Attempt at making an online version of softmax

softmax_online.jl

function softmax_online(x::AbstractArray) # seems slower than softmax
    max_ = fill(convert(eltype(x), -Inf), 1, tail(size(x))...)
    sum_ = zeros(eltype(x), 1, tail(size(x))...)
    for j in CartesianIndices(tail(size(x))), i = 1:size(x,1)
        if x[i,j] > max_[1,j]
            sum_[1,j] *= exp(max_[1,j] - x[i,j])
            max_[1,j] = x[i,j]
        end
        sum_[1,j] += exp(x[i,j] - max_[1,j])
    end
    exp_ = exp.(x .- max_)
    return exp_ ./ sum_
end