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module Mind
( NeuronIndex (..)
, getNeuronIndex
, Edge (..)
, Network (..)
, createEmptyNetwork
, connectNeurons
, compute
) where
import Data.Ix
import Data.Maybe
-- index different neuron types
data NeuronIndex = Input Int | Internal Int | Output Int deriving (Show, Eq, Ord)
getNeuronIndex :: NeuronIndex -> Int
getNeuronIndex (Input i) = i
getNeuronIndex (Internal i) = i
getNeuronIndex (Output i) = i
-- define incident edges
newtype Edge = Edge (NeuronIndex, Float) deriving (Show, Eq)
-- define networks
data Network = Network
{ numInput :: Int
, internalNeurons :: [[Edge]]
, outputNeurons :: [[Edge]]
} deriving (Show, Eq)
-- create a completely empty network
createEmptyNetwork :: Int -> Int -> Int -> Network
createEmptyNetwork i h o = Network i (replicate h []) (replicate o [])
-- connect two neurons together with a new edge
connectNeurons :: Network -> NeuronIndex -> NeuronIndex -> Float -> Maybe Network
-- internal sink
connectNeurons (Network i h o) source (Internal sink) weight =
if (validSource (Network i h o) source) then do
newH <- insertEdge h sink $ Edge (source, weight)
return $ Network i newH o
else Nothing
-- output sink
connectNeurons (Network i h o) source (Output sink) weight =
if (validSource (Network i h o) source) then do
newO <- insertEdge o sink $ Edge (source, weight)
return $ Network i h newO
else Nothing
--
connectNeurons _ _ (Input _) _ = Nothing
-- helpers for connectNeurons
-- check if a given NeuronIndex can be used as a valid source
validSource :: Network -> NeuronIndex -> Bool
validSource _ (Output _) = False
validSource (Network i _ _) (Input x) =
if (inRange (0, i) x)
then True else False
validSource (Network _ h _) (Internal x) =
if (inRange (0, length h) x)
then True else False
-- insert a new edge into a neuron list, possibly failing
insertEdge :: [[Edge]] -> Int -> Edge -> Maybe [[Edge]]
insertEdge ns i e
| (inRange (0, (length ns)-1) i) = let (front, es:back) = splitAt i ns
in Just $ front ++ [e:es] ++ back
| otherwise = Nothing
-- network computation
compute :: Network -> [Float] -> [Float] -> Either String ([Float], [Float])
compute net input state
| (length input) /= (numInput net) = Left $ "Bad input length: " ++ (show $ length input)
| (length state) /= (length $ internalNeurons net) = Left $ "Bad state length: " ++ (show $ length state)
| otherwise =
let
s = newState net input state
state' = map (Just) s
in Right $ (output net input state state', s)
type InputState = ([Float], [Float])
type NewState = [Maybe Float]
output :: Network -> [Float] -> [Float] -> NewState -> [Float]
output net input state state' =
let
numOutput = length $ outputNeurons net
in
map ((fst . getValue net (input, state) state') . Output) [0..numOutput-1]
newState :: Network -> [Float] -> [Float] -> [Float]
newState net input state =
let numInternal = length $ internalNeurons net
in fst $
foldr
(\x (r, ns) ->
let (value, ns') = getValue net (input, state) ns (Internal x)
in (value:r, ns')
)
([], replicate numInternal Nothing)
[0..numInternal-1]
updateValue :: NewState -> Int -> Float -> NewState
updateValue state' i value =
let (front, _:back) = splitAt i state'
in front ++ (Just value):back
getValue :: Network -> InputState -> NewState -> NeuronIndex -> (Float, NewState)
getValue _ (input, _) state' (Input x) = (input !! x, state')
getValue net inputState state' (Internal x) =
let cached = state' !! x
in
if isJust cached then (fromJust cached, state')
else let
(value, ns) = foldEdges net inputState state' (Internal x) (internalNeurons net !! x)
nss = updateValue ns x value
in (value, nss)
getValue net inputState state' (Output x) =
foldEdges net inputState state' (Output x) (outputNeurons net !! x)
foldEdges:: Network -> InputState -> NewState -> NeuronIndex -> [Edge] -> (Float, NewState)
foldEdges net (input, state) state' sink edges =
let
(t, ns) = foldl
(\(total, nss) (Edge (source, w)) ->
let
(value, nss') = if (sink == source)
then (state !! (getNeuronIndex source), ns)
else getValue net (input, state) nss source
total' = (w * value) + total
in (total', nss')
)
(0, state')
edges
in (tanh t, ns)
|
