AI.BPANN

Basic backpropagation neuronal network inspired by hnn

Types for computation

type ALayer a = [(Neuron, a)]

type ANetwork a = [ALayer a]

type Network = ANetwork ()

data ForwardPassInfo

information generated during a simple forward pass

Constructors

FPInfo

Fields

o :: Double

output

net :: Double

sum of weighted inputs

xs :: [Double]

inputs

Instances

Show ForwardPassInfo

data Neuron

the neuron

Constructors

Neuron

Fields

ws :: [Double]

input weights

fun :: Double -> Double

activation function

fun' :: Double -> Double

first derivation of the activation function

Instances

Show Neuron

Types for serialisation

type PackedNeuron = [Double]

Activation functions

sigmoid :: Double -> Double

1/(1+e^(-x))

sigmoid' :: Double -> Double

first derivation

Network creation

type NeuronCreator = PackedNeuron -> Neuron

sigmoidNeuron :: PackedNeuron -> Neuron

outputNeuron :: PackedNeuron -> Neuron

activation function is id

biasNeuron

Arguments

:: Int

number of inputs

-> Neuron

createLayer :: [PackedNeuron] -> NeuronCreator -> ALayer ()

sigmoidLayer :: [PackedNeuron] -> ALayer ()

outputLayer :: [PackedNeuron] -> ALayer ()

createRandomNetwork

Arguments

:: Int

seed for random weigth generator

-> [Int]

number of neurons per layer

-> Network

serialisation deserialization

icNcToPackedNeurons :: Int -> Int -> [Double] -> ([PackedNeuron], [Double])

unpackNetwork :: [[PackedNeuron]] -> Network

packNetwork :: Network -> [[PackedNeuron]]

backpropagation algorithm

forward pass

passForward :: Network -> [Double] -> ANetwork ForwardPassInfo

generate forward pass info for a network

passForward' :: ALayer a -> [Double] -> ALayer ForwardPassInfo

generate forward pass info for a layer

passForward'' :: Neuron -> [Double] -> ForwardPassInfo

generate forward pass info for a neuron

calcNet :: [Double] -> [Double] -> Double

calculate the weigtet input of the neuron

weight update

weightUpdate

Arguments

:: Double

learning rate alpha

-> ANetwork ForwardPassInfo

-> [Double]

desired output value

-> Network

updates the weigts for an entire network

weightUpdate' :: Double -> ALayer ForwardPassInfo -> (Network, [Double]) -> (Network, [Double])

updates the weigts for a layer

weightUpdate'' :: Double -> (Neuron, ForwardPassInfo) -> Double -> (Neuron, Double)

updates the weigts for a neuron

forward pass and weigtupdate put together

backprop

Arguments

:: Double

learning rate alpha

-> Network

-> ([Double], [Double])

inpit and desired output

-> Network

Evaluation

calculate :: Network -> [Double] -> [Double]

calculates the output of a network for a given input vector

calculate' :: [Double] -> ALayer a -> [Double]

calculates the output of a layer for a given input vector

Training

quadErrorNet :: Network -> ([Double], [Double]) -> Double

quadratic error for a single vector pair

globalQuadError :: Network -> [([Double], [Double])] -> Double

quadratic error for for multiple pairs

trainAlot

Arguments

:: Double

learning rate alpha

-> Network

-> [([Double], [Double])]

list of pairs of input and desired output

-> [Network]

produces an indefinite sequence of networks

train

Arguments

:: Double

learning rate alpha

-> Double

the maximum error epsilon

-> Network

-> [([Double], [Double])]

list of pairs of input and desired output

-> Network

trains a network with a set of vector pairs until a the globalQuadError is smaller than epsilon