feat(crossEntropy): crossEntropy cost function
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Mahdi Dibaiee
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49606406d1
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493a20eb0a
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examples/xor
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examples/xor
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@ -7,20 +7,27 @@ module Main where
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main = do
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let learning_rate = 0.5
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(iterations, epochs) = (2, 1000)
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rnetwork = randomNetwork 0 2 [8] 1 -- two inputs, 8 nodes in a single hidden layer, 1 output
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a = (logistic, logistic')
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rnetwork = randomNetwork 0 2 [(8, a)] (1, a) -- two inputs, 8 nodes in a single hidden layer, 1 output
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inputs = [vector [0, 1], vector [1, 0], vector [1, 1], vector [0, 0]]
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labels = [vector [1], vector [1], vector [0], vector [0]]
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initial_cost = zipWith crossEntropy (map (`forward` rnetwork) inputs) labels
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network = session inputs rnetwork labels learning_rate (iterations, epochs)
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results = map (`forward` network) inputs
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rounded = map (map round . toList) results
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cost = zipWith crossEntropy (map (`forward` network) inputs) labels
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putStrLn "parameters: "
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putStrLn $ "- inputs: " ++ show inputs
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putStrLn $ "- labels: " ++ show labels
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putStrLn $ "- learning rate: " ++ show learning_rate
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putStrLn $ "- iterations/epochs: " ++ show (iterations, epochs)
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putStrLn $ "- initial cost (cross-entropy): " ++ show initial_cost
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putStrLn "results: "
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putStrLn $ "- actual result: " ++ show results
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putStrLn $ "- rounded result: " ++ show rounded
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putStrLn $ "- cost (cross-entropy): " ++ show cost
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@ -19,6 +19,7 @@ library
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build-depends: base >= 4.7 && < 5
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, hmatrix
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, random
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, deepseq
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default-language: Haskell2010
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executable sibe-exe
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95
src/Sibe.hs
95
src/Sibe.hs
@ -8,49 +8,84 @@ module Sibe
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Layer,
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Input,
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Output,
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Activation,
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forward,
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randomLayer,
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randomNetwork,
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saveNetwork,
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loadNetwork,
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train,
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session,
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shuffle,
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logistic,
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logistic',
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crossEntropy,
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genSeed,
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replaceVector
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) where
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import Numeric.LinearAlgebra
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import System.Random
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import Debug.Trace
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import Data.List (foldl', sortBy)
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import System.IO
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import Control.DeepSeq
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type LearningRate = Double
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type Input = Vector Double
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type Output = Vector Double
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type Activation = (Vector Double -> Vector Double, Vector Double -> Vector Double)
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data Layer = L { biases :: !(Vector Double)
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, nodes :: !(Matrix Double)
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} deriving (Show)
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, activation :: Activation
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}
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instance Show Layer where
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show (L biases nodes _) = "(" ++ show biases ++ "," ++ show nodes ++ ")"
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data Network = O Layer
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| Layer :- Network
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deriving (Show)
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infixr 5 :-
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saveNetwork :: Network -> String -> IO ()
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saveNetwork network file =
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writeFile file ((show . reverse) (gen network []))
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where
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gen (O (L biases nodes _)) list = (biases, nodes) : list
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gen (L biases nodes _ :- n) list = gen n $ (biases, nodes) : list
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loadNetwork :: [Activation] -> String -> IO Network
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loadNetwork activations file = do
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handle <- openFile file ReadMode
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content <- hGetContents handle
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let list = read content :: [(Vector Double, Matrix Double)]
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network = gen list activations
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content `deepseq` hClose handle
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return network
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where
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gen [(biases, nodes)] [a] = O (L biases nodes a)
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gen ((biases, nodes):hs) (a:as) = L biases nodes a :- gen hs as
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runLayer :: Input -> Layer -> Output
