I have following std::vector declaration:
std::vector<std::vector<std::vector<int> > > m_input;
I am initializing it as follows:
    m_input.resize (100);
    m_output.resize(100);
    for (int i = 0; i < 100; ++i) {
        m_input [i].resize(100);
        m_output[i].resize(100);
        for (int j = 0; j < 100; ++j){
            m_input [i][j].resize(100);
            m_output[i][j].resize(100);
        }
    }
How can I achieve this via the member initializer list?
std::vector<T> has a constructor that takes two arguments, a number of elements and an initial value. In your case, you want to initialize m_input with 100 copies of a std::vector<std::vector<int> > , so it'd be : m_input(100, X). Now, that X in turn is a vector of 100 std::vector<int>, which in turn contains a hundred ints: 
: m_input(100, std::vector<std::vector<int> >(100, std::vector<int>(100, 0)))
my_class::my_class()
 : m_input(100, std::vector< std::vector<int> >(100, std::vector<int>(100) ))
{
}
That said, implementing a multi-dimensional field should be done by projecting into a one-dimensional one, as Viktor said in his comment to the question.
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