ('D3 inputRows inputCols 1) runForwards c (S2D input) = runForwards c (S3D input :: S ('D3 inputRows inputCols 1))
runBackwards c tape grads = case runBackwards c tape grads of (c', S3D back :: S ('D3 inputRows inputCols 1)) -> (c', S2D back)
-- | A two dimensional image may have a convolution filter applied to it producing-- a two dimensional image if both channels and filters is 1.instance ( KnownNat kernelRows , KnownNat kernelCols , KnownNat strideRows , KnownNat strideCols , KnownNat inputRows , KnownNat inputCols , KnownNat outputRows , KnownNat outputCols , ((outputRows - 1) * strideRows) ~ (inputRows - kernelRows) , ((outputCols - 1) * strideCols) ~ (inputCols - kernelCols) , KnownNat (kernelRows * kernelCols * 1) , KnownNat (outputRows * 1) ) => Layer (Convolution 1 1 kernelRows kernelCols strideRows strideCols) ('D2 inputRows inputCols) ('D2 outputRows outputCols) where type Tape (Convolution 1 1 kernelRows kernelCols strideRows strideCols) ('D2 inputRows inputCols) ('D2 outputRows outputCols) = S ('D3 inputRows inputCols 1) runForwards c (S2D input) = case runForwards c (S3D input :: S ('D3 inputRows inputCols 1)) of (tps, S3D back :: S ('D3 outputRows outputCols 1)) -> (tps, S2D back)
runBackwards c tape (S2D grads) = case runBackwards c tape (S3D grads :: S ('D3 outputRows outputCols 1)) of (c', S3D back :: S ('D3 inputRows inputCols 1)) -> (c', S2D back)
-- | A three dimensional image can produce a 2D image from a convolution with 1 filterinstance ( KnownNat kernelRows , KnownNat kernelCols , KnownNat strideRows , KnownNat strideCols , KnownNat inputRows , KnownNat inputCols , KnownNat outputRows , KnownNat outputCols , KnownNat channels , ((outputRows - 1) * strideRows) ~ (inputRows - kernelRows) , ((outputCols - 1) * strideCols) ~ (inputCols - kernelCols) , KnownNat (kernelRows * kernelCols * channels) , KnownNat (outputRows * 1) ) => Layer (Convolution channels 1 kernelRows kernelCols strideRows strideCols) ('D3 inputRows inputCols channels) ('D2 outputRows outputCols) where type Tape (Convolution channels 1 kernelRows kernelCols strideRows strideCols) ('D3 inputRows inputCols channels) ('D2 outputRows outputCols) = S ('D3 inputRows inputCols channels) runForwards c input = case runForwards c input of (tps, S3D back :: S ('D3 outputRows outputCols 1)) -> (tps, S2D back)
runBackwards c tape (S2D grads) = runBackwards c tape (S3D grads :: S ('D3 outputRows outputCols 1))