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runLayer input (L !biases !weights) = input <# weights + biases
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runLayer input (L !biases !weights _) = input <# weights + biases
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forward :: Input -> Network -> Output
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forward input (O l) = logistic $ runLayer input l
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forward input (l :- n) = forward (logistic $ runLayer input l) n
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forward input (O l@(L _ _ (fn, _))) = fn $ runLayer input l
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forward input (l@(L _ _ (fn, _)) :- n) = forward ((fst . activation $ l) $ runLayer input l) n
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randomLayer :: Seed -> (Int, Int) -> Layer
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randomLayer :: Seed -> (Int, Int) -> Activation -> Layer
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randomLayer seed (wr, wc) =
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let weights = uniformSample seed wr $ replicate wc (-1, 1)
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biases = randomVector seed Uniform wc * 2 - 1
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in L biases weights
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randomNetwork :: Seed -> Int -> [Int] -> Int -> Network
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randomNetwork seed input [] output =
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O $ randomLayer seed (input, output)
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randomNetwork seed input (h:hs) output =
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randomLayer seed (input, h) :-
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randomNetwork :: Seed -> Int -> [(Int, Activation)] -> (Int, Activation) -> Network
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randomNetwork seed input [] (output, a) =
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O $ randomLayer seed (input, output) a
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randomNetwork seed input ((h, a):hs) output =
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randomLayer seed (input, h) a :-
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randomNetwork (seed + 1) h hs output
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logistic :: Vector Double -> Vector Double
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@ -59,6 +94,14 @@ module Sibe
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logistic' :: Vector Double -> Vector Double
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logistic' x = logistic x * (1 - logistic x)
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crossEntropy :: Output -> Output -> Double
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crossEntropy output target =
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let pairs = zip (toList output) (toList target)
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n = fromIntegral (length pairs)
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in (-1 / n) * sum (map f pairs)
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where
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f (a, y) = y * log a + (1 - y) * log (1 - a)
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train :: Input
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-> Network
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-> Output -- target
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@ -67,30 +110,31 @@ module Sibe
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train input network target alpha = fst $ run input network
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where
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run :: Input -> Network -> (Network, Vector Double)
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run input (O l@(L biases weights)) =
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run input (O l@(L biases weights (fn, fn'))) =
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let y = runLayer input l
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o = logistic y
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o = fn y
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delta = o - target
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de = delta * logistic' y
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-- de = delta * fn' y -- quadratic cost
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de = delta -- cross entropy cost
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biases' = biases - scale alpha de
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weights' = weights - scale alpha (input `outer` de) -- small inputs learn slowly
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layer = L biases' weights' -- updated layer
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layer = L biases' weights' (fn, fn') -- updated layer
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pass = weights #> de
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-- pass = weights #> de
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in (O layer, pass)
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run input (l@(L biases weights) :- n) =
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run input (l@(L biases weights (fn, fn')) :- n) =
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let y = runLayer input l
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o = logistic y
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o = fn y
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(n', delta) = run o n
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de = delta * logistic' y
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de = delta * fn' y -- quadratic cost
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biases' = biases - scale alpha de
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weights' = weights - scale alpha (input `outer` de)
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layer = L biases' weights'
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layer = L biases' weights' (fn, fn')
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pass = weights #> de
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-- pass = weights #> de
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@ -115,3 +159,18 @@ module Sibe
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in map snd $ sortBy (\x y -> fst x) (zip ords list)
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where ord x | x == 0 = LT
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| x == 1 = GT
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genSeed :: IO Seed
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genSeed = do
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(seed, _) <- random <$> newStdGen :: IO (Int, StdGen)
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return seed
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replaceVector :: Vector Double -> Int -> Double -> Vector Double
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replaceVector vec index value =
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let list = toList vec
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in fromList $ rrow index list
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where
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rrow index [] = []
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rrow index (x:xs)
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| index == index = value:xs
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| otherwise = x : rrow (index + 1) xs
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