Calculating parity (even or odd number of 1 bits) with a neural network.

parity.R

## Including the required R packages.
packages <- c('caret', 'RSNNS')
if (length(setdiff(packages, rownames(installed.packages()))) > 0) {
  install.packages(setdiff(packages, rownames(installed.packages())))  
}
#

library(caret)
library(RSNNS)

# Generate bit arrays for a bunch of numbers.
numbers <- sample(1:1000, 1000)

# Convert the numbers to their binary representations.
data <- sapply(numbers, function(n) as.numeric(intToBits(n)))
# Note, to convert the binary back into numbers:
# sapply(data, function(d) list(packBits(as.raw(d), 'integer'))) == numbers
data <- as.data.frame(t(data))

# Calculate parity for each row (number of 1's in the row being even (0) or odd (1)).
maxVal <- max(rowSums(data == 1))
#data$y <- rowSums(data == 1) / maxVal
data$y <- as.factor(rowSums(data == 1) %% 2)

#train <- data[1:50,]
#cv <- data[51:100,]
train <- data[data$y == 0,][1:250,]
train <- rbind(train, data[data$y == 1,][1:250,])
cv <- data[data$y == 0,][251:500,]
cv <- rbind(cv, data[data$y == 1,][251:500,])

fit <- train(y ~ ., data = train, method = 'nnet', tuneGrid = expand.grid(decay = c(0.01), size = c(8)))

#results <- predict(fit, newdata = cv) * maxVal
#conf <- confusionMatrix(round(results), cv$y * maxVal)

# Calculate accuracy.
results <- predict(fit, newdata = train)
conf <- confusionMatrix(results, train$y)
length(which(results == train$y)) / nrow(train)

# Calculate accuracy.
results <- predict(fit, newdata = cv)
conf <- confusionMatrix(results, cv$y)
length(which(results == cv$y)) / nrow(cv)