In tomaszbiegacz/yan: Yet Another Neuron

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

devtools::load_all('./../R')

Each neuron is composed of three layers:

Additive and linear part, responsible for selecting output passed from previous neural network layer.
Non linear neuron logical unit, responsible for learning patterns in input data.

Non linear neuron logical unit

Logical unit itself is composed of:

Non linear input unit with negation capabilities
Logical conjunction unit over inputs

Non linear input unit

Non linear input unit behaviour

x <- seq(0.1, 1.99, length.out = 100)

plot(x, propagation(as.yan.neuronLogicalUnitInput(-1.5), x), col='dark green', type = 'l', xlab = 'x', ylab = 'y')
lines(x, propagation(as.yan.neuronLogicalUnitInput(-0.5), x), col='green', type = 'l')
lines(x, propagation(as.yan.neuronLogicalUnitInput(1.5), x), col='blue', type = 'l')
lines(x, propagation(as.yan.neuronLogicalUnitInput(5.5), x), col='dark blue', type = 'l')

legend(0.5, 14, legend=c("cutOff=-1.5", "cutOff=-0.5", "cutOff=1.5", "cutOff=5.5"), col=c('dark green', 'green', 'blue', 'dark blue'), lty=c(1,1,1,1))

a <- seq(-10, 10, length.out = 100)

plot(a, sapply(a, function(av) propagation(as.yan.neuronLogicalUnitInput(av), 1)), col='green', type = 'l', xlab = 'a', ylab = 'y')
lines(a, sapply(a, function(av) propagation(as.yan.neuronLogicalUnitInput(av), 1.1)), col='blue', type = 'l')
lines(a, sapply(a, function(av) propagation(as.yan.neuronLogicalUnitInput(av), 0.9)), col='red', type = 'l')

legend(-2, 10, legend=c("x=1", "x=1.1", "x=0.9"), col=c('green', 'blue', 'red'), lty=c(1,1,1))

Derrivatives

model <- as.yan.neuronLogicalUnitInput(2)
x <- seq(0.1, 1.99, length.out = 100)
y <- propagation(model, x)
dy <- backpropagation(model, x, y)

plot(x, y, col='yellow', type = 'l', xlab = 'x', ylab = 'y')
lines(x, dy$dX, col='green', type = 'l')
lines(x, dy$dCutOff, col='blue', type = 'l')

legend(0.5, 4, legend=c("y", "d_y/d_x", "d_y/d_cutOff"), col=c('yellow', 'green', 'blue'), lty=c(1,1,1))

model <- as.yan.neuronLogicalUnitInput(-2)
x <- seq(0.7, 5, length.out = 100)
y <- propagation(model, x)
dy <- backpropagation(model, x, y)

plot(x, y, col='yellow', type = 'l', xlab = 'x', ylab = 'y', ylim=c(min(c(y, dy$dX, dy$dCutOff)), max(c(y, dy$dX, dy$dCutOff))))
lines(x, dy$dX, col='green', type = 'l')
lines(x, dy$dCutOff, col='blue', type = 'l')

legend(2, -1, legend=c("y", "d_y/d_x", "d_y/d_cutOff"), col=c('yellow', 'green', 'blue'), lty=c(1,1,1